Coherent interference at a low photon flux rate

[tistemfnp]

Homework Statement

A laser with a power of 2mW and a sufficiently large coherence length is split into two paths using a 50/50 splitter.

Path 1 directly enters a 2:2 50/50 coupler. Path B includes a 10m delay line, followed by an attenuator, and then connects to the same 50/50 coupler.

In a preparatory step, path 1 is disconnected from the coupler. Photon counters are connected to both outputs of the coupler. The sample rate is set at 100 MHz. The attenuator is adjusted so that, on average, the photon counter detects 10 photons per 10,000 samples per photon counter.

Question 1: Are the statistics governing these detection events consistent with a Poisson distribution? (Let's assume that the dark count rate is nearly zero.)

After the adjustment, both photon counters are disconnected. The outputs of the 2:2 coupler are now linked to a balanced detector. Path 1 is reconnected. Since both paths originate from a single source, they interfere.

Question 2: Does interference only occur in time bins where the photon counters (if they were still connected) would detect a photon? Or does interference occur in all time bins? Please elaborate.

(The primary concern I'd like to address is that when a low photon flux rate results in interference, and fractional portions of photon energy are detected within each time bin, this description no longer aligns with the concept of photons as indivisible entities according to Quantum Mechanics. In practice, the indivisibility of photons appears to be compromised.)

Relevant Equations

detection ~ N1 + sqrt(N1xN2) + N2

(Attempted answer:)

Question 1: Yes, the detection events follow a Poisson distribution.

Question 2: Yes, interference phenomena are clearly observed across all time bins even in the regime of much less than one photon per bin (N2 per bin << 1), which implies that the detection of supposedly "quantized" energy is distributed over time intervals, refuting the notion of strict quantization. As quantization stands synonym for the existence of photons -> there are no photons.

 

[mfb]

Does interference only occur in time bins where the photon counters (if they were still connected) would detect a photon?

These time bins are not physical constants that would be unchanged independent of the setup. Trying to "identify them" in the other setup is meaningless.

You get interference in every time bin although it will be negligible (won't change your photon count) in most.

which implies that the detection of supposedly "quantized" energy is distributed over time intervals, refuting the notion of strict quantization.

It does not. The photon detection is always quantized - you'll never measure 5.6 photons.

there are no photons

This is obviously wrong.

 

[tistemfnp]

When I refer to time bins I mean it statistically. Statistically it is of course valid to ask, if interference occurs at all time bins or if it only occurs (statistically) at time bins where (or better when) a photon counter would indicate a detection.

The detection is quantized, but the field is not:


So when it comes to interference, the fields of both inputs of the coupler add at each output (half of them) before a detection takes place. As the sum is detected and the energy per time bin is known, it can be shown, that fractions of energy of a photon are detected in the path where the photon flux is attenuated (a part of the overall detection of the interference). It then doesn't make sense to talk of quantization here.

 

[mfb]

The detection is quantized, but the field is not:

The overall energy in the field is quantized. The amplitude at a given point is not (and no one claimed so).

it can be shown, that fractions of energy of a photon are detected in the path where the photon flux is attenuated

No, you never detect fractions of a photon. That's not a thing. The detection is a number of photons, which is always an integer. That (and only that) is what it means for the electromagnetic field to be quantized.