Uploaded by GoogleTechTalks on 28.10.2010

Transcript:

>>

I'd like to welcome Anirban Bandyopadhyay from the National Institute for Material Science

in Tsukuba, Japan. Thank you very much. >> BANDYOPADHYAY: Thank you very much. First

of all, I would like to thank Hartmut Neven for organizing this and also Stewart for taking

this, all the hard work, and making this a possibility. And I will talk about remarkable

electronic properties of a microtubule. So here is the outline of my talk, so I will

talk about Fröhlich condensation and the microtubule, most of which has already been

said by Professor Porconi. And then I will talk about coherent transport in microtubule

and temperature independent conductivity of microtubule; then detection of topological

qubit in microtubule; then ferroelectric property of microtubule, this prediction was done by

Jack Tuszynski, and then dynamic instability; and finally, I will conclude. So microtubule

basically is a polymer made by proteins and it has three concentric layer of cylinders,

so one on top of another. And the inner core is water channel and on top of it, we have

tubulin dimers rolling around. And then on extreme outer surface is our nucleus. So if

we just think of microtubule as a physicist who wants to think of energy terms, so you're

alternating signal frequency, for the same true of microtubule, what will happen? So

we have to basically divide the microtubule into three functional parts. The outer layer

is ionic part, so basically kilohertz range signal makes a resonance with the outer surface.

Then we have the dipolar protein part which is--which responds merely in the megahertz

frequency range. And the water signal, the water channel inside, it's the hydrogen-oxygen

bonds that vibrate so we expect a resonance in the gigahertz frequency range. So this

makes microtubule unique. Unique in the sense that if we send, say, its particular band

of signal ranging from kilohertz to gigahertz range, when it enters into the microtubule;

first, it will find the ionic chains; then it will be absorbed. Some of them will be

left. Then to hit to a kilohertz signal, it will not be able to see the proteins or the

waters. The megahertz signal will see the proteins and the gigahertz signal will see

the waters, so it will be filtered out. And the interesting thing of a microtubule is

that all, everything, all of it is crystals. So it has three distinct symmetries one top

of another. So those who are interested in information processing, though you know that

symmetry has very close relation with the information content and information path.

So that means whenever there is a symmetry condition, you are going to have some information

exchange and other processes. So these are some of the points which I will ignore in

the--in today's talk. I will concentrate only on the protein parts. So

okay, let me go forward. So the question that we asked for our research two years back was

to understand how molecule is born spontaneously in the cell and how it survive and then disappear.

So we have 50 trillion cells in our body, and if microtubule is responsible for the

information processing, that means somehow microtubule is processing information and

is able to coherently link up the entire body that we have. So how is it being possible?

I mean, if continuous change of length of microtubule, does it have anything to do with

the information processing? And if it has, how exactly can we define the information

in it and how exactly we can prove it, how exactly we can tell that, "Okay, look if,

you give me, say, 10 micrometer long microtubule, okay, this is the information content, these

are the informations, these are the things it is doing." So we want to define it in the

exact terms. So, if we know about Fröhlich's theorem in 1968, some of which has already

been told by Professor Proconi, but I would like to tell once again. The debate was about

how first life came into being on Earth. I mean, was it just a chemical reaction or some

energy was available and constrained dipoles took that suitable energy and formed a structure

or architecture automatically? So the theory that was prevalent was something like, along

with the chemical energy there was also electromagnetic energy involved in it which took energy from

the environment, right energy, right electromagnetic energies from some source, and it formed us

from molecular architecture that was the first form of life. So this proposal went on and

this proposal says something like that we need a heat bath and we need a constrained

dipole electric--field constrained dipoles and we need electromagnetic energy. So we--and

there is--there was no experimental--direct experimental evidence of this Fröhlich condensation

process until now. And there are some papers in 2009 by J. R. Reimers who has discussed

well in details how to realize this Fröhlich condensation in practice, how to do the experiment.

So we did this experiment in reality and we have successfully realized the Fröhlich condensation

process. None of my videos are running. Can we do something about it?

>> Do you have some separate stuff there? Open it in separate files, you could just

execute... >> There you are.

>> BANDYOPADHYAY: Okay. Okay, so this is the heat bath and we have electrodes. These are

positive and negative arrays, red and blue-colored. And we supply the AC signal into it and microtubule

grows spontaneously within three to four seconds only, not 30, 40 or 60 minutes. So you have

four seconds and we have plotted average length with frequency and you will find that if we

go on increasing the frequency from, say, 10 hertz to 50 megahertz, we will find that

the maximum, the highest long--length of microtubule that we get is around 23.5 micrometer. That

is grown within two to three seconds, not 60 minutes. Only two to three seconds. Just,

you apply the AC frequency, connect the wires, done. And you will see the large microtubules,

the giant dipoles predicted by Fröhlich is formed at the bottom of the surface. So this

is the experimental result and some of the FM pictures. And I have not done any filtration

on these images but when I will publish in the papers, they will be made beautiful. So

just raw images, just you see now. And here you can see the--at particular frequency,

the giant dipoles are formed. So the smallest length that we'd be able to see--or even two

seconds if you apply, say, a 500 kilohertz signal, then you can get only 200 nanometers

long within two seconds. And if you apply, let's say, four megahertz signal or five megahertz

signal, you get 23 or 24 micrometer long chains all along the surface within two seconds.

So you can--you can see the selection. Once we realized the Fröhlich condensate--now

we should--we should keep it in mind that it could also be a classical process because

Reimers have challenged Fröhlich other--in different ways. But before I move on, I must

say that Professor Proconi who is sitting here, he was the first person who said that

this kind of condensation could occur also in megahertz range. Because Fröhlich condensation--Fröhlich

himself said it should be in the gigahertz frequency region but he calculated and said

that it's megahertz. So, our experimental results directly relates his proposal. Now,

where to go from Fröhlich condensate? So shall we try to find out the quantum qubit

or try to find out classical bit of information how things are happening? I mean, it is--is

it a Bose-Einstein condensate or where--which direction should we go? So we decided to leave

the--that--the issue of detecting matter wave for this moment and we decided to go towards

bit and topological qubit. Because topological qubit, those who are interested in quantum

computing, those who know that topological qubit is a version of quantum qubit in which

you are more interested in the space rather than simultaneous multiple steps coexisting

together. So instead of this concept, if you just switch a little bit towards space along

with it, then the entire concept changes and it becomes much easier to detect, much easier

to handle and to--and it becomes more practically feasible. That's why for the last 12 to 13

years, topological qubit has been--has been in the forefront and we have tried to see

this. Also, there were some experimental evidences which prompted us to move towards this direction.

So coherent transport in microtubule, we wanted to detect whether the transport along the

microtubule is coherent or not, and this is a very straightforward and easy experiment

to detect. So--and this is a nice image. We have--we can do filtering and you can see

that it is beautifully done. And instead of two probe measurement, so there is a microtubule

chain and the two gold electrodes are there. So two probe measurement are always faulty,

because if you have two probes and you are sending the signal to understand what is the

electronic property of a device or of a material, and on--and using the same two probe you are

reading out of the system, then you are always taking into account the noise of the system,

the context potentials, and all related phenomenon that is associated with the material. So,

always it is preferred that we should go for the four probe system. In the four probe system,

what we do is we save the current from the outer two terminals and read the voltage from

the inner two terminals. Or the signal that we want to change, we send by far apart from

the farthest points, and from the nearest point, we want to read what is going on inside.

