# The Validity of the Data Set of the Elitzur-Vaidman Quantum Bomb Tester Experiment

In the shown data set of the experimental realization of the Elitzur-Vaidman quantum bomb tester, at least the one published in Physical Review Letters and written by Kwiat et al., there is a set of points that show the photon counts at a detector that should receive no photons due to destructive interference that does show photon counts, some points even suggesting photon counts into the hundreds. Is this normal and to be expected of experiments dealing with such sensitive equipment and is the set of points representing this null result still valid? Furthermore, the experiment shows that only around 4,000 photons were detected per 5-second trial, which seems to be extremely few, even for usual SPDC efficiencies. Is this normal for experiments using older (1995) and/or less efficient SPDC methods? I understand that this question is extremely specific, but it would mean a lot if someone could inform me. Below are pictures of the data set and the experimental setup:

The data points you are asking about (labelled "C(Dark), no object" in the legend) correspond to photon detections in the dark port of the Michelson interferometer used in the experiment. Measuring the data points in the figure we see that, as you said, the detected photon coincidences in this port range from around 150 to 300 per 5s integration interval.

To know if this is little or a lot we need to put it in relation to the photon counts in the other port. Unfortunately the authors don't measure the photon rate in the bright port (same as the input port) of the interferometer, but we can infer the photon rate from the "Obj" port. We can assume that the beam-splitter of the interferometer has a splitting ratio of 50%, and the reflectivity of the object is stated to be 43% in the figure. Therefore, $$0.5\cdot0.43 = 21.5\%$$ of the input photons should be expected to reach the Obj port.

Measuring "C(Obj), with object" in the figure I found the coincidence rate to be about 2300 counts per 5s, and we can infer that the total input rate was $$2300 / 0.215 \approx 10700$$. We can now calculate the visibility of the interferometer as

$$V = \frac{C_{\mathrm{max}} - C_{\mathrm{min}}}{C_{\mathrm{max}} + C_{\mathrm{min}}} = \frac{10700 - 225}{10700 + 225} \approx 96\%$$

Here I used the average $$(150+300)/2 = 225$$ as the count rate for the dark port.

So, is this number any good? It depends on the context. In this experiment the authors were essentially trying to show the existence of the interference effect. If you plot a sine curve with a visibility of 96% it looks like this:

As you can see, this level of visibility is clearly enough to show the interference effect. What affects the visibility? It's primarily the fact that the fact that the photons don't overlap perfectly on the beam-splitter. The photons have some transverse profile, for example a $$\mathrm{TEM}_{00}$$ mode, and in order for full destructive inteference to occur these two spatial modes must 1) be identical and 2) overlap perfectly. The authors could have dedicated more effort and resources to increasing the level interference, but the question is if this would have qualitatively changed the result. My answer is that it wouldn't have, because the quality of the interference is already good enough that we clearly see the difference between it being there and not. Because the authors didn't use a fully opaque object in the beam path the effect is not as dramatic as it could have been, but it is still unambiguous.

For your second question, the photon counts were not abnormally low. Again, we established that the total two-photon event rate was somewhere around 11000 / 5s. We can compare this to other papers published around the same time, such as New High-Intensity Source of Polarization-Entangled Photon Pairs and Ultra-bright source of polarization-entangled photons. These achieved 10000 / 200s (250 / 5s) and 15000 / 10s (3000 / 5s), respectively. To be fair, these were sources of entangled photon pairs, whereas the one in the experiment you cite generated separable photons. It is also worth remarking that the absolute photon rate from a down-conversion photon source is not a particularly useful metric, since it does not quantify the purity (quality) of the single photons, and also depends on the power of the pump laser used.

• Thank you for your in-depth and full-coverage answer. Just for curiosity's sake, how difficult is it to reach that 100% interference mark (or as close to it as possible)? Aug 30, 2023 at 2:09
• Often you would classify this in terms of the extinction ratio; the optical power in the dark port divided by the power in the bright port, measure in dB. A ratio of -30dB, or 1:1000, is achievable with standard optical components. To reach -40dB you will need to be more careful and perhaps used specialized components, as even say a small mismatch in the reflectivities of your mirrors would degrade the interference (the optical power in both arms of the interferometer needs to be equal, otherwise the two beams can't fully destructively interfere). Aug 30, 2023 at 8:42
• For higher extinction ratios than that you would typically need to use integrated photonics rather than bulk optics. There you can find examples of interferometers with extinction ratios of up to at least -70dB, or 1:10,000,000. Aug 30, 2023 at 8:42