Okay, so welcome to the lecture on quantum optical phenomena in nanophysics.

Okay, so let me start by having yet another brief introduction just to give you a general context.

So first let me just remind you of how quantum physics started out basically 100 years ago.

People did spectroscopy on atoms and they found certain spectral lines and then they went about explaining these particular spectral lines

and so they evolved towards the current day explanation of quantum physics.

So the typical setup you would have at that time would be you would have a light beam and a cloud of atoms

and you would test for the spectral lines that get absorbed in the cloud of atoms.

So you would plot say the absorption versus frequency.

You would observe a number of discrete lines and a few years later this was explained as being due to transitions between discrete energy levels.

So if I plot the potential inside an atom, the coulomb potential as seen by the electron, then quantum physics tells us we have discrete energy levels.

And the rule would be that if you excite a transition between two such levels, say between these two, then you need light whose frequency measures the energy difference.

And the relation would be h by omega equals the difference between energies, say the difference between the initial energy and the final energy.

So this is spectroscopy and even though the explanation of course was given in terms of what happens to an individual atom,

you should notice that in these experiments spectroscopy was done on a gas cloud that is a large, large number of atoms.

In other words, only for explaining the results of the experiments people were looking at individual quantum systems,

but in real experiments they did not yet have access to individual quantum systems.

And that is okay for some aspects, for example in explaining these particular transition lines,

you don't need to learn anything about the individual atom in the experiment,

but there are other fundamental aspects of quantum physics which you cannot learn about if you just have an ensemble of atoms.

Let me give you an example. So quantum physics tells us that if you take an atom, say in the ground state,

and you bring it into the excited state, then say after some time it will react back to the ground state, emitting a photon,

and this process is known as a quantum jump. And of course if you excite billions of atoms,

you will have the same kind of processes going on, only the points in time that these different quantum jumps happen are random.

And that means the signal you see, the light they emit, is just very smooth, it does not display any quantum jumps.

So you can have a chance of observing a single quantum jump only if you have access to a single individual atom.

And that is why people started wondering, could it be possible to access single atoms?

This is very challenging, and actually it was achieved only, say around the 1980s or 1990s,

when people started trapping individual atoms and doing spectroscopy on those individual atoms using laser light.

So that was so to speak the trend towards accessing single quantum systems.

And the typical setup would need some way of trapping an individual atom.

One way of doing this would be to charge the atom, to rip an electron off the atom,

so you create an ion and then you can trap it using electric or magnetic fields.

Another way would be to have neutral atoms and to have these neutral atoms, for example, being trapped in the light field of a laser wave.

And in all these cases it was then finally possible to have not only a single atom,

but also possibly to let it interact with a single photon.

Again, in contrast to what happened when you do spectroscopy on a cloud of atoms,

not only do you have billions of atoms, but you also have billions of photons coming in.

So in that way one was able to realize the Gedanken experiments,

which were used to explain the phenomena and the beginning of quantum mechanics, but have never been realized before.

Now again, I already told you why this might be interesting.

One of the interests is in fundamental physics,

and the things you can observe is, for example, the quantum measurement process, quantum jumps being observed in single quantum systems.

Another issue, and we will come back to that in the course of the lecture, is we can create more interesting quantum states.

For example, you can have the different individual quantum systems interact with each other,

and then you create states that have correlations between the quantum systems,

and these correlations can be far stronger than anything you can achieve in a classical system,

and that would be called entangled states.

So these are some aspects on the side of fundamental physics.

You can also think of applications of quantum physics.

And one of the ways to use individual quantum systems is to make them into very sensitive detectors.