Good morning. We will have this course and I immediately have some suggestion that there

is a lecture overlapping of Joachim von Santier that starts at 12 and if someone...

So actually there are two students who you are attending that lecture so I

suggest in the future to start this lecture at 10.30. Is this fine? Yeah? Okay.

Then let's start. So this will be quantum optics. I'm going to give you 12 or 13

lectures. I'm not sure how many exactly and there will be also a problem class

led by Gaetano. So after the lecture you should somehow contact him and give your

email addresses and then you will fix, you will schedule the problem class time.

And then I will give some small tasks at every lecture and depending on how you

solve these small tasks the exam will be easier or more difficult. I mean the

conditions for passing the exam will be easier. So I will give some bonuses to

those who regularly solve these tasks and the exam will be a written exam in

the end but we will decide about the date of the exam. Okay so let's start.

There will be first lecture, will be first three lectures will be actually on

the statistical optics because I think you some of you have gaps in statistical

optics but I suppose that you know quantum mechanics. So quantum optics was

started, it is believed that quantum optics started in 1956 when Hanbury

Brown and Twiss made their experiment. Hanbury Brown and Twiss, I will write.

And Twiss, two different people yeah. And they they made experiment on observing

correlation of intensity fluctuations. They did two kinds of experiment. First

was with the mercury lamp so it was a source like let's show these sources

mercury lamp and light from this source was split on a beam splitter so this is

a semi-transparent plate where part of light can be reflected, part of light is

transmitted. Yes, come in. And then there were two detectors and each detector

registered intensity and what was at the output was photocurrent so I will write

current. The current was proportional to the input intensity. I1, I2 is the

current of the second detector and then they looked at the correlation so at the

output was I1, I2 mean value. I will write it like this. Well mean value can be

just something averaged over time. In quantum optics further we will use this

notation for averaging over a quantum state but you can you can just imagine

that you register these currents multiply them and average. Yeah and it

turned out that this average was not equal to the result of averaging one

current and the other current separately. In fact here what stood here was not

equal but larger, always larger. So it looked like there were correlated

events here and here and because by that time it was of course typical to speak

about light as consisting of photons of course yeah we know that light

consists of photons. It was said generally that photons bunch so as

if this source emits groups of photons, photons bunch into groups and these

groups lead to the correlated events in these detectors so whenever

this detector detects something the other detector will also detect something.

So this effect was called bunching of photons and at about the same time they

did another experiment which was aimed and and I will discuss it in more detail

later I'm just giving you some idea of how it all started. Observing the

radiation from stars from some stars rather the the brightest stars because

for a weak star it was not really possible. So imagine there is a star and

on the earth somewhere we have two detectors again but this time there is

no beam splitter there they are just separated in space so one detector is

here D1 and the other detector is here D2 and they give I1 and I2 also currents

and we do the same so light comes from the same object to two detectors and

again they observe that I1 I2 mean value was larger than taking just mean value