Okay, so we want to start a new chapter and learn about another system or class of systems

where quantum optics and condensed matter meet.

And the field which I want to explain to you now is called Optomechanics because it deals with how light covers mechanical motion.

Now first of all, there are mechanical systems on the micron or nano scale and the typical thing to think of would be a kind of beam or cantilever that can vibrate.

So you would have for example a beam that is freely suspended between two parts of a substrate and it could vibrate.

Or you would have what is called a cantilever which is attached to some substrate and again which can vibrate.

And now over the past ten years or so people have understood a variety of approaches of how to control these systems, how to copy to them, how to read out their motion.

And the first kind of approach was actually to couple these two electrical circuits.

So if you do that to nano-mechanical systems then you would call them nano-electromechanical systems.

And there is even an abbreviation for this kind of system, namely they are taught in NEMS.

It's not hard to imagine how that might work. For example if you charge any of these beams and then you apply an electric field nearby and have a time dependent electric field then you can just drive the motion of this beam.

In addition if this beam then starts to vibrate and for example it is part of an electrical circuit because it is metallic then you might observe a change of its resistance or change of the voltage applied to this beam and so you could read out the motion.

So that is one approach. And another approach that is more recent would be to couple these systems to the electromagnetic field in the optical domain.

And I will explain later that typically this looks like having an optical cavity with some vibrating part which is driven by a laser.

Now before I start to talk about optomechanics in particular I want to give a sort of overview of what are the goals of people who investigate nano or micro-mechanical systems in general.

There are two different directions into which people go. One of them is more research into fundamental physics especially if it comes to quantum effects and the other is research into possible applications that involve for example sensitive detection.

So let me write down a few notes for both of them.

One of the goals that people have with regard to fundamental physics is to take one of these objects and place it into some non-classical state for example into a superposition state or entangle it with another quantum object.

And the idea is simply the following that these objects are so heavy they are consisting of so many atoms that this would test quantum mechanics in an entirely new regime.

Now why would you want to test quantum mechanics in this regime of heavy masses?

Well the idea is that we all know that for really large objects, macroscopic objects, we don't need to talk about superpositions, we don't need to talk about quantum mechanics, we usually can apply classical physics.

And the question is how does this work, how do you have a gradual transition or again an abrupt transition from the quantum world to the classical world, to the classical behavior that we observe.

So there is a commonly accepted notion of how this works because as you go to larger and larger objects they couple just more and more strongly to the unavoidable fluctuations of the noisy environment.

And so this would lead to decoherence, it would quickly destroy all the superpositions and if the objects are large enough you may not even be able to produce a superposition in the first place because it would decoherence so quickly.

So that is a process that is known as decoherence.

And one of the goals would be to test how decoherence evolves for these heavy objects and there are some speculations that if you go to really heavy objects then additional mechanisms for decoherence might kick in.

For example there is a speculation by Roger Penrose who speculates that since we do not yet have a consistent theory of quantum gravity we might as well speculate that if you place a heavy object in a superposition of being in two places then there is an additional decoherence rate induced by gravitation.

And that could be tested but it could be tested only if the objects are sufficiently heavy so this is one of the reasons why people would prefer to be able to put these objects into a superposition rather than just putting a single atom into a superposition of two places which of course has been done but which would not be susceptible to this mechanism because the decoherence rate would be so low that you can't possibly test it.

Okay so this is speculative but it is clear that decoherence will play an important role for these objects and so you learn more about decoherence if you investigate superpositions.

And there is a possible applied side to quantum physics which we discussed already which would be quantum information processing so how do these objects possibly come into the picture for quantum information processing?

Well you can already guess at this point that these are not two-level systems, they are harmonic oscillators.

So they would rather take the role say of the microwave cavity that we discussed for coupling to superconducting qubits.

And so one of the possibilities for exploiting these objects would be to store some quantum information inside these objects just in the same manner that you could store quantum information say photons inside a microwave cavity and to read it out later.

And so when we talk about storing quantum information in them there is also another possibility which has to do with transferring quantum information between different systems.

So we will turn out and we will discuss this.

Not only can you couple these systems to light but you can also couple them to electrical circuits in particular superconducting circuits, in particular superconducting qubits and there is the possibility that you would have the information first in the superconducting qubit.

You want to put it into the light field but it is very hard to do that directly because you cannot easily couple the optical field to a superconducting circuit because at the optical frequencies you would simply destroy superconductivity if a photon is absorbed.

This is far beyond the superconducting.

So the idea would rather be to have a superconducting qubit, couple it to some mechanical system and then couple this mechanical system to light and thereby indirectly transfer the quantum information from the superconducting qubit to the photons.

So that would be transfer.

Now for all of these things obviously you need to be able to look at quantum dynamics and in order to have quantum dynamics you need to be in or close to the quantum ground state of these objects.

And we will discuss the typical scales of these objects and find that this is not so easy.

So I should remark that the typical mechanical frequencies for these objects are in the range of kilohertz up to gigahertz and if you convert this into temperatures you will see that typically if you say h bar omega equals kVT these are temperatures that are smaller than the 20 millikarabit that can conventionally be reached in a laboratory.

So we will learn a method by which you can use laser cooling in order to reduce the effective temperature even below what you could reach in the laboratory usually.

But this is an important issue reaching the quantum ground state.

Okay so this is quantum physics and it provides a motivation for many people in the field.

But then there is another very important aspect which I mentioned already which would be applications.

And while for applications it is also good to reduce thermal fluctuations you do not always need to go to the quantum ground state. There are many interesting applications that already work in the classical domain.

So one application of mechanical devices in general is very sensitive detection for example of tiny forces. And this is in particular evident since cantilevers of this kind have conventionally been used, I mean since over 20 years being used in atomic force microscopy.

So there the idea is to use these cantilevers to scan across the surface of some material and to look at the surface of the material with atomic resolution.