Let me describe first a one photon interference experiment.

The one photon source was the heralded one photon source that I described earlier.

Two lasers exactly tuned on

a two photon resonance excited calcium atoms in an atomic beam and

a gating scheme based on the detection of

the first photon allowed us to isolate one photon wave packets.

The interferometer with the size of about 50 x 40 centimeters

had mirrors and beam splitters flat to 1/100th of a micrometer.

This is the reason why they are so thick to avoid any deformation.

Sophisticated mounts allowed us to

change the path difference keeping the mirrors and beams splitter

apart to each other within a fraction of a wavelength over the whole surface.

The path difference was controlled within a small fraction of

a wavelength by the electric tension applied to the piezo-transducer.

We could keep it constant for a chosen duration and for

each path difference we would register the number of counts at D5 and D6.

The plots here show what we observed when we stayed only 0.1 second at

each value of delta L.

The mean total number of detected counts at each position is about 1.

So there is a broad spread of the results with many occurrences of 0 count.

The signal to noise ratio is not good enough to decide

unambiguously whether there is an interference pattern or not.

The second row of panels shows the results

for a waiting time of one second at each value of delta L.

You can now observe the clear modulation with a maximum value of about 20 counts.

Assuming a Gaussian random variable the theoretical standard deviation is

root of 20, that is to say about 4.5.

You can check that the statistical fluctuation around the maxima is of the order

of two times that standard deviation in agreement with the Gaussian model.

The third row, where the time spent is ten times larger shows

beautiful modulated signals with maxima of about 200 counts.

The theoretical standard deviation is 14 and you can check that the fluctuations

around the maxima are of the order of two times that standard deviation.

The visibility of the fringes is close to one, actually slightly more than 98%.

A remarkable value for a wide beam interferometer.

In the previous lesson,

I mention sources of one photon on demand.

Here is an example where a single molecule is addressed by

a confocal microscope allowing one to excite it and capture the re-emitted photon.

After expansion, the beam is sent onto a double prism

which deflects half the beam towards D1 and half the beam towards D2.

For a real one photon source detection happens either at D1 or at D2.

But there is no joint detection.

It is obviously possible to define the alpha parameter as in

the beam splitter case and the result of the measurement is α = 0.13.

A clear evidence of one Photon wave packets.

This is a source that I described at the end of section three and

the alpha parameter is the same with the double prism or with a beam splitter.

In fact this double prism is a device that was invented by

Fresnel to observe interference fringes in the overlap of the two beams.

At the time of Fresnel,

the fringes were observed with the naked eye behind an eye piece.

There was no electric bulb and the light was

sunlight concentrated onto a slit and collimated.

In this one photon interference experiment, one uses a CCD

camera that can detect a single photon and show the place of detection.

It is placed in the overlap of the two beams receiving the one photon

wave packets from the one photon source on demand just described.

The CCD camera allows

one to observe single photons arriving at various positions.

You can find the record of the signal as a document joined to this lesson.

Panel (a) shows the accumulated data after 20 seconds.

The 272 impacts of the photons seems to

be randomly spread over the surface of the CCD chip.

But after 200 seconds the 2240 photon-counts are clearly

concentrated on vertical bands which correspond to

bright fringes with the period of 0.12 millimeter.

After 2000 seconds, we have registered

almost 20000 counts and the interference pattern is yet more impressive.

Binning all the points of the same vertical line

we can plot the profile shown here in red dots.

The solid line is the result of the calculation describing

the experiment with only one fitting parameter the vertical scale.

But how can we calculate what happens with

one photon wave packets in that specific interferometer?

Do we need to embark again in

a lengthy quantum optics calculation

as the one we have just seen for the Mach–Zehnder interferometer?

The answer is fortunately no.

I am going to teach you now a very important result of

quantum optics for a one photon wave packet.

The probability of a single detection in

any optical device can be calculated with the classical model of light.

The rate of photodetection at each point is

proportional to the classical light intensity,

that is to say to what would have been calculated in the semi-classical model.

This is how we have obtained the solid line of

panel (d) using the classical model of propagation

of a beam with a transverse intensity profile

corresponding to what is collected by the microscope objective.

The only fitting parameter is a multiplying factor to adjust the vertical scale.