We haven't finished what I wanted to finish at the last lecture, namely that was about

the Hanbury Brown Twist experiment and bunching and super bunching.

And anti-bunching, sorry.

As I showed you at the last lecture, the method to investigate the second order correlation

function which is a characteristic of intensity correlations is to split a beam on a beam

splitter, ideally 50% beam splitter, but I don't remember if we discuss it or not, but

we will definitely discuss it in the further.

It doesn't really matter much whether the reflectivity and transmissivity of the beam

splitter are equal or not, but it just makes the experiment more convenient if you know

what I mean.

So here are two detectors and as I said there are three ways to process the data.

Either you take photo currents from the detectors and multiply them and average.

The recipe is here, photo current 1, photo current 2, average and divide it by mean value

of I1 and I2.

Or you register coincidences, detectors give you clicks when they receive photons, you

register the number of clicks.

So what I show here is a correlator, coincidence circuit.

So the third way is you do the same but instead of photo currents you have single pulses which

is just photo current is unity or zero which is basically the same.

So this is the measurement of second order correlation function.

The reason why I said it doesn't matter whether the transmissivity and reflectivity are the

same is because you assume that the photo current 1 is basically the transmission of

the beam splitter times some other parameter because t is dimensionless and I'm going to

write here the intensity of the input light but of course there is some dimensional parameter.

Let's call it some x for instance and I2 is some y times r times intensity and then if

you plug it in this formula you will have both in the numerator and in the denominator

this x t y r.

So you can write it as intensity squared mean value divided by mean value of intensity squared.

It doesn't matter what t and r.

Of course you can also change it to intensity at r1 t1 intensity at r2 t2 and here intensity

just mean value squared because we assume that we assume that everything is stationary

and uniform so it doesn't matter the mean value is measured at what point and at what

time moment but now it becomes a function of it becomes a function of the coordinate

difference r1 minus r2 rho and t1 minus t2 which is tau.

So I more or less repeated you the same things I was telling you in the previous lectures

but now let's consider what happens if you for instance measure g2 as a function of tau

and you change this tau you change the delay between two the time moments where you measure

the intensities the easiest way as I probably mentioned is to put this delay electronically

into one of the outputs and as we derived for coherent light you will get a value of

one regardless of the delay so for coherent light you get this and then for thermal light

and this was home task by the way to calculate the value here and it will be two so for thermal

light this value exactly this value is going to be a two and then from some even simple

considerations that if you make this delay very very large larger than anything in your

in your experiment it will eventually go to one so somewhere it will decay right and how

it will decay is governed by the zigart relation which I wrote that g2 for thermal light so

it only relate to thermal light g2 is one plus as a function of tau actually it is more

general it's g2 always so I can write here rho and tau both so for thermal light g2 is

one plus squared g1 also of course of rho and tau squared yeah so rho is a vector and

so we see here already we see the recipe how to how it decays at what typical times it

decays and this typical time is the time of decay of g1 and this time of decay of g1 is