So these are defined structures we have created and it is--and we didn't use any chem--external

chemicals and other materials. It was everything--was very pure and we used dry lithography technique

so that there is no flow of ions along the microtubule. And the first experimental evidence

is this. So we made that AC resistance at different frequencies. As you can see that

we go on increasing frequency and near around eight point--around eight, near around nine

in this region, on the resistance of the device of the microtubule falls and it goes around

3 to 48 or 50--50 kilo ohm with a very--a small AC voltage bias. So for the coherent

or ballistic transport, we need around to 25 kilo ohm, or 40 or 50 kilo ohm is sufficient.

So we did another experiment. We measured the current voltage, by two probe and also

the four probe measurement and we found that you can see nearly one volt is applied on

one MPR current we are getting. So nearly one ohm resistance and this is the direct

evidence for that. So it is the evidence too for the coherence transport along the microtubule

at 300 Kelvin. That means it's the room temperature so it is not blasted off. And one point I

would like to, you know, draw your attention, if you look at the central part, you will

find that it's something like heat resistance are embedded so we--we will, later part of

my talk, we will figure out what it is. Now the third evidence is, if some system is coherent,

that means if you change the link, if it is 1 meter or 100 meter or 1 kilometer, there

should be no change in the resistance. That is the fundamental definition of a coherent

system. So we took--here you can see that four length devices we have measured, 800

nanometer to two micrometer, and there is no change in resistance and we go to approximately

10 to the minus four, minus five MPR current, you go to the ballistic region. If you go

a higher current, resistance will go down. Another evidence, the fourth evidence for

coherent transport is that we measure the power loss. If we send a power stream one

side of the microtubule and then we check the other side, then we find that it is nearly

0.5% or something like that. At particular frequency you can--it is around 9.03 or something.

That means, in this region, definitely the microtubule is becoming coherent so there

is no power loss while information transport. Temperature independent conductivity. So before

we get into this temperature independent conductivity, we got--we found that microtubule is independent

of--microtubule conductivity is independent of temperature. That means if you start from

5 Kelvin, you go up to 300 Kelvin, you find conductivity remains constant, absolutely

no change. So first, when we got this, we didn't believe ourselves. We thought that

there is something wrong. We repeated our measurements several times then we handed

over our material to our superconducting material center, Professor Hirata, and he also measured

and he found the same thing, there is no change in conductivity. We thought that we are the

first person who have discovered such a material, but when we went for the literature, we found

it was--first, one Indian saw this in M. Chowdhury in 1981 in some materials in high pressure

condition and then in 1988, there was another observer, and there were at least five reports

before us where conductivity did not temp--change with temperature in the extreme conditions.

But in our case, it is the normal condition, normal room temperature and ambient atmospheric

conditions. In 2004, I found that the coherence theory for when and how coherence can appear

in a room temperature system. It was explained by Kunio Takayanaki and he published this

paper in Science. And he took golden nanowire, which is helical, and he measured and found

that it is coherent. And also, there was a report in 1997 on carbon nanotube, which was

in room temperature coherent but carbon nanotube experiment is a little bit debated because

what did they do? They took mercury liquid and then they put the carbon nanotube from

top and then they measured it. But when later people tried to reproduce their result on

a--keeping the carbon nanotube on the surface and putting two electrodes lithographically

the way we did, then they found that carbon nanotube is not room temperature ballistic.

So that makes microtubule--that our experiment, the second candidate after Dr. Kunio Takayanagi's

gold nanowire which is showing room temperature conductivity. Now the theory says that if

you have a periodic potential-like system, then in the Hamiltonian, you--what happens

is fluxes get quantized and starting conditions if it is there, then you are naturally going

to see coherent transport. And there are several papers since 2004 to 2010 you can find where

you can find coherent transport. So what happens is something like this. So we calculated the

energy level diagram. Please try to see the bending of the orbitals, bending of the energy

levels. This right here. Go back. Because this is important because when we will apply

external thermal fluctuation, then we will see what happens to those. So what happens

basically is this, all point contexts are formed. So it is not like metal, not like

semi-conductor, not like insulator. So, multiple point contact gaps are formed between the

valence band and the conduction bend. And these--and energy, when we supply external

energy, it sews the electrons at the edge of the connection bands and then lifts it

up in the--in a particular frequency or in a particular energy, and that's why the coherent

transport occurs. So if we see varied temperature, we see conductivity like this. So it is not

absolutely constant. It changes quantized manner with temperature and it fluctuates

in a quantized way. So we could encode any resistance by powering it to a particular

conducting state. Why we could include particular conducting state of our choice? That, I will

explain when we will discuss about the ferroelectric property. So, we can include a particular

conducting state and we can vary the temperature, and that conducting state, that conductivity

retains along the sweep. So Professor Kagita in 1997, he first explained theoretically

with some experimental materials how and for what reason this kind of temperature independent

conductivity could be realized in practice. So, if we zoom out, we will find that their

encoded energy level, which are shown with an arrow, this has a pair of levels also just

beside it. So both side, upper and lower value, you have--and their conducting states where

it basically jumps. So it is not a random jump. It is always quantized. So these are

different experimental results. And when we encode very low resistance, say, we can encode

a couple ohms in microtubule, here we encoded 40 kiloohm, so then we find that this resistance

variation goes very lowered, two to three kiloohm. If we encode, say, 10 ohm, it will

be nearly one ohm. That means you'll get almost a straight line. So we tried to find out an

explanation, and then we, what we did in the Hamiltonian, we added another thermal fluctuation

term. And then we found that our energy band diagram changes a little and it forms two

other kind of versions where the point-to-point contact is like the circular point contact

instead of a single point. And the fluctuation occurs from black to red, red to blue, blue

to black continuously and it maintains that particular conducting state. So, microtubule

is neither metal, insulator, or semiconductor. Its density of states is in between metal

and semiconductor and it switches back and forth. And conducting--conduction needs accumulation

by standard calculation, we found that it is 0.23 dG; dG is the 2e squared by H at the

quantum conductance. Then we go for detecting the topological qubit in MT. Initially, what

we did is we tried to find out the ferroelectric conduction modes that is--that was all ready

proposed. But later we thought that, let's try--start from scratch. Let's try to do some

picture. Let's try to play with the--with what could be possible or what could be not--could

not be and then later stage of our research, we will try to find out how much ferroelectric

conduction modes are feasible. So what are the differences between bit, qubit, and the

topological qubit? Bit--in--suppose we have a molecule and then we change the conducting

state of the molecule by reducing it or by changing confirmation of the molecule, then

classically, we can observe it, we can measure its conductivity so it is called bit. When

qubit, then that means the--two or three are multiple states. It can coexist. And at a

particular time, we cannot say that we are surely this. And a topological qubit is also

similar like that but topoligical qubit is associated with their particular space. If

you want to destroy a topological qubit, you have to destroy the space. If you disturb

the space, if you change it by any means, you cannot destroy it. So, topological qubit

was first proposed by Kitaev maybe in 1997 and the topological qubit until now has been

realized only in the superconducting systems in the millikelvin temperatures. And the basic

reason has been that you need quantum liquid and flux of quantum liquid to flow and--if

you want to detect it. Because quantum mechanical states, if you want to detect it, they are

very solitary in nature. If you want to detect it, it will change into something else. But

in topological qubit, there is a good possibility of detection because suppose one space changed

to another space, some energy will be released, and then you can detect it. That's why there

is no direct evidence of detecting qubits very feasible manner. But there are many papers

of detection of topological qubits. In the last 10 years, you can find that topological

qubit has been detected several times. And so, in case of topological qubit, you can

measure the phase slip directly. That means if you have any space, if you have topological

qubit, you send your signal from one side, you measure from other side, you will find

very defined quantized phase change in the signal. If you change the length of the space,

you will find in some length, the distance decreases; in some length, jumps, so all the

benefit should be there. So very nice ways and simple experiments are there as in which

you can verify that topological qubits are there. So here are some simple things.

