Okay, good morning.

The number of people here reduces, the number of people who signed for the exam is frighteningly

high.

It means that most of you are listening online to these lectures and I have very little feedback,

which is bad.

Because today I wanted to discuss the date of the exam and to tell you when the next

lectures will be.

So we'll have the last lecture in this semester in a week and then there will be still four

lectures left.

And the first one should be on the 10th of January, but I am not here on the 10th of

January because I'm at a conference.

And so the first lecture in the new year will be on the 17th of January.

That makes 17th, 24th, 31st of January and 7th of February, the dates of the last lectures.

After which I suggest an exam on the 21st of February or on the 28th of February, which

is better.

21st is better, I also think so because it's better to have it not too much later than

the end of the lectures.

And of course Cameron will make several sessions of the problem class.

I think one is still next week.

I don't know, he's in touch with you, in contact with you, but the others will be in the new

year.

I don't know, two, three sessions.

Does everybody know when the new exercise is going to be?

Okay, so now let's start with today's lecture.

Again, if someone gives me home task, please do it during the lecture.

But I will not explain how the task is solved because it was a very easy task, a very easy

problem.

Today there will be a difficult problem.

And today we'll continue discussing the discrete variable approach and then we'll discuss the

continuous variable approach.

And as I planned, I will explain both the methods of calculation and the methods of

measurement.

So I believe at the last lecture we introduced the quantum mechanical version of second order

correlation functions.

I introduced gk as averaged over the state, quantum state, not over the ensemble as before.

The kth moment normally ordered of the photon number operator.

You know what it means hopefully by now and we proved some theorem that it is equal to

n times n minus 1 times and so on times n minus k plus 1.

And this property we will use further.

Actually, I call this a function.

Some of you mentioned that it doesn't look like a function, looks like a number.

But the full definition is that gk has of course arguments, space and time arguments

like in classical optics.

So it's t1 x1 and so on tk xk and it means that we have to take the full definition is

that we have to take all negative frequency field operators which will be now operators

at time 1 x1 and so on e negative frequency at tk xk and then and these are, well these

are field operators not classical fields and then do the same with the positive frequency

parts e.

But now they are operators.

That is the only difference from the classical optics.