Single Photon Detection Experiment

## Coincidences and the Anti-Correlation Parameter

Prior to the twentieth century, light was indisputably thought of as a wave; the possibility of it possessing a particle nature was rarely considered. In 1922, however, Einstein’s interpretation of the photoelectric effect changed all that when he brought the particle nature of light into the realm of possibility. Even though it has recently been proven that the photoelectric effect can be interpreted classically (or at least semi-classically) in non-particle, wavelike terms, Einstein’s interpretation questioned the purely wave-like nature of light. Physicists continued in Einstein’s footsteps, searching for experiments that would provide more concrete evidence for the existence of quantized light particles, or photons. The key to designing such an experiment is the concept of coincidence counting (for more information on our coincidence counting equipment, see the coincidence counting page).

Coincidence counting experiments rely on the most intrinsic quality of “particleness” for verifying the existence of photons: if we are dealing with an individual particle, we are dealing with an object that has a definite location in space. A particle will exist in one location or another, but never multiple locations at once. Thus, if we configure two detectors separated by a reasonable distance along the same plane and shine a light source consisting of single photons in their general direction, the two detectors should never “click” at the same time. If we find a photon at one detector, we should never find a photon at the other detector at the same time if we are dealing with a source that consists of individually existing particles. The case in which we do find a photon at each detector at the same time is known as a coincidence [1].

The basic idea is to send light through a beam splitter, and align two detectors in the paths of the two split beams. We then measure the number of coincidence counts between the two detectors relative to each detector’s individual number of recorded counts. Using these three parameters (detector 1 counts, detector 2 counts, and number of coincidences) we construct what is known as the anti-correlation parameter, a quantity that should have a value of zero if we are dealing with single photons:

(1)
\begin{align} A = {N _c \over {N_1 N_2}} \left(TPE \right) = {N _c \over {N_1 N_2}} \left({T \over {\Delta t}} \right) \end{align}

Here A is our anti-correlation parameter , Nc is the number of coincidences counted in a run, N1 is the number of counts from detector 1, N2 is the number of counts from detector 2, TPE is the total possible number of events we can measure in any series of measurements. In this case, our total possible number of events is equal to T, the total time duration of the run, divided by delta t, the pulse width of our detectors. Thus, if we really have single photons, the light should only be able to travel along one of the split beams at a time. We should therefore have no coincidences and Nc should be zero, making our anticorrelation parameter zero. If light is purely wave-like, i.e. randomly distributed over space, there should be a high chance that the light travels along both of the split beams at once, and we should get coincidences. This would mean a non-zero anti-correlation parameter; in fact, it can be easily proven that we should get an anti-correlation parameter of one [1].

## Experiment with HeNe laser

We first performed this test using a standard HeNe light source aimed at our beam splitter:

with the following results:

We thus find that using the HeNe laser as a light source in our experiment results in an anti-correlation parameter very close to 1, suggesting that this light is a classical wave. Why did we not receive an anti-correlation parameter of zero, suggesting that we have single photons? Ultimately the problem with the HeNe laser is that even if the laser light does consist of photons, it exists in a superposition of photon number states, and it is thus unclear that there are actually single photons. What we need to suggest that single photons do actually exist is a light source that consistently produces light that exists in a single photon number state.

## Experiment with Down Converted Light

We can produce just such a source through a process known as spontaneous parametric down conversion (see the down converted light page). Starting with a powerful light source, of much lower wavelength than the HeNe (~405nm), this process splits the initial beam (or pump) into two light cones (the signal and idler). This process is different from using a beam splitter because it involves the splitting of one photon into two through a BBO crystal, and must obey conservation of energy and momentum [2]. As a result, the two light cones should each have twice the wavelength of the pump (~810nm) and they should be separated by an angle of three degrees in either direction from the propagation direction of the pump:

By exploiting the non-local, quantum connection between the two cones of light, we can make a detection on one of the beams, marking it as existing in a single photon state (i.e. our detection collapses the light from a superposition state to a single photon state), and then we know that our other beam must exist in the same state. We can then take this other beam, which we now believe consists of single photons, and send it through our same beam splitter setup as we used for the HeNe and observe what our resultant anti-correlation parameter is. The following shows the experimental setup for our down converted light:

and here is the data for our anti-correlation measurements:

As you can see, the majority of our g(2) counts, 1 per second for 120 seconds, are exactly zero and there are a few non-zero counts but even they are extremely low, nowhere near the value of around 1 we were getting with the HeNe laser. Because the anti-correlation parameter we obtain using the down converted light is so precisely zero for the majority of our measurements, we conclude that the down converted light is indeed a source of single photons [3].

## Follow up notes on our g(2) parameter in the experiment with down converted light

It is important to note that in our second experiment, we were measuring coincidences between three detectors: A (detector making initial measurement on bottom beam in figure 4), B (detector on other side of beam splitter parallel to top beam in figure 4), and B' (detector on other side of beam splitter perpendicular to top beam in figure 4). Our anti-correlation parameter thus looks slightly different when we take into account three-fold coincidences:

(2)
\begin{align} A = {N _{ABB'} \over {N_{AB} N _{AB'}}} \left({N_A} \right) \end{align}

Here, NABB' is the number of coincidences between all three detectors, NAB is the number of coincidences between A and B detector, NAB' is the number of coincidences between A and B' detector, and NA is the number of counts in A detector. The reason we never deal with single counts in B or B' is because we are only concerned with the light that exists in the same state as A. That is, we want to see that the light in the top beam coinciding with the light in the bottom beam (when we have coincidences between the two beams) will be in the same single photon state that we believe we collapse the bottom beam into. For a more complete derivation of this forumula, go here.

What is important about this updated g(2) calculation is that it depends explicitly on the number of counts we detect in A detector, and therefore also depends on the pulse width even though this dependence is not present in the formula. We expect our g(2) measurement to thus be proportional to both of these factors. To verify this we took g(2) measurements while first varying our pulse width and keeping our A counts constant, and then varying our A counts (using a filter) and keeping our pulse width constant. The results of this experiment are shown below, revealing that the g(2) does indeed have a linear dependence on both factors:

We thus conclude that the measurements we made using the g(2) parameter in our experiment with down converted light are consistent with the theoretical calculation of the anti-correlation parameter for three-fold coincidences.

References
1. Greenstein and Zajonc. The Quantum Challenge. Jones and Bartlett Publishers: Massachusetts. (2006).
2. J.J. Thorn, M.S. Neel, V.W. Donato, G.S. Bergreen, R.E. Davies, and M. Beck, "Observing the quantum behavior of light in an undergraduate laboratory," Am. J. Phys. 72 (9): 1210-1219 (September 2004)
3. Galvez E.J., C. H. Holbrow, M. J. Pysher, J. W. Martin, N. Courtemanche, L. Heilig, and J. Spencer, “Interference with correlated photons: Five quantum mechanics experiments for undergraduates,” Am. J. Phys. 73 (2): 127-140 (February 2005)
page revision: 30, last edited: 01 May 2009 19:06