>> Well, can you clarify what you mean by a topological qubit?

>> BANDYOPADHYAY: Huh? >> Can you clarify what you mean by a topological

qubit? >> BANDYOPADHYAY: Yes. A topological qubit--shall

I explain with the microtubule? >> Yes.

>> BANDYOPADHYAY: The meaning of topological qubit, because I already said a lot, because

now if you will see the picture then I think it will be easier to go on. Also, I'm sorry,

I don't have very simple cartoons, but you can find in Google many simple cartoons what

is topological qubit and how it is done. So, basically, it is associated with the space

to some certain patterns, and it has quantum state, quantum state is similar to the qubit,

but it is a very typical space. And if you change the shape of the space, the fundamental

property of the pattern does not change. So that is the basic difference with the qubit

with the topological qubit. But there are many, many different specifications right

there. So microtubule is a 2D hexagonal close packing structure and eight nanometer is a

dimer. Now we try to form the topological qubit patterns. And if we repeat the first

layer on the 14th, 1, 2, 3, 4, 5, 6, 7, 8, up to 13, 14th, we find that they are the

same so hexagonal packing breaks there, so this is called of type lattice B. And if we

want to start from one side of the blue and reach to the next state, we'll find that six-cell

gap, we get periodicity, that means 48 nanometer pairs, so more than this we cannot create.

Similarly, if we change the hexagonal close packing a little bit, we can get to lattice

A where there is no break in the hexagonal close packing. And then, 26 cells is required

for it to come back to the same point, one periodicity, that is 208 nanometers. So that

means if there is a topological qubit, so you need a minimum 200 nanometer revolutions

gap. So we--what we did is we did not consider any mathematics or something, we just took--if

we have a gap 2, that means one line starts, we count one, two. We draw the second one

and then the third one. In this way, we went on creating different lines, so it would be

spherical lines continuously, so we call each lines as one topological qubit, this goes

one unit. Now, if you see, you'll find that in gap 2, it is a direct overlap of two lines.

So if you have 100 lines on a particular space you cannot differentiate how many lines are

there, so that means we'd take only one restriction that is if they touch, they disappear. So

we just neglect that possibility. So in this way, we have found that if you send 8, at

the gap of 8, which is a Fibonacci number, then you will find that when you come back

and start, you will find it decomposes into 8, 5. If you send 7 gap, you will get to 7,

6. In this way decomposition occurs. And if we try to put multiple qubits, we will find

only four sets of combinations; 8, 5, 10, 13; 7, 9, 11, 13; 5, 7, 10, 13 and 5, 7, 9,

13. And the decomposition lists are also given here. So if you just, on a piece of paper,

you play with the pen, you can find this kind of relations. Okay, so this is about horizontally

if we send signals into a microtubule. What if it takes information from the environment,

E1, E2, E3, then we can find that if we start with topological qubit eight, then it decompose

into--if another signal enters, decompose into 5, 3. Another signal enters 5, 3, 2.

Another signal enters 3, 2. Another signal enters, qubit then will disappear because

we said touch, disappear. So in these operations, in the future, people can work on. But if

we go to lattice B, I got very interesting things. That is, gap 2 survives, gap 3 survives,

gap 4 decompose and it goes to 2, and you can send signals straight. If we--if the gap

is X, that is straight, then helicity c is infinite. If you put it in the Hamiltonian,

you will find that you get a typical situation where MPCG, or the Multiple Point Contact

Gaps, that we showed at the beginning of my talk, that appears spontaneously. That means,

if this kind of microtubule is there then it is coherent. You don't need to have any

external energy supply, it is always ready to do that. And this, lattice B, is very prompt

towards information transport. Lattice C and lattice B are complementary to each other.

So lattice B, you know, gives us 2, 3Q, 2, 3, 4, and X and it gives us 5 to 13 something.

Together, they cover entire series. One is good for computing, that is simply we are

finding it decomposes into its states, other don't want to decompose. So, what can we detect

about the topological qubit for different lengths? So for four different lengths of

MT, we should be able to get four different sets. So let's go for the experiment. Now,

we cannot do--the biggest problem when we wanted to do this experiment, we wanted to

measure quantum hall--fractional quantum hall effect which is the easiest and the direct

mean to detect the topological quantum qubit but microtubule does not respond to Rxy, that

is the particle, because we have in the megahertz frequency range only one molecular layer thick

so we cannot create the magnetic flux gradient which is essential for the Rxy. So we have--we

are left with only Rxx. But we found that when magnetic flux gradient is created, basically

Rxx, the horizontal resistance, also changes. Our principle is that we cannot absolute time,

we cannot detect a quantum state. But we can change the--we can change the transformation

from one topological qubit to another. That means, if we can convert topological qubit

A to topological qubit B, energy will be released or absorbed. So what did we do? We sent an

AC signal in the middle part, the shaded region. So AC signal, we know very well that does

not change the resistance of a device, the DC resistance of a device, because DC resistance

of a device depend on the topological order. AC signal cannot change unless--until there

exists some topological order and that undergoes a quantum transition. So, this is a simple

experimental set-up. So we have a function generator with two capacitor because DC's

part doesn't come into it, and a resistance measurement device. So we measure only the

DC resistance of the system. We change the function near the frequency and see what we

find. We find four, always, four different regions where you see the large DC resistance

change. This figure almost looks like, if you have gone through the literatures of fractional

quantum hall effect results, the result--this result, if you leave frequency to B and DC

resistance, this looks nearly similar. That means we are seeing the absorbance and we

find that seven distinct peaks appear and disappear repeatedly on different lengths.

So we measured--we repeated this measure on different devices. Then, if there is a qubit,

there should be a quantum phase slip. That means, one side we will send a signal, on

the next side there should be a phase difference. So, you find the phase difference and they

are also quantized, 45, 90, 135, 180, and 0, these repeats statistically. Then we try

to find out the condition, Q, ABCPCDE, that peaks that we have, and 8, 5, 10, 13. We,

again, we used the condition, topological qubits don't touch, and we find that exactly,

unless until you have this topological qubit you cannot get these peaks. You can verify.

So quick summary of the energy levels that we have got. So 9.03 megahertz, you get a--you

get resonance in the microtubule. It becomes coherent and no phase change, nor it is even

phase coherent. 20.56 megahertz; again, phase coherent; 16.35, 18.15 megahertz, in this

megahertz you get 135 degree phase difference and--or 180 degree phase difference and they

are coupled to each other. And the 23.00, 24.00, 23.27, 24.06, and 24.91 megahertz also

add to that absorbance peaks, which varies. What we did is we measured, we, you know,

changed the length of the microtubule from 200 nanometers up to say 10 or 20 micrometers.

