Another way in which physicists commonly prepare quantum states is by using partial reflectors as a way of placing a photon in a superposition of states at two different positions. Look out at night through any window in your house and you are essentially looking through a beam splitter. This is because you can see light coming through the window from the outside, but you will also be able to see a partial reflection of the light from your own indoor lights.
As shown in Figure 122, the beam splitters we will use are much more reflective than your windows. They allow 50% of the light to be transmitted, and reflect the other 50%. When a single photon encounters the beam splitter, it has a 50% probability of being transmitted and a 50% probability of being reflected.
Figure 122 A beam splitter divides a light beam in two. (a) A 50/50 beam splitter equally divides the incoming light intensity into a transmitted beam and a reflected beam. (b) When a single photon encounters the beam splitter, it has a 50% probability of being transmitted and a 50% probability of being reflected.
There are many different materials and optical assemblies that act as beam splitters. Not all of them behave in exactly the same way, so let’s take a look at the two best alternatives for our work. As shown in Figure 123, the simplest is a half-silvered or semireflecting mirror. This type of beam splitter, also known as a plate beam splitter, is simply a plate of glass with a very thin coating of aluminum or another metal of a thickness such that 50% of light incident at a 45° angle is transmitted, and the remainder is reflected. Pellicle beam splitters are an improved type of semireflecting mirror that is manufactured by stretching an extremely thin (e.g., 5-μm) polymer membrane over a flat metal frame. The extreme thinness eliminates secondary reflections by making them coincident with the original beam. These membranes are very delicate, but make the beam splitters useful over a very wide range of wavelengths. Stay away from “economy” beam splitters that polarize the output beams in an uncontrolled manner.
Figure 123 Different materials and optical components can be used to make beam splitters. (a) The simplest is a half-silvered mirror or plate beam splitter, which has the disadvantage of causing ghosting. (b) A pellicle beam splitter is the best choice to reduce ghosting and wavelength sensitivity, but it is very delicate. (c) Cube beam splitters comprise two right-angled prisms with a dielectric coating applied to the hypotenuse surface. Since there is only one reflecting surface in a cube, it inherently avoids ghost images. The nonpolarizing kind is ideal for our experiments at this point.
The other type of beam splitter useful for our experiments is a glass cube made from two triangular glass prisms glued together at their bases (Figure 123c). In cube beam splitters, the glue acts as a dielectric coating capable of reflecting and transmitting a portion of the incident beam. Since there is only one reflecting surface, this design inherently avoids the ghost images that occur with plate-type beam splitters. Please note that cube beam splitters come in polarizing and nonpolarizing versions. You want the nonpolarizing kind for the experiments.
As simple as it is, the beam splitter is a fascinating item to physicists interested in quantum mechanics. For starters, it provides us with the most direct evidence of the particle nature of photons. When we heard the clicks of single photons from a highly-attenuated laser beam striking our PMT probe (Figure 33), we could still claim that light generated by the laser or detected by the PMT comes as tight wavepackets that we call photons. Similarly, in the double-slit experiment with single photons (Figure 90), we could claim that the photon hits detected by the image intensifier were produced by wavepackets that divided at the double-slit slide and then recombined at the intensifier’s photocathode. As shown in Figure 124, however, a beam splitter clearly forces a choice on the direction that the photon must take. The resulting detection cannot be the result of recombination of the wavepacket. Only one of the PMTs detects each photon that is sent through the beam splitter. The photon never splits in two to cause detections on both PMTs simultaneously.
Figure 124 A single-photon beam-splitter experiment provides us with the most direct evidence of the particle nature of light. Photons are either transmitted through the beam splitter (a) or reflected by the beam splitter (b), but the photon’s wavepacket never splits in two to cause detections on both PMTs simultaneously.
To conduct this experiment, as shown in Figure 125, you will need two PMT probes (Figure 30) and two PMT processing circuits (Figure 34). Neutral-density filters attenuate the laser beam—just as we did before—to a level that ensures only one photon encounters the beam splitter at any single time. The beam splitter randomly allows photons to pass through (which from now on we’ll call “T” photons for “transmitted”) or reflects them (which from now on we’ll call “R” photons for “reflected”) with approximately 50%/50% probability. T and R photons are detected separately by PMT probes. As in the single-photon detection experiment of Figure 33, laser-line filters and washers with 1/4-in. openings filter out any stray photons that do not come directly from the laser. These are optional if the optical path from the attenuators to the PMTs is completely enclosed within light-tight optical tubes, as shown in Figure 125. However, they are absolutely required if you omit the light-tight tubes and instead build the apparatus inside a darkened box (with the laser outside the box).
Figure 125 We use this optical setup to demonstrate the particle nature of photons using a beam splitter.
We use three Veeder-Root A103-000 totalizer modules to tally the T, R, and coincidence counts. Figure 126 shows the simple AND gate (U1B) we use to detect coincidences. The T and R inputs connect directly to the discriminator outputs of the PMT amplifiers (Figure 34). We adjusted the pulse output width from each of the discriminators (R28) to be around 90 μs. We powered both PMT probes from the same low-ripple, high-voltage power supply.
Figure 126 We used low-cost totalizer modules to count photons detected by each of the photomultipliers, as well as to count coincidence events. These modules can count events at a rate of up to 10 kHz. They must be presented with pulses that are least 45-μs wide.
When you conduct this experiment, adjust the gain of the PMT probes to the same level, and the discriminator thresholds such that clicks are heard only when the laser is on. Reset the counters and run the experiment for a while. You should end up with around 50% of the counts in the T-photon counter, and the other approximately 50% in the R-photon counter. These won’t be exact, not only because of real-world differences in the components used on each leg, but because a random sequence will rarely divide a group exactly down the middle. You should expect the coincidence counts to be low, but you may nevertheless see some counts. These are produced by bunched photons that coincidentally pass through the attenuators at the same time, as well as the coincidental detection of a real photon by one PMT with a “dark count” (noise) by the other.
Coincidence counting is one of the most important techniques used in quantum and particle physics. Coincidence detectors are usually more complicated than the simple AND gate we used, because many experiments require tight control over the “window” during which events must be detected to consider them to be coincidental. In addition, when the window is tightened down to the nanosecond level, controlled delays must be introduced to equalize the timing of the detections. In any case, the analysis of coincidence events always requires a detailed look at statistics. Confidence in coincidence counting is always reduced by uncertainties associated with the statistical timing errors that may occur from the detection process, uncertainties in the electronics, slight changes in gain that skew the time of detection, as well as noise. Nevertheless, this simple coincidence counter should give you a good understanding of the basic concept behind this important technique.
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