It’s a great pleasure to be here of course and I’m looking forward to meeting with the students.
Obviously it was a great thrill to receive the Nobel Prize with Serge Haroche.
And what I’m going to tell you about here
is maybe completely on the other end of the spectrum of what you heard from Brian Kobilka this morning.
Here we’re dealing with extremely simple systems but we’re trying to control them with high precision.
So I can start maybe with this example of Schrödinger’s cat.
And one of the interesting things to me is that Schrödinger, one of the inventors of quantum mechanics,
in thinking about the consequences he became uncomfortable with the theory
because basically the theory by itself just describes continuous evolutions of systems.
And the way he expressed his discomfort with this is that in principle although we can really only apply,
in practice apply quantum mechanics to relatively small simple systems.
In principle it should apply to very large systems.
So his way of expressing his discomfort was this idea of this example he posed
where a cat is inside of a sealed box so it can’t interact with the rest of the world.
And also in the box is, say, a single radioactive particle.
And if the radioactive particle decays it will trigger some mechanism which releases poison and kills the cat.
And basically in principle you could write down equations, the quantum-mechanic equations, that describe this situation.
And all quantum theory tells us is that after one half-life of the particle the cat is neither dead nor alive,
it’s dead and alive at the same time.
And of course this is a very strange situation.
But anyway this case of these simultaneous existences of states is commonly called superposition.
So there’s actually a simple analogue which I like which gives the flavour of superposition.
And from this... If you look at this image of a cube, sometimes you’ll see this face here be in the foreground.
Or you might see this face be in the foreground.
And this is very similar to superposition in the sense that as you tend to see either one situation or the other.
But in some sense it has both, possesses both properties at the same time.
And I think this is a good analogy to superposition that it’s neither one nor the other.
It’s both when you see them in that perspective there.
The other interesting thing about this example I think is that it exhibits in a nice way the idea of quantum measurement.
That is where we learn in our quantum mechanics classes
then when we measure a system we project or collapse a superposition state in one configuration or the other.
So when you tend to see one of these 2 perspectives, that’s very much like measurement and quantum mechanics.
And coming back to Schrödinger’s example.
So, quantum mechanics would predict this superposition state.
And this is... It was dubbed a tangled superposition
in that the state of the cat is correlated with the state of the particle being un-decayed or decayed.
And this was given this name of entanglement where you get these correlations or these systems.
And one thing that’s interesting at least on the small scale is that we can show that these correlations exist
even when the constituents are separated by large distances where they can’t communicate in a relevant time scale.
But that’s a little bit aside from what I’m going to talk about here.
One of the ways that Schrödinger was bothered by the consequences if you scale quantum mechanics to large scale.
And in the ‘50s he posed one way out of this.
And at that time he could say: “Well, we never really experiment with just one electron or atom or molecule.
And we do in thought experiments.”
So as these thought experiments extended from small systems up to the macroscopic world like cats.
But maybe basically I think that what he’s saying here is maybe we’re leading ourselves astray
by thinking about the simple system because if we scale it up, it leads to these ridiculous consequences.
But of course we’re now able to enter this world where at least with small systems
we can play these games of superposition and entanglement.
And as I say we’re only able to do this with very small systems.
But eventually maybe we can go to much larger systems.
And what I’m going to describe here is just kind of a very narrow perspective.
I’m going to talk about the work at our institute, the National Institute of Standards and Technology.
But certainly this is the work of many other groups around the world.
And you’ll hear a different perspective from Serge Haroche on some very similar application of these ideas.
So let me... I won’t have time to describe all the techniques we use.
But let me give you an idea of what we can do.
In our experiments we use typically singly ionised atoms.
And one example is beryllium.
And we put it in a trap, an electromagnetic trap.
And what you can think of is just like a marble in a bowl.
And one situation we can realise is where we...
for different internal states of the beryllium ion which we can just assign these labels.
They do have magnetic moments so we can talk about a spin.
So we can associate at some instant of time where this atomic marble...
It can be, say, on the left side of the bowl correlated with the internal state
being in one position and then simultaneously on the right side of the bowl correlated with some other internal state.
And so we can actually realise these situations.
And what we want to say is: Obviously it’s not very, it’s not really macroscopic.
In fact it’s very small. And these experiments...
The wave packet size of that describes the position of the beryllium atom as in the order of 7 nanometres in this experiment.
And with these separate parts of the wave function were only separated by about 10 times the size of the wave packet.
And you might argue: Well, this isn’t really Schrödinger’s cat.
It’s just too small. But one of the interesting things about quantum mechanics,
if you say, you know, this is too small to be called macroscopic classical, where do you make that dividing line?
And this is something we continue to struggle with.
At this point there’s no way to find this classical and quantum barrier.