And we found for every length which are the qubit peaks appear which are--which disappear.

So we tried to find out--we found that it is strongly dependent on the length and follows

a very particular algorithm continuously along the length. That means if you now give me

a particular length, let's say 22 micrometer, what should be the qubit properties? I can

tell exactly that this, and this, and this, and this energy band will get the absorption,

and this energy band we will get the absorption with this angled phase change and that angle

phase change so I can exactly tell you. Okay, two interesting thoughts. One is that one

period for this particular operation that we say that phase locking is a two micrometers

and 12 different ways it could be done. So, 24 to 30 micrometer long microtubules are

necessary to get all the states. And there is negative delta R minus delta R, plus and

minus delta R. That means in microtubule, particular signals you can send from this

direction and particular signal at the same time you can send from this direction; both

direction you cannot. So we tried to create in both directions but we didn't get. And

last experiment that we did to detect whether there exists quantum topological qubit or

not is quantum interferrometry. The experiment--it suggests theoretically that if you have from

both two ends, if you generate topological qubits into the system, and if you can make

it feel gradient in such a way that you trap it, then what happen, the middle region will

automatically create pulse with a certain time. So the--here is the two end qubits that

we created with two signals and the top radars we got continuous oscillations from that so

there must be existing some sort of topological order inside the system. What kind of TQs

are these? There in literature you will find there are at least 15 different kind of topological

qubits. We do not want to definitely define right now because we have got the experimental

radars and seven different kinds of signatures we have got of why this is topological qubit.

But still, since it is room temperature, we want to be very, very sure what is the real

nature of this kind of topological qubits. Finally, ferroelectric property of microtubule.

In the month of April, I came to Center for Consciousness conference and I saw the bottom

result. We'd--we had lots of noise at that time. We removed the noise and we have got

perfectly square. So there's--this is noise-less. Any kind of--if you get perfectly square behavior,

that means to store energy you don't need to spend energy to retain a particular bit.

And if you change the temperature, the information is not lost. It retains. As you can see, 250

K and 300 K at different bias we can create. So multiple states, you can write and you

can retain. Both kind of measurement could be done simultaneously. And as I have all

ready said, that if there is a length change continuously, that was first sentence of my

doc files, our objective, that if there is a dynamic instability, that a microtubule

is continuously changing, why it is changing and what are the nature of a particular length

of microtubule, we can tell exactly what qubits are. So, we want to build now the languages

in which we want to communicate with the cellular organisms. So this is the conclusion. Microtubule

processes classical bit and quantum topological bits together. Its conductivity is independent

of temperature. But whether it should be classified in metals, semiconductor, or insulator, we

don't know. But we think that it should not be classified in any of this. Lattice C and

lattice B are complementary to each other as far as topological qubits are concerned.

And together, they build a fantastic system of information processing by changing length,

MT tunes, nature of its topological qubits, MT stores and processes bit without releasing

or consuming heat, it's perfectly solitary. So finally, I would like to acknowledge Hartmut

and to Stuart for their contributions, AOARD [INDISTINCT] is here. I cannot--I would like

to acknowledge him for his kind grants, and JSPS, Center for Consciousness Studies for

some of the grants. And Professor Daisuke Fujita and Dr. Satyagit Sahu, and Dr. Subrata

Ghosh, and Professor Kazuhiro Hirata. Satyajit and Subrata are my post-docs, they have done

majority of the experiments and Professor Hirata reproduced our results because it's--it

was hard to believe at the beginning. And Professor Fujita also generously helped in

AFM measurements because he is very expert and he suggested that we should move to 4th

probe systems all to prove data useless. And also finally, I would like to thank all of

you for listening for this long time. Thank you very much.

>> Thank you. Thank you very much. Thank you. Are there any questions? Maybe we can take

one question. Yes? >> One question. You said that the conductivity

is not metal, not semiconductor, and so on. What type of the conductivity is this?

>> BANDYOPADHYAY: I don't know. But it is... >> Is that not electron conductivity? Or what

type? Because if you transport electricity, you must transport charge and therefore that

is something that should be explained. Because I assume that there is a certain amount of

electrons in the--I may say, conductivity band of microtubules.

>> BANDYOPADHYAY: Yes. I have shown the conductivity band. I have shown the picture, the point

contact. So it is--there is no--and in case of metal, there is no gap. In case of semiconductor,

you have a gap, a small gap. And in case of insulator, you have a large-band gap, right?

So it is very well-known. But in this kind of material, you have a point contact gap

in between the valence band and the conduction band so you can say it is another kind of

material, new kind of material, that does not fall into this category, so you can find

a new name. >> Thank you.

>> Thank you. Any more questions? Yes? >> Hi. So I guess I have a couple of questions.

First, I'm trying to understand why you call these topological qubits bits [INDISTINCT]

how do you read that information from them? >> BANDYOPADHYAY: Okay.

>> Yes. >> BANDYOPADHYAY: First, I call this topological

qubit for three reasons. Topological quantum bit. We have got the bit, we detected it.

We have got the topological order of change by measuring DC resistance change with the

AC particular frequency. >> I'm sorry, what are you detecting?

>> BANDYOPADHYAY: "What are you detecting" means?

>> Like, what does your--like, you're showing like a loop around the microtubule. What's

that loop mean? >> BANDYOPADHYAY: No, no, no, no, no, no,

no, no. You saw the experiment of--when DC resistance change using the AC signal frequency

that we supplied to the device? Did you check that? So if we apply a very particular energy

you will find sudden fall in the DC resistance. So, DC resistance of a system, you know, DC

resistance of a system determines the topology, the confirmation, and the structure. When

there is a sudden change in that that is quantized. That's why I call it topological qubit.

>> So... >> BANDYOPADHYAY: So at a particular frequency,

at six and seven different frequencies, always, whatever be the length of the microtubule,

you will find it will be enhanced, or I mean, dominated or sub-dominated. But in those frequencies,

if we apply a signal at a very small part of the system, AC signal, purely AC signal,

you will find the DC resistance is getting changed. So that is how we did it. Of course,

there are many other detection process by which we said. So there are standard five

different experiments, five or six different experiments, which has been established theoretically

to detect topological qubits which you can find in the literatures.

>> So could you store--could you store a quantum state? I mean, could you store a superposition?

>> BANDYOPADHYAY: No. The--when we tried to do this kind of experiment basically what

we do is we send a particular kind of current, particular magnitude of current which reaches

the material to the coherent state. For an example, suppose we are working with, say,

we know if we send DC current of 1 microampere we know that the resistance will fall below,

say, 20 kilo-ohm or 1 kilo-ohm. We know that. That means it is going to the coherent state.

So externally, we first send that current. When you send that current, we take it to

the coherent state and we store the topological qubits. Then, we try to transform one set

of qubit to another set of qubit. One qubit, we cannot write. One topological qubit, we

cannot write. But a particular set is possible to write. But what set we will write depends

on the length of the system. >> Let's...

>> BANDYOPADHYAY: We cannot control... >> Okay, let's--can we take this discussion

off-line because I'd actually like to join in it too, because I don't think this is a

topological qubit to be honest. >> BANDYOPADHYAY: Yes.

>> But next speaker is Stuart Hammeroff, and we'll reconvene in about five minutes. Thank

you.

