Okay, so once again good morning, my name is Maria Chekhova. The course is quantum optics,

it's a standard course of quantum optics and it will be filmed this time because one of you

studies in Regensburg and is supposed to listen to this course and she wants to have the access

to video, so the lectures will be somewhere on the internet, hopefully, yeah. There will be 12

lectures and I want to introduce my assistant Cameron Okos, who is a PhD student in Max Planck

Institute and he will lead the problem class. Usually after each lecture I will give some home

task, it will be good if you solve the home task, the task by the next lecture, if not then not,

and there will be about four, I think, sessions of this problem class which Cameron is going to

organize with you. Today he will send around a sheet of paper where you write your email address,

so he will contact you, run a doodle and you can choose the time for this problem class. Okay,

so the course, as I said, it will be 12 lectures, the first three lectures will be on statistical

optics, so nothing quantum so far, because I believe that to learn about quantum stuff one

should first get used to some statistical optics and I assume that you know already quantum mechanics,

so please raise your hands who did not hear a course on quantum mechanics. Oh, that's a

problem. Okay, I'll try to be clear enough, but really I assume that standard quantum mechanics

you know, not quantum optics, yeah, and then you are supposed to know the probability theory to

some extent, so please raise your hands who did never, who never heard of probability theory.

Good, everybody heard of probability theory. So three lectures will be on statistical optics,

then there will be one lecture on nonlinear optics to the extent that is needed to derive

the interactions that lead to the production of quantum states of light, and there will be

one lecture about the interaction between atom and photon, because it's also necessary for

understanding some of the quantum optics, then there will be one lecture on polarization optics,

because polarization is essentially used in quantum optics. By the way, last semester I

taught a whole course about polarization in optics and I will teach this course again next year,

so if some of you want to learn about polarization of light in more details, then you can attend this

course, but here there will be just one lecture, and finally there will be a lecture, a special

lecture about applications of non-classical states of light, quantum states of light. Okay,

so let's start, and I'm going to give first an introduction of how quantum optics appeared,

and what is quantum optics and how it's related to the other fields of science. It is believed

that the start of the quantum optics was in 1956 by the famous Hanbury Brown and Twisse experiment.

This is generally accepted, this idea that quantum optics started from this experiment, so what they

did, they studied two kinds of sources of light, one was a mercury lamp, so just a lamp, well,

I will just show it like this, and light from this source was split by a beam splitter and sent by

two detectors. When I say detectors, it can be anything, but probably you know some kind of

detectors, for instance photodiode, or for instance avalanche photodiode, or for instance photomultiplier,

they used photomultiplier tubes. Those were devices that, there are two kind of photomultiplier tubes,

some can give you really a pulse, a strong pulse, of electric pulse, when at the input there is a

photon, so these devices can really count photons, but some just give you photocurrent, just give you

current, you shine light on them and at the output there is a current, electric current, and the

stronger the current, the stronger the light, the stronger the current, so to say, so they used these

kind of devices and then at the output they looked at the correlation, so correlation, is it clear,

do you see what I write here, yeah, there is no problem with the sun, okay, so correlation of the

photocurrents, and it was noticed that light from even mercury lamp shows some correlation

compared to the presence of independent sources at the inputs of the photomultipliers, and the

second example was so-called stellar interferometer, before that time there existed an interferometer

built by Michelson that could analyze light from the stars and that could be used to even measure

the size of stars, what Hanbury Brown and Twiss made, they, imagine that this is a star, and imagine

there are two detectors and this time there is no beam splitter, there is no plate splitting light

into two beams, but we just observe light that's coming from the star, and these detectors are

placed close enough, so what in their case means meant close enough, it meant few meters, up to three