Okay.

I wanted to finish these lectures by telling you something about real electronic transition

in the solid state, single emitters that can be coupled to the electromagnetic field. So

in the beginning we did talk about a single emitter so to speak, namely the Cooper-Pell

box inside a microwave resonator, but of course that wasn't microwave frequencies. And then

we talked about optomechanics where the light rather couples to the mechanical motion. Now

we do want to couple the optical radiation field to electronic transitions in the solid

state in the sense that you can tune these quantum systems and integrate them into cycles.

I will talk about two different kinds of these solid state emitters. The first will be quantum

dots, excitons and quantum dots, and then the second one will be so-called M-B centers

in diamond. Okay, so here we are talking about semiconductor materials and I first will have

to tell you or remind you what an exciton actually is. The idea is that you have some

semiconductor, that is you have a conduction band which is filled with electrons, excuse

me, a valence band which is filled with electrons plus a conduction band which intrinsically

is empty. And then the idea is what happens if you shine a photon with sufficient energy

on this sample. Well, what happens is that an electron gets kicked out of the valence

band and gets kicked somewhere into the conduction band if the energy is right. Now there are

several possibilities of what happens next. So the one possibility is that if the energy

is really large then the electron and the hole that have been created will simply fly

away. So that is the possibility that is not that interesting for us. What can happen as

well is that if the energy is just right and a little bit smaller than the band cap then

instead you don't access this state where the electron and the hole run freely away

from each other but rather you produce a bound state and that is a bound state between an

electron and the hole. This bound state then is called an exciton. The exciton I have drawn

here is obviously a neutral object, it is bound and then it can move just like a neutral

atom. Now this is one part of the story but we already learned in the examples that it

is good to be able to localize things and to create localized discrete quantum levels.

And so that is achieved by not simply having a bulk semiconductor but by somehow patterning

it in the sense that at some point in the sample you create so to speak a trap for electrons

and holes and that is what we call a quantum dot. So a quantum dot in general would simply

be a region with localized states, localized electronic orbitals by electrons and in this

case also holes can reside. And there are many different versions of quantum dots so

let me just recount two of the most important ones. One of them are laterally structured

quantum dots. Now as the name implies you do something in a plane and what you really

have is a sample where some 100 or 200 nanometers below the surface you create what people call

a two dimensional electron gas. Now that occurs at the interface between two different semiconductor

materials and then the idea is that if this is filled with electrons you have a uniform

gas of electrons moving in this two dimensional plane. Now this would still be a completely

two dimensional extended electron system but what you can do next is obviously you can

try to apply some potentials in order to confine the electrons. So you want to apply some electric

potentials and the easiest way of doing this is to produce some electrodes on the surface

of the sample which are simply metallic pieces that you can charge up to some voltage and

in particular you would charge them to a negative voltage in order to deplete the electron gas

beneath them and in order to repel the electrons and to create a trap for the electrons in

between the electrodes. So you charge them negatively and then somewhere in the two dimensional

electron gas you can create a confined region for the electrons and that would be a quantum

dot. You can imagine that by changing the gate voltages that is changing the voltages

on the electrons you can shape and change the potential even in the course of time.

Now this is not typically the kind of structure that is accessed when we talk about optical

access. This is used for electronic transport experiments. So what people produce when they