I'd like to welcome Anirban Bandyopadhyay from the National Institute for Material Science

in Tsukuba, Japan. Thank you very much. >> BANDYOPADHYAY: Thank you very much. First

of all, I would like to thank Hartmut Neven for organizing this and also Stewart for taking

this, all the hard work, and making this a possibility. And I will talk about remarkable

electronic properties of a microtubule. So here is the outline of my talk, so I will

talk about Fröhlich condensation and the microtubule, most of which has already been

said by Professor Porconi. And then I will talk about coherent transport in microtubule

and temperature independent conductivity of microtubule; then detection of topological

qubit in microtubule; then ferroelectric property of microtubule, this prediction was done by

Jack Tuszynski, and then dynamic instability; and finally, I will conclude. So microtubule

basically is a polymer made by proteins and it has three concentric layer of cylinders,

so one on top of another. And the inner core is water channel and on top of it, we have

tubulin dimers rolling around. And then on extreme outer surface is our nucleus. So if

we just think of microtubule as a physicist who wants to think of energy terms, so you're

alternating signal frequency, for the same true of microtubule, what will happen? So

we have to basically divide the microtubule into three functional parts. The outer layer

is ionic part, so basically kilohertz range signal makes a resonance with the outer surface.

Then we have the dipolar protein part which is--which responds merely in the megahertz

frequency range. And the water signal, the water channel inside, it's the hydrogen-oxygen

bonds that vibrate so we expect a resonance in the gigahertz frequency range. So this

makes microtubule unique. Unique in the sense that if we send, say, its particular band

of signal ranging from kilohertz to gigahertz range, when it enters into the microtubule;

first, it will find the ionic chains; then it will be absorbed. Some of them will be

left. Then to hit to a kilohertz signal, it will not be able to see the proteins or the

waters. The megahertz signal will see the proteins and the gigahertz signal will see

the waters, so it will be filtered out. And the interesting thing of a microtubule is

that all, everything, all of it is crystals. So it has three distinct symmetries one top

of another. So those who are interested in information processing, though you know that

symmetry has very close relation with the information content and information path.

So that means whenever there is a symmetry condition, you are going to have some information

exchange and other processes. So these are some of the points which I will ignore in

the--in today's talk. I will concentrate only on the protein parts. So

okay, let me go forward. So the question that we asked for our research two years back was

to understand how molecule is born spontaneously in the cell and how it survive and then disappear.

So we have 50 trillion cells in our body, and if microtubule is responsible for the

information processing, that means somehow microtubule is processing information and

is able to coherently link up the entire body that we have. So how is it being possible?

I mean, if continuous change of length of microtubule, does it have anything to do with

the information processing? And if it has, how exactly can we define the information

in it and how exactly we can prove it, how exactly we can tell that, "Okay, look if,

you give me, say, 10 micrometer long microtubule, okay, this is the information content, these

are the informations, these are the things it is doing." So we want to define it in the

exact terms. So, if we know about Fröhlich's theorem in 1968, some of which has already

been told by Professor Proconi, but I would like to tell once again. The debate was about

how first life came into being on Earth. I mean, was it just a chemical reaction or some

energy was available and constrained dipoles took that suitable energy and formed a structure

or architecture automatically? So the theory that was prevalent was something like, along

with the chemical energy there was also electromagnetic energy involved in it which took energy from

the environment, right energy, right electromagnetic energies from some source, and it formed us

from molecular architecture that was the first form of life. So this proposal went on and

this proposal says something like that we need a heat bath and we need a constrained

dipole electric--field constrained dipoles and we need electromagnetic energy. So we--and

there is--there was no experimental--direct experimental evidence of this Fröhlich condensation

process until now. And there are some papers in 2009 by J. R. Reimers who has discussed

well in details how to realize this Fröhlich condensation in practice, how to do the experiment.

So we did this experiment in reality and we have successfully realized the Fröhlich condensation

process. None of my videos are running. Can we do something about it?

>> Do you have some separate stuff there? Open it in separate files, you could just

execute... >> There you are.

>> BANDYOPADHYAY: Okay. Okay, so this is the heat bath and we have electrodes. These are

positive and negative arrays, red and blue-colored. And we supply the AC signal into it and microtubule

grows spontaneously within three to four seconds only, not 30, 40 or 60 minutes. So you have

four seconds and we have plotted average length with frequency and you will find that if we

go on increasing the frequency from, say, 10 hertz to 50 megahertz, we will find that

the maximum, the highest long--length of microtubule that we get is around 23.5 micrometer. That

is grown within two to three seconds, not 60 minutes. Only two to three seconds. Just,

you apply the AC frequency, connect the wires, done. And you will see the large microtubules,

the giant dipoles predicted by Fröhlich is formed at the bottom of the surface. So this

is the experimental result and some of the FM pictures. And I have not done any filtration

on these images but when I will publish in the papers, they will be made beautiful. So

just raw images, just you see now. And here you can see the--at particular frequency,

the giant dipoles are formed. So the smallest length that we'd be able to see--or even two

seconds if you apply, say, a 500 kilohertz signal, then you can get only 200 nanometers

long within two seconds. And if you apply, let's say, four megahertz signal or five megahertz

signal, you get 23 or 24 micrometer long chains all along the surface within two seconds.

So you can--you can see the selection. Once we realized the Fröhlich condensate--now

we should--we should keep it in mind that it could also be a classical process because

Reimers have challenged Fröhlich other--in different ways. But before I move on, I must

say that Professor Proconi who is sitting here, he was the first person who said that

this kind of condensation could occur also in megahertz range. Because Fröhlich condensation--Fröhlich

himself said it should be in the gigahertz frequency region but he calculated and said

that it's megahertz. So, our experimental results directly relates his proposal. Now,

where to go from Fröhlich condensate? So shall we try to find out the quantum qubit

or try to find out classical bit of information how things are happening? I mean, it is--is

it a Bose-Einstein condensate or where--which direction should we go? So we decided to leave

the--that--the issue of detecting matter wave for this moment and we decided to go towards

bit and topological qubit. Because topological qubit, those who are interested in quantum

computing, those who know that topological qubit is a version of quantum qubit in which

you are more interested in the space rather than simultaneous multiple steps coexisting

together. So instead of this concept, if you just switch a little bit towards space along

with it, then the entire concept changes and it becomes much easier to detect, much easier

to handle and to--and it becomes more practically feasible. That's why for the last 12 to 13

years, topological qubit has been--has been in the forefront and we have tried to see

this. Also, there were some experimental evidences which prompted us to move towards this direction.

So coherent transport in microtubule, we wanted to detect whether the transport along the

microtubule is coherent or not, and this is a very straightforward and easy experiment

to detect. So--and this is a nice image. We have--we can do filtering and you can see

that it is beautifully done. And instead of two probe measurement, so there is a microtubule

chain and the two gold electrodes are there. So two probe measurement are always faulty,

because if you have two probes and you are sending the signal to understand what is the

electronic property of a device or of a material, and on--and using the same two probe you are

reading out of the system, then you are always taking into account the noise of the system,

the context potentials, and all related phenomenon that is associated with the material. So,

always it is preferred that we should go for the four probe system. In the four probe system,

what we do is we save the current from the outer two terminals and read the voltage from

the inner two terminals. Or the signal that we want to change, we send by far apart from

the farthest points, and from the nearest point, we want to read what is going on inside.

