S18_Single Photon Quantum Entanglement and Young's Double Slit Experiment

Photon Entanglement and Ghost Interference

Aliza Beverage and Meg Foster

Spring 2018

Abstract

The effects of quantum entanglement are observed through "ghost interference" which is accomplished using entangled photons produced in a BBO crystal. First, we proved that two down converted beams from this source are coincident. We then proved that our setup produces single photons, thereby ensuring the effects observed are quantum mechanical. Finally, we sent one beam through a Young's double slit hoping to observe "ghost interference," by observing an interference pattern in the other beam, but were not successful.

Introduction

One of the most striking features of quantum mechanics is entanglement. It is the basis for some of the most exciting new fields, such as quantum computing and quantum cryptography. While we have known about quantum entanglement for almost 100 years, the theory behind the nonlocal realism of entanglement is still far from understood. Many historical and modern experiments have embarked on quantum optics experiments to explore this aspect of entanglement. Specifically, Strekalov et al. (1995) conducted an experiment where they took two entangled photons and only sent photon 1 through a double slit. What they found was remarkable - even though photon 2 did not go through the slits, it still produced a diffraction pattern. This effect has been named "ghost interference,” where "ghost” refers to Einstein’s concern over ``spooky action at a distance” (Spalding 2016). Another remarkable result in Strekalov et al. (1995) was that the fringe width of the interference pattern was proportional to the distance photon 2 would have traveled had it back-tracked from the double slit, to the BBO, and then to detector B. Note that photon 2 does not even travel that much of a distance. The reason for this result has been largely debated, and the literature has not converged on a single description. In this study we hope to investigate and confirm the "backwards travel" distance accomplished by photon 2.

In order to confirm "backwards travel," we need to understand the wave-particle duality of single photons. One of the primary methods used to demonstrate this quality is Young’s double slit experiment. It shows that interference fringes are produced when spatially coherent light is sent through a double slit. Surprisingly, these fringes exist even when the light source is reduced to an intensity such that only one photon enters either slit at a time. This is quite remarkable, as it suggests that a single photon is capable of interfering with itself. Classically, it is counter intuitive that a single photon can be described as both wave-like and particle-like. It is this lack of intuition when it comes to quantum mechanics which makes the field so difficult to understand, but also greatly intriguing.

We attempt to recreate the experiment conducted by Strekalov et al. (1995). In order to do so, we need to create pairs of entangled photons through spontaneous parametric down-conversion (SPDC) using a non-linear Barium Borate (BBO) crystal. From here we will show that they are entangled by directing the two beams of entangled photons towards different detectors. We will then show that there is high coincidence between the beams. The next step is to prove that the experiment is in a quantum realm by demonstrating that we are observing single photons and not classical waves. Finally, we will evaluate the techniques outlined in Strekalov et al. (1995), Spalding et al. 2016, and papers thereafter to demonstrate ghost interference.

Theory and Setup

i) Showing entanglement

Demonstrating the entanglement of photons requires an understanding of Poisson statistics, electronic noise, and the existence of accidental detections.

Two key components of this experiment are 1) reducing the intensity of the 405nm, 85mW pump laser from around 10¹⁶ counts per second to less than 500,000 and 2) entangling the photons that come out of it. Both of these tasks are accomplished with a BBO crystal. This crystal takes a beam (in our case at a wavelength of 405nm) and through spontaneous parametric down conversion (SPDC), splits the beam of photons into two separate beams of entangled photons. The process of SPDC is extremely inefficient, meaning that only 1 in 10 billion of all of the original photons are split into entangled pairs. The rest of the light is simply transmitted through the crystal. Key to the process of entanglement are the laws of conservation of energy and momentum because the resulting beams, when added, must have the same energy and momentum as the original beam. The resulting entangled beams will leave the BBO in a conical shape of 3 degrees and have twice the wavelength (810nm) of the incident beam. At this point, the laser light will no longer be visible. The BBO has successfully accomplished the two necessary tasks: it significantly reduced the intensity of the laser light and simultaneously produced entangled photon pairs.

After leaving the BBO, the two photon beams travel down separate paths towards two single photon counting modules (SPCMs), A and B. If a detection is made in both A and B within a time window, τ_c, the event is considered a coincidence. When the rate of coincidence is larger than we expect according to Poissonian statistics, we can conclude that the BBO is producing entangled photons.

Given the low intensity of the entangled beams, and by using a time frame of 10 ns to define the coincident window, τ_c, we only expect to detect a coincidence for every 1000 photon pairs. However it remains possible that regardless of how small the window, accidental coincidence detections will occur as a result of thermal and electronic noise. The rate at which these accidental detections occur, R_acc, is dependent on the rate of detections made by detectors A and B and is also dependent on the size of τ_c. It is defined as the product of these three quantities Pearson et al. (2010),

Demonstrating an α greater than one will suggest that coincidences are happening at a higher rate than expected (given the setup) and that the two photon beams are entangled.

Apparatus

ii) Proving single photons

To show that we are indeed in the realm of quantum mechanics, this experiment will demonstrate the existence of single photons. To do this we will capitalize on the fact that when photons reach a beam splitter, they are either reflected or transmitted; not both. If we can prove single photons behave in this way, we can confirm that the experiment is purely quantum mechanical and cannot be explained classically.