So in some... even though it’s very small, we would say it has very similar properties, analogues properties to Schrödinger’s cat.
And I’ll come back to that in just a little bit.
So as I mentioned in the abstract a couple of applications of these ideas of superposition might be in clocks.
And I’ll say a little bit about quantum computers.
For the clock application what you can think about is that for example if we have an electric dipole transition in an atom
and if we put the atom in a superposition state, -this would be a ground S state and a P, excited P orbital-
then we get a wave function that we can write down as I’ve indicated there.
Now in fact this... What this describes then is an oscillating dipole.
What I’ve written here or shown here in this view is a plot of the electron density versus time oscillates back and forth.
So it’s very much like a pendulum clock.
And we can utilise this property in fact to make a clock which I’ll say a little bit now here.
So in fact the practical mode of operation
when we make an atomic clock is that in this example here we would start the atom in the ground S state.
And then we would apply radiation at a frequency.
Say, this would be a laser transition where it’s very close to this transition frequency here.
And then what we do is we would measure after applying this radiation.
We would measure the probability that the atom has gone from this ground state to this excited state.
And so this is closer to what we do in practice.
We follow this protocol here.
And when the laser frequency in this example is equal to this transition frequency
which is given by the energy difference divided by Planck’s constant,
when that transition probability is maximised, then we know
that the laser frequency is in synchronism with the natural frequency of the atom.
And I’ll come back... I just want to keep on this theme of superposition.
Before we do the measurement, in general the atom is in some superposition of its ground and excited state.
So why atomic clocks?
And there’s some simple reasons that convince you why that’s interesting.
Basically all atoms are given ions... aluminium ions, or beryllium ions, magnesium ions,
any of the given species are exactly identical.
So if we can agree on a transition to make an atomic clock,
in principle they should run at the same rate independent of a comparison.
Now of course in the experimental challenges that we’re always stuck trying to...
with environmental effects that we have to calibrate out.
So that’s the real challenge.
And the other thing of course as opposed to pendulum clocks: Atoms don’t wear out.
They can be used over and over again without hurting their properties.
So these days what we’re focusing on is using optical transition
and one example here is for aluminium where the transition frequency is about 10^15th Hz.
And the reason the high frequency is interesting is basically:
With the higher tick rate you can define any time interval into finer and finer steps.
And so you get higher time resolution that way.
And the other thing is interesting is that some transitions including aluminium...
the lifetime of the excited state is about 20 seconds.
And we can get resolutions down to about 1/10 Hz which defines very precisely then this condition where the laser is tuned...
laser frequency is tuned to the atomic transition frequency.
So I’ll give you another example here.
We started out in our lab working on mercury ions.
That has a similar transition that could be used as a clock.
The way we detect these transitions is actually very simple.
We’ll find some other transition in the atom.
In this case this is one that can... we can scatter a lot of photons.
And the basic idea is after applying this clock radiation,
if we’re off resonance and the atom remains in the ground state, and then we see fluorescence.
On the other hand if we’ve promoted it to the excited state, then there’s no state for the laser photons to scatter off of.
And so this is nice because even with a single atom we can easily discriminate when the atom has made a transition when it’s dark.
When we don’t see fluorescence that means it’s promoted to the excited D state in this case.
And when we see fluorescence that means it hasn’t made the transition.
And of course as I say we can use this then as a reference in the clock.
So an example from our lab is the following.
Jim Bergquist who... we started this project in 1981.
And we’re still working on it.
Just some of the advantages of using ions.
I haven’t described at all.
But we do... First of all just the fact that we’re holding the ions in one location means
that on average the velocity goes to 0.
So one measurement effect we have to worry about is the so-called first-order Doppler effect,
the usual Doppler effect you’re thinking about.
And since the average velocity is 0 that tends to go to 0.
And I haven’t described laser cooling as a technique.
And a lot of atomic physics experiments where we can use radiation pressure from lasers to cool the temperature of the ions down.
And the reason that’s important is
because of the consequences of Einstein’s theory of relativity for moving objects, time moves slower.
And this has a small effect on any scale we’re used to.
But we’re at such high precisions now that we do have to worry about that effect.
And by doing this laser cooling we can suppress that time relationship.
There’s many other things we have to worry about.
And I won’t go into that.
But anyway the result of this work was that in around 2006 the standard
that defines the second is a hyper fine transition in caesium.
And of course it kept getting better over the years.
So it was a moving target.
At this time then finally we could get to a systematic uncertainty of about 7 parts in 10^17
which was better than the existing caesium standards.
So, these days most standards labs are thinking in terms of these optical transitions
where you can get very high precisions and very high accuracies.
And as I mentioned this is an example from our lab.
There’s other ions people are thinking about.