So these are defined structures we have created and it is--and we didn't use any chem--external

chemicals and other materials. It was everything--was very pure and we used dry lithography technique

so that there is no flow of ions along the microtubule. And the first experimental evidence

is this. So we made that AC resistance at different frequencies. As you can see that

we go on increasing frequency and near around eight point--around eight, near around nine

in this region, on the resistance of the device of the microtubule falls and it goes around

3 to 48 or 50--50 kilo ohm with a very--a small AC voltage bias. So for the coherent

or ballistic transport, we need around to 25 kilo ohm, or 40 or 50 kilo ohm is sufficient.

So we did another experiment. We measured the current voltage, by two probe and also

the four probe measurement and we found that you can see nearly one volt is applied on

one MPR current we are getting. So nearly one ohm resistance and this is the direct

evidence for that. So it is the evidence too for the coherence transport along the microtubule

at 300 Kelvin. That means it's the room temperature so it is not blasted off. And one point I

would like to, you know, draw your attention, if you look at the central part, you will

find that it's something like heat resistance are embedded so we--we will, later part of

my talk, we will figure out what it is. Now the third evidence is, if some system is coherent,

that means if you change the link, if it is 1 meter or 100 meter or 1 kilometer, there

should be no change in the resistance. That is the fundamental definition of a coherent

system. So we took--here you can see that four length devices we have measured, 800

nanometer to two micrometer, and there is no change in resistance and we go to approximately

10 to the minus four, minus five MPR current, you go to the ballistic region. If you go

a higher current, resistance will go down. Another evidence, the fourth evidence for

coherent transport is that we measure the power loss. If we send a power stream one

side of the microtubule and then we check the other side, then we find that it is nearly

0.5% or something like that. At particular frequency you can--it is around 9.03 or something.

That means, in this region, definitely the microtubule is becoming coherent so there

is no power loss while information transport. Temperature independent conductivity. So before

we get into this temperature independent conductivity, we got--we found that microtubule is independent

of--microtubule conductivity is independent of temperature. That means if you start from

5 Kelvin, you go up to 300 Kelvin, you find conductivity remains constant, absolutely

no change. So first, when we got this, we didn't believe ourselves. We thought that

there is something wrong. We repeated our measurements several times then we handed

over our material to our superconducting material center, Professor Hirata, and he also measured

and he found the same thing, there is no change in conductivity. We thought that we are the

first person who have discovered such a material, but when we went for the literature, we found

it was--first, one Indian saw this in M. Chowdhury in 1981 in some materials in high pressure

condition and then in 1988, there was another observer, and there were at least five reports

before us where conductivity did not temp--change with temperature in the extreme conditions.

But in our case, it is the normal condition, normal room temperature and ambient atmospheric

conditions. In 2004, I found that the coherence theory for when and how coherence can appear

in a room temperature system. It was explained by Kunio Takayanaki and he published this

paper in Science. And he took golden nanowire, which is helical, and he measured and found

that it is coherent. And also, there was a report in 1997 on carbon nanotube, which was

in room temperature coherent but carbon nanotube experiment is a little bit debated because

what did they do? They took mercury liquid and then they put the carbon nanotube from

top and then they measured it. But when later people tried to reproduce their result on

a--keeping the carbon nanotube on the surface and putting two electrodes lithographically

the way we did, then they found that carbon nanotube is not room temperature ballistic.

So that makes microtubule--that our experiment, the second candidate after Dr. Kunio Takayanagi's

gold nanowire which is showing room temperature conductivity. Now the theory says that if

you have a periodic potential-like system, then in the Hamiltonian, you--what happens

is fluxes get quantized and starting conditions if it is there, then you are naturally going

to see coherent transport. And there are several papers since 2004 to 2010 you can find where

you can find coherent transport. So what happens is something like this. So we calculated the

energy level diagram. Please try to see the bending of the orbitals, bending of the energy

levels. This right here. Go back. Because this is important because when we will apply

external thermal fluctuation, then we will see what happens to those. So what happens

basically is this, all point contexts are formed. So it is not like metal, not like

semi-conductor, not like insulator. So, multiple point contact gaps are formed between the

valence band and the conduction bend. And these--and energy, when we supply external

energy, it sews the electrons at the edge of the connection bands and then lifts it

up in the--in a particular frequency or in a particular energy, and that's why the coherent

transport occurs. So if we see varied temperature, we see conductivity like this. So it is not

absolutely constant. It changes quantized manner with temperature and it fluctuates

in a quantized way. So we could encode any resistance by powering it to a particular

conducting state. Why we could include particular conducting state of our choice? That, I will

explain when we will discuss about the ferroelectric property. So, we can include a particular

conducting state and we can vary the temperature, and that conducting state, that conductivity

retains along the sweep. So Professor Kagita in 1997, he first explained theoretically

with some experimental materials how and for what reason this kind of temperature independent

conductivity could be realized in practice. So, if we zoom out, we will find that their

encoded energy level, which are shown with an arrow, this has a pair of levels also just

beside it. So both side, upper and lower value, you have--and their conducting states where

it basically jumps. So it is not a random jump. It is always quantized. So these are

different experimental results. And when we encode very low resistance, say, we can encode

a couple ohms in microtubule, here we encoded 40 kiloohm, so then we find that this resistance

variation goes very lowered, two to three kiloohm. If we encode, say, 10 ohm, it will

be nearly one ohm. That means you'll get almost a straight line. So we tried to find out an

explanation, and then we, what we did in the Hamiltonian, we added another thermal fluctuation

term. And then we found that our energy band diagram changes a little and it forms two

other kind of versions where the point-to-point contact is like the circular point contact

instead of a single point. And the fluctuation occurs from black to red, red to blue, blue

to black continuously and it maintains that particular conducting state. So, microtubule

is neither metal, insulator, or semiconductor. Its density of states is in between metal

and semiconductor and it switches back and forth. And conducting--conduction needs accumulation

by standard calculation, we found that it is 0.23 dG; dG is the 2e squared by H at the

quantum conductance. Then we go for detecting the topological qubit in MT. Initially, what

we did is we tried to find out the ferroelectric conduction modes that is--that was all ready

proposed. But later we thought that, let's try--start from scratch. Let's try to do some

picture. Let's try to play with the--with what could be possible or what could be not--could

not be and then later stage of our research, we will try to find out how much ferroelectric

conduction modes are feasible. So what are the differences between bit, qubit, and the

topological qubit? Bit--in--suppose we have a molecule and then we change the conducting

state of the molecule by reducing it or by changing confirmation of the molecule, then

classically, we can observe it, we can measure its conductivity so it is called bit. When

qubit, then that means the--two or three are multiple states. It can coexist. And at a

particular time, we cannot say that we are surely this. And a topological qubit is also

similar like that but topoligical qubit is associated with their particular space. If

you want to destroy a topological qubit, you have to destroy the space. If you disturb

the space, if you change it by any means, you cannot destroy it. So, topological qubit

was first proposed by Kitaev maybe in 1997 and the topological qubit until now has been

realized only in the superconducting systems in the millikelvin temperatures. And the basic

reason has been that you need quantum liquid and flux of quantum liquid to flow and--if

you want to detect it. Because quantum mechanical states, if you want to detect it, they are

very solitary in nature. If you want to detect it, it will change into something else. But

in topological qubit, there is a good possibility of detection because suppose one space changed

to another space, some energy will be released, and then you can detect it. That's why there

is no direct evidence of detecting qubits very feasible manner. But there are many papers

of detection of topological qubits. In the last 10 years, you can find that topological

qubit has been detected several times. And so, in case of topological qubit, you can

measure the phase slip directly. That means if you have any space, if you have topological

qubit, you send your signal from one side, you measure from other side, you will find

very defined quantized phase change in the signal. If you change the length of the space,

you will find in some length, the distance decreases; in some length, jumps, so all the

benefit should be there. So very nice ways and simple experiments are there as in which

you can verify that topological qubits are there. So here are some simple things.