We start with the setup in Figure 1 and alter it so that it looks like the schematic in Figure 2. Along path B a beam splitter is added along with a third detector, B’. When an entangled photon leaves the crystal and reaches detector A, we are guaranteed a photon at either detector B or B'. This is because these photons are completely correlated. This source at A is often called a ``heralded” single-photon source because its presence announces the arrival of the other (Pearson 2010).

To quantitatively prove that this is indeed the case, the anticorrelation parameter, α, is now derived using the fact that observing a photon at B or B' is conditioned on A. This increases the probabilities because knowing precisely when to look means we are

much more likely to detect an event. This leads to a decrease in the anticorrelation parameter. α is now defined as:

Since quantum mechanically one photon cannot possibly reach all three detectors at once, we expect the triple coincidence rate to be near zero. This again is not intuitive if we imagine the classical case: a laser beam that splits at the BBO, traveling as a wave, will reach A, B, and B' at the same time.

Accidental detections now effect our results via two mechanisms: Poissonian statistics and the other accidentals mentioned earlier. A Possionian distribution is given by the following function:

where x is a positive integer and RA is the mean rate of photons reaching the detector.

Poisson statistics describes the probability of rare events and in our experiment the photons exiting the BBO crystal are described in this way. For example, most of the time we expect zero photons at the individual detectors, occasionally one, but rarely two or more. Only for the case when two or more photons leave the BBO at the same time (in the direction of B) can we expect a detection at both B and B' within τ_c. Since there are truly two photons, it is likely that one could be transmitted to B, while the other is reflected to B'. In this case we would detect coincidences for photons that are not entangled. This effect will give the anti-correlation parameter a non-zero value.

By using A as a Heralding detector, and turning on B and B' only in response to a detection made by A, we effectively reduce the amount of accidental detections in A since it is not continuously looking for coincidences.

By detecting single photons, this experiment will allow us to determine whether we are truly in the classical realm. This will be verified if the value of α is much less than one.

iii) Ghost Interference

The purpose of this experiment is to observe ghost interference. This phenomena occurs when one of two entangled photons is diffracted through a double slit but both photons experience interference and produce a diffraction pattern. To see if this ``spooky" ghost phenomena is present in our experiment, a double slit is placed in front of detector A. When the beam of photons traveling toward detector A passes through the double slit, the second beam experiences a virtual double slit. Table 1 shows the experimental set-up parameters used. By fixing detector A, and replacing the detector B mount with a movable mount that scans detector B along a horizontal plane, we can monitor the coincident counts between A and B as a function of horizontal translation, x. The interference pattern obtained at detector B can be found in the data analysis section.

a is the slit separation, D_A and D_B represent the distance between the slit and detectors A and B respectively, and λ is the wavelength of the down-converted photon beams.

Figure above represents what we expect to see in this experiment. The coincidence should be near-zero in between fringes, however due to the fact that detector A will not be exactly centered on the central fringe and because accidentals detections will exist, the coincidences we expect between fringes will be nonzero. The ratio between the peak and the minimum will be calculated and reported as the ``visibility'' of the experiment.

Once we have the interference pattern created by the "virtual slit," we will use Equation 5 - Young's double slit equation of diffraction - along with the wavelength of the light and the distance between fringes, x, to determine the distance between the detector and the slit D

Results

The data analysis for this project is straightforward. For experiments i and ii, we used a LabVIEW code that computes the coincident rates and count rates for each detector, given by the equations in the theory and setup section. It continuously computes α and reports its average value for the entire run. For experiments i and ii, we took five 25 second runs at 4 different coincidence windows (10ns, 20ns, 40ns, 60ns). For the photon entanglement experiment we report the averaged results for low, intermediate, and high detection rates in Tables 2-4. For the single photon experiment we present the averaged low and high detection rates in Tables 5-6.

The first experiment proved to be successful in that our anti-correlation parameter, α, was much larger than one. We noticed in literature and during the experiment, that the rates in detectors A and B played a role in α. Lower rates produced a higher α regardless of the time window τ_c. This indicates that coincidences are more common when rates are low --something that we expected based on our understanding of Equation (2). The numerator grows linearly with photon intensity while the bottom grows by (roughly) the rate squared.

The single photon experiment also proved to be successful in that our alpha parameter was much lower than one indicating that triple coincidences were indeed rare. This result along with the previous experiment which demonstrated coincident detections between down converted photons, we were finally qualified to pursue the quantum realm by looking at the diffraction patterns of entangled photons.

For the interference experiment, we used a movable detector B, and record the coincidence rates between the fixed detector A and detector B, along with the position (in mm) of detector B [see Figure 5]. Since detector A is fixed at the largest fringe, when detector B is located at a secondary fringe, the coincidences observed will be much less than the coincidences when detector B is at the central fringe. This is simply due to the fact that the photon has a smaller probability that it will end up at the second fringe. Using Equation 5 and the parameters in Table 1 we predicted that a second peak should appear near 4mm.