This article here summarises that work.
And of course at the same time there’s many experiments using neutral atoms, trapped neutral atoms.
So there’s a huge number of labs around the world working on these atomic clocks based on atoms or in this case atomic ions.
So let me say a little bit about this idea of quantum computing.
The basic...
again relies on superposition.
As opposed to a classical bit which can exist in one state
or the other we’re going to play on this idea that in this case a quantum bit which we’re changing the labels here...
these could be energy levels in the atom that we can...
in some sense it can be both in the 0 and the 1 state at the same time.
That is both pieces of information at the same time.
And where that might be interesting then is in this... is if you think how it scales.
So for example if we have 3 qubits in a classical register that could hold 1 number.
But in the superposition sense we can hold all 8 numbers at once for these 3 qubits, quantum bits.
So that’s 2^3. And of course you see this has exponential scaling.
And kind of an interesting example: If we had 300 bits and that might store line of a text in a classical computer
but in this superposition stance it will store 2^300 or about 10^90 decimal numbers simultaneously.
And if we had to make a memory that would hold that much information, a classical memory,
it would take more matter than there exists in the universe to do that.
So that sounds pretty good.
The other thing is that if we make a superposition state, the operations that we perform,
they act on all these numbers simultaneously.
So in some sense we have this massive parallel processing.
That sounds pretty good too.
Now the catch is that coming back to the example of the box and the different perspective.
When we measure a quantum system...
For example if we measure the superposition of 3 bits.
When we measure the system it collapses down just to one of these configurations.
So we have to design...
a useful algorithm is one where we want to make most of these coefficients
before we do the measurement and after the computation.
We want to collapse down the state to at least a very number of possibilities.
And so one example where that might be possible is Shor’s factoring algorithm.
I’m not telling you the history.
There’s a lot of interesting history behind these ideas of quantum computation.
But the thing that really set it off was an algorithm that Peter Shor came up with to factorise large numbers.
And the reason that’s important, because it affects encryption.
So you can imagine all the government agencies are interested in that.
So let me give you an idea.
Just to give you some comparison with classical computing.
Although it may not be the most efficient way.
In principle you could construct a universal classical computer just composed of 2 gates.
And there’s other combinations.
But those would be 2 examples.
In the quantum world it’s also true.
We need 2 operations as opposed to just a bit flip.
We need something more general.
So for the chemists here... you think of NMR, where you’re able to rotate the spins by various angles.
These are the kind of operations we’re talking about here.
You also need some sort of non-trivial logic gate.
In this case here where if we act on Eigenstates of the system...
Of course we could reproduce this classically with a classical electronic chip.
But in this case remember that we’re thinking of this working on superpositions.
So actually Peter Shor’s algorithm is very involved.
It’s very interesting.
But it takes a long time to describe.
But nevertheless the basic feature, the way it could be implemented is basically you have some input register.
And you actually start out with the superposition of all possible numbers up to the number you’re trying to factorise.
And then you would perform a series of these rotations in these 2 cubic gates.
At least this is one form of how you could do computing.
And then at the end you have some superposition here.
But what you can think about this is...
it’s kind of like a complicated interference experiment where all these possible states
that the atoms might be, they interfere in such a way
that you still end up with a finite number of states not much smaller than 2^N.
But you still end up with a very large number of states.
But the state that you measure could be used in a classical algorithm to extract the factors of a number.
So this is the basic idea.
And of course just even to factorise 150 digit decimal number
which probably isn’t interesting to the coding people these days, you have to at least to get to there.
But it would require a huge number of operations and tens of thousands of qubits.
And we’re not anywhere close to that right now.
But one thing to say at this is, coming back to this idea of Schrödinger’s cat.
At some intermediate time in these operations you could say just single out the ‘i’ bit.
And in this case then it looks very much like Schrödinger’s cat.
Because all this collection of the other bits would be in substantially different states much like Schrödinger’s cat.
So this is kind of why we talk about raising Schrödinger’s cat.
This is the kind of thing we’re aiming for.
So in the circumstance of atomic ions the way we could think about making such a device
was put forth by Peter Zoller and Ignacio Cirac, 2 theorists well known in the quantum optics field.
And their idea was: We have some electrode structure and we can arrange things so that the ions form a linear array.
The basic idea is this is 3 dimensional harmonic well and the Coulomb repulsion holds them apart into some regular array.
And you can... This is the closest I’ll get to most of the chemists here.
This is like a pseudo molecule that we can manipulate.
And it turns out that we can using laser cooling techniques, we can freeze out the motion.
We can put all the vibration modes of this pseudo molecule into the ground state.
And so their idea was that if we have...
in general the qubits are going to be based on some internal states in each of the ions.
And their idea for the tricky part is to make a gate between 2 ions.