>> Well, can you clarify what you mean by a topological qubit?

>> BANDYOPADHYAY: Huh? >> Can you clarify what you mean by a topological

qubit? >> BANDYOPADHYAY: Yes. A topological qubit--shall

I explain with the microtubule? >> Yes.

>> BANDYOPADHYAY: The meaning of topological qubit, because I already said a lot, because

now if you will see the picture then I think it will be easier to go on. Also, I'm sorry,

I don't have very simple cartoons, but you can find in Google many simple cartoons what

is topological qubit and how it is done. So, basically, it is associated with the space

to some certain patterns, and it has quantum state, quantum state is similar to the qubit,

but it is a very typical space. And if you change the shape of the space, the fundamental

property of the pattern does not change. So that is the basic difference with the qubit

with the topological qubit. But there are many, many different specifications right

there. So microtubule is a 2D hexagonal close packing structure and eight nanometer is a

dimer. Now we try to form the topological qubit patterns. And if we repeat the first

layer on the 14th, 1, 2, 3, 4, 5, 6, 7, 8, up to 13, 14th, we find that they are the

same so hexagonal packing breaks there, so this is called of type lattice B. And if we

want to start from one side of the blue and reach to the next state, we'll find that six-cell

gap, we get periodicity, that means 48 nanometer pairs, so more than this we cannot create.

Similarly, if we change the hexagonal close packing a little bit, we can get to lattice

A where there is no break in the hexagonal close packing. And then, 26 cells is required

for it to come back to the same point, one periodicity, that is 208 nanometers. So that

means if there is a topological qubit, so you need a minimum 200 nanometer revolutions

gap. So we--what we did is we did not consider any mathematics or something, we just took--if

we have a gap 2, that means one line starts, we count one, two. We draw the second one

and then the third one. In this way, we went on creating different lines, so it would be

spherical lines continuously, so we call each lines as one topological qubit, this goes

one unit. Now, if you see, you'll find that in gap 2, it is a direct overlap of two lines.

So if you have 100 lines on a particular space you cannot differentiate how many lines are

there, so that means we'd take only one restriction that is if they touch, they disappear. So

we just neglect that possibility. So in this way, we have found that if you send 8, at

the gap of 8, which is a Fibonacci number, then you will find that when you come back

and start, you will find it decomposes into 8, 5. If you send 7 gap, you will get to 7,

6. In this way decomposition occurs. And if we try to put multiple qubits, we will find

only four sets of combinations; 8, 5, 10, 13; 7, 9, 11, 13; 5, 7, 10, 13 and 5, 7, 9,

13. And the decomposition lists are also given here. So if you just, on a piece of paper,

you play with the pen, you can find this kind of relations. Okay, so this is about horizontally

if we send signals into a microtubule. What if it takes information from the environment,

E1, E2, E3, then we can find that if we start with topological qubit eight, then it decompose

into--if another signal enters, decompose into 5, 3. Another signal enters 5, 3, 2.

Another signal enters 3, 2. Another signal enters, qubit then will disappear because

we said touch, disappear. So in these operations, in the future, people can work on. But if

we go to lattice B, I got very interesting things. That is, gap 2 survives, gap 3 survives,

gap 4 decompose and it goes to 2, and you can send signals straight. If we--if the gap

is X, that is straight, then helicity c is infinite. If you put it in the Hamiltonian,

you will find that you get a typical situation where MPCG, or the Multiple Point Contact

Gaps, that we showed at the beginning of my talk, that appears spontaneously. That means,

if this kind of microtubule is there then it is coherent. You don't need to have any

external energy supply, it is always ready to do that. And this, lattice B, is very prompt

towards information transport. Lattice C and lattice B are complementary to each other.

So lattice B, you know, gives us 2, 3Q, 2, 3, 4, and X and it gives us 5 to 13 something.

Together, they cover entire series. One is good for computing, that is simply we are

finding it decomposes into its states, other don't want to decompose. So, what can we detect

about the topological qubit for different lengths? So for four different lengths of

MT, we should be able to get four different sets. So let's go for the experiment. Now,

we cannot do--the biggest problem when we wanted to do this experiment, we wanted to

measure quantum hall--fractional quantum hall effect which is the easiest and the direct

mean to detect the topological quantum qubit but microtubule does not respond to Rxy, that

is the particle, because we have in the megahertz frequency range only one molecular layer thick

so we cannot create the magnetic flux gradient which is essential for the Rxy. So we have--we

are left with only Rxx. But we found that when magnetic flux gradient is created, basically

Rxx, the horizontal resistance, also changes. Our principle is that we cannot absolute time,

we cannot detect a quantum state. But we can change the--we can change the transformation

from one topological qubit to another. That means, if we can convert topological qubit

A to topological qubit B, energy will be released or absorbed. So what did we do? We sent an

AC signal in the middle part, the shaded region. So AC signal, we know very well that does

not change the resistance of a device, the DC resistance of a device, because DC resistance

of a device depend on the topological order. AC signal cannot change unless--until there

exists some topological order and that undergoes a quantum transition. So, this is a simple

experimental set-up. So we have a function generator with two capacitor because DC's

part doesn't come into it, and a resistance measurement device. So we measure only the

DC resistance of the system. We change the function near the frequency and see what we

find. We find four, always, four different regions where you see the large DC resistance

change. This figure almost looks like, if you have gone through the literatures of fractional

quantum hall effect results, the result--this result, if you leave frequency to B and DC

resistance, this looks nearly similar. That means we are seeing the absorbance and we

find that seven distinct peaks appear and disappear repeatedly on different lengths.

So we measured--we repeated this measure on different devices. Then, if there is a qubit,

there should be a quantum phase slip. That means, one side we will send a signal, on

the next side there should be a phase difference. So, you find the phase difference and they

are also quantized, 45, 90, 135, 180, and 0, these repeats statistically. Then we try

to find out the condition, Q, ABCPCDE, that peaks that we have, and 8, 5, 10, 13. We,

again, we used the condition, topological qubits don't touch, and we find that exactly,

unless until you have this topological qubit you cannot get these peaks. You can verify.

So quick summary of the energy levels that we have got. So 9.03 megahertz, you get a--you

get resonance in the microtubule. It becomes coherent and no phase change, nor it is even

phase coherent. 20.56 megahertz; again, phase coherent; 16.35, 18.15 megahertz, in this

megahertz you get 135 degree phase difference and--or 180 degree phase difference and they

are coupled to each other. And the 23.00, 24.00, 23.27, 24.06, and 24.91 megahertz also

add to that absorbance peaks, which varies. What we did is we measured, we, you know,

changed the length of the microtubule from 200 nanometers up to say 10 or 20 micrometers.

And we found for every length which are the qubit peaks appear which are--which disappear.

So we tried to find out--we found that it is strongly dependent on the length and follows

a very particular algorithm continuously along the length. That means if you now give me

a particular length, let's say 22 micrometer, what should be the qubit properties? I can

tell exactly that this, and this, and this, and this energy band will get the absorption,

and this energy band we will get the absorption with this angled phase change and that angle

phase change so I can exactly tell you. Okay, two interesting thoughts. One is that one

period for this particular operation that we say that phase locking is a two micrometers

and 12 different ways it could be done. So, 24 to 30 micrometer long microtubules are

necessary to get all the states. And there is negative delta R minus delta R, plus and

minus delta R. That means in microtubule, particular signals you can send from this

direction and particular signal at the same time you can send from this direction; both

direction you cannot. So we tried to create in both directions but we didn't get. And

last experiment that we did to detect whether there exists quantum topological qubit or

not is quantum interferrometry. The experiment--it suggests theoretically that if you have from

both two ends, if you generate topological qubits into the system, and if you can make

it feel gradient in such a way that you trap it, then what happen, the middle region will

automatically create pulse with a certain time. So the--here is the two end qubits that

we created with two signals and the top radars we got continuous oscillations from that so

there must be existing some sort of topological order inside the system. What kind of TQs

are these? There in literature you will find there are at least 15 different kind of topological

qubits. We do not want to definitely define right now because we have got the experimental

radars and seven different kinds of signatures we have got of why this is topological qubit.

But still, since it is room temperature, we want to be very, very sure what is the real

nature of this kind of topological qubits. Finally, ferroelectric property of microtubule.

In the month of April, I came to Center for Consciousness conference and I saw the bottom

result. We'd--we had lots of noise at that time. We removed the noise and we have got

perfectly square. So there's--this is noise-less. Any kind of--if you get perfectly square behavior,

that means to store energy you don't need to spend energy to retain a particular bit.

And if you change the temperature, the information is not lost. It retains. As you can see, 250

K and 300 K at different bias we can create. So multiple states, you can write and you

can retain. Both kind of measurement could be done simultaneously. And as I have all

ready said, that if there is a length change continuously, that was first sentence of my

doc files, our objective, that if there is a dynamic instability, that a microtubule

is continuously changing, why it is changing and what are the nature of a particular length

of microtubule, we can tell exactly what qubits are. So, we want to build now the languages

in which we want to communicate with the cellular organisms. So this is the conclusion. Microtubule

processes classical bit and quantum topological bits together. Its conductivity is independent

of temperature. But whether it should be classified in metals, semiconductor, or insulator, we

don't know. But we think that it should not be classified in any of this. Lattice C and

lattice B are complementary to each other as far as topological qubits are concerned.

And together, they build a fantastic system of information processing by changing length,

MT tunes, nature of its topological qubits, MT stores and processes bit without releasing

or consuming heat, it's perfectly solitary. So finally, I would like to acknowledge Hartmut

and to Stuart for their contributions, AOARD [INDISTINCT] is here. I cannot--I would like

to acknowledge him for his kind grants, and JSPS, Center for Consciousness Studies for

some of the grants. And Professor Daisuke Fujita and Dr. Satyagit Sahu, and Dr. Subrata

Ghosh, and Professor Kazuhiro Hirata. Satyajit and Subrata are my post-docs, they have done

majority of the experiments and Professor Hirata reproduced our results because it's--it

was hard to believe at the beginning. And Professor Fujita also generously helped in

AFM measurements because he is very expert and he suggested that we should move to 4th

probe systems all to prove data useless. And also finally, I would like to thank all of

you for listening for this long time. Thank you very much.

>> Thank you. Thank you very much. Thank you. Are there any questions? Maybe we can take

one question. Yes? >> One question. You said that the conductivity

is not metal, not semiconductor, and so on. What type of the conductivity is this?

>> BANDYOPADHYAY: I don't know. But it is... >> Is that not electron conductivity? Or what

type? Because if you transport electricity, you must transport charge and therefore that

is something that should be explained. Because I assume that there is a certain amount of

electrons in the--I may say, conductivity band of microtubules.

>> BANDYOPADHYAY: Yes. I have shown the conductivity band. I have shown the picture, the point

contact. So it is--there is no--and in case of metal, there is no gap. In case of semiconductor,

you have a gap, a small gap. And in case of insulator, you have a large-band gap, right?

So it is very well-known. But in this kind of material, you have a point contact gap

in between the valence band and the conduction band so you can say it is another kind of

material, new kind of material, that does not fall into this category, so you can find

a new name. >> Thank you.

>> Thank you. Any more questions? Yes? >> Hi. So I guess I have a couple of questions.

First, I'm trying to understand why you call these topological qubits bits [INDISTINCT]

how do you read that information from them? >> BANDYOPADHYAY: Okay.

>> Yes. >> BANDYOPADHYAY: First, I call this topological

qubit for three reasons. Topological quantum bit. We have got the bit, we detected it.

We have got the topological order of change by measuring DC resistance change with the

AC particular frequency. >> I'm sorry, what are you detecting?

>> BANDYOPADHYAY: "What are you detecting" means?

>> Like, what does your--like, you're showing like a loop around the microtubule. What's

that loop mean? >> BANDYOPADHYAY: No, no, no, no, no, no,

no, no. You saw the experiment of--when DC resistance change using the AC signal frequency

that we supplied to the device? Did you check that? So if we apply a very particular energy

you will find sudden fall in the DC resistance. So, DC resistance of a system, you know, DC

resistance of a system determines the topology, the confirmation, and the structure. When

there is a sudden change in that that is quantized. That's why I call it topological qubit.

>> So... >> BANDYOPADHYAY: So at a particular frequency,

at six and seven different frequencies, always, whatever be the length of the microtubule,

you will find it will be enhanced, or I mean, dominated or sub-dominated. But in those frequencies,

if we apply a signal at a very small part of the system, AC signal, purely AC signal,

you will find the DC resistance is getting changed. So that is how we did it. Of course,

there are many other detection process by which we said. So there are standard five

different experiments, five or six different experiments, which has been established theoretically

to detect topological qubits which you can find in the literatures.

>> So could you store--could you store a quantum state? I mean, could you store a superposition?

>> BANDYOPADHYAY: No. The--when we tried to do this kind of experiment basically what

we do is we send a particular kind of current, particular magnitude of current which reaches

the material to the coherent state. For an example, suppose we are working with, say,

we know if we send DC current of 1 microampere we know that the resistance will fall below,

say, 20 kilo-ohm or 1 kilo-ohm. We know that. That means it is going to the coherent state.

So externally, we first send that current. When you send that current, we take it to

the coherent state and we store the topological qubits. Then, we try to transform one set

of qubit to another set of qubit. One qubit, we cannot write. One topological qubit, we

cannot write. But a particular set is possible to write. But what set we will write depends

on the length of the system. >> Let's...

>> BANDYOPADHYAY: We cannot control... >> Okay, let's--can we take this discussion

off-line because I'd actually like to join in it too, because I don't think this is a

topological qubit to be honest. >> BANDYOPADHYAY: Yes.

>> But next speaker is Stuart Hammeroff, and we'll reconvene in about five minutes. Thank

you.