And their idea was the following where we... if we focus a laser beam on this ion here, we can do a mapping.
We map this internal state of that ion on to the ground and first excited motional state of this pseudo molecule.
And the thing we’re playing on here is
that all the motion of any particularly mode in general is shared with all the ions so all the ions see this motional mode.
And then if we can somehow make a gate between the motional mode then and say this ion here,
then we’ve effectively made a gate between the 2 ions.
So let me give you an idea how that works.
So, this first step of mapping the internal state onto the motional mode is...
If we think about... If we have our internal states of the ion
and then we dress those with harmonic or the ladder of states associated with this vibrational mode....
So I’ve said ideally we put the ions in the motional mode ground state.
And then it turns out if we just turn a laser on for a duration
such that it takes this component of the wave function and maps it into this level down here,
then basically we’ve made this mapping from the internal state onto the motional mode.
And then the idea is that
if we can make a logic gate between the motional mode and the internal state of the second selected qubit...
And the idea there is that... This is a bit simple but it gives the basic idea.
Suppose we call the motional mode the control bit.
And the target bit is the internal state of the second ion.
In this example here if we... In general that second ion we selected has...
it sees the superposition, the motion and the internal states.
And so the idea is that if the control bit, the motion mode, is in the first excited state,
then we can drive this transition which means we flip the internal state bit.
And on the other hand if it’s in the lowest state there’s no level up here for it to go to.
So that invokes this logic.
Now this is a bit of a cheat.
This one doesn’t work exatly.
You know it is not universal.
But it gives this idea that selective dynamics can construct these logic gates.
Anyway in our group we were able to implement this basic idea of Cirac and Zoller.
This is Chris Monroe who is a member of our group from ’92 to 2000.
And we could make that logic gate that they talked about.
But what I want to say is that this gives you an idea.
These are just the groups around the world using atomic ions
to play with these ideas of quantum information processing.
And so there’s about 35 by my count now.
So it’s a huge operation that we’re dealing with.
Just to give you an idea where the experiments go.
There’s this idealised structure that I showed in the cartoon form earlier.
And it turns out we’d like to make these devices small with all other conditions being the same.
The gate speeds go with the motional frequencies and those scales.
1 over the dimension squared.
So we’ve started to think over the last decade or so now about how to shrink things down.
And one thing we can do is use lithographic techniques to pattern electrodes.
In this case it was alumina electrodes that we made slots in.
And if we overlay these electrodes on here you get the idea of how we would make a structure, a small structure like this.
This shows some real pictures.
In this case we have several regions where the ions could sit.
But it gives you kind of an idea of the things we’re dealing with.
And there’s a picture of 6 ions that are located in a zone indicated there.
And these days we’re even going further
where we can pattern electrodes into a surface using well established micro-electronic techniques.
And then the atoms are suspended above the surface.
And each one... In this example each one of these little tiny squares is a zone where we can hold the ions.
So this is the idea of how we might scale up.
So let me just give you an idea.
So these chips, these multi zone chips, that we’re able to store the ions we put in a vacuum system.
And I think all these labs, often in atomic physics, we’re just consumed by lasers.
All the students and postdocs, this is where they spend their lives.
And of course the computer occupies a very tiny space over in a corner of the room.
So I think I mentioned this idea of factoring.
And in fact it was important to get the field stimulated.
But one of the things we’re hoping for comes from Richard Feynman who was thinking about some ideas early on.
You know, how the quantum computing might be important.
And his idea was to get one quantum system to mimic another system.
And I won’t have time.
There’s a lot of work going on in this.
I just want to... I’m highlighting 2 of the characters from our lab working on these ideas.
Rainer Blatt our host here.
He actually, his group they have the lowest error gates.
And they’ve done the most in this area of quantum simulation.
And although at this point the simulations we can do, that is the ion traverses a hole, are not really...
We can simulate on a classical computer.
We’re hoping that maybe in the next decade
or so we’ll actually do a problem on a quantum simulator that we haven’t been able to do on a classical computer.
And just this very, very small sample of what work is going on.
There’s many other groups.
So I’d like to thank my colleagues at NIST.
I’ve been blessed to work with that group of people.
We have some younger guys now.
But Jim Bergquist, Bob Drullinger and Wayne Itano and I have basically been together for our whole careers.
And we have some good young guys now coming up.
And this gives you an idea of the size of our group now.
And I can’t properly acknowledge everybody.
The other thing I want to say is that it was really a pleasure to share this last year’s award with Serge Haroche.
He’s been...
Well, I’ve known his work for 35 years and got to know him personally 25 years ago and our wives have become friends.
So it was certainly a great, you know, pleasure to be able to share with him.
And he’s going to tell you about his work now, thanks.
Applause.