s19spqi
Creating Correlated Single Photons
Steven Winship & Kai Petersen
University of Minnesota School of Physics and Astronomy
Introduction:
Modern optics experiments are often pushing into the realm of quantum mechanics, and creating single photon pairs is an important process in quantum optics. These pairs of photons can be used in many ways, including quantum computing, entanglement, quantum teleportation, and single photon quantum interference such as the Hong-Ou-Mandel effect. These photon pairs are called correlated photons, because they are created through a process known as spontaneous parametric down conversion (SPDC). In this experiment, we set out to prove that we could create single correlated photons. For a guide on how to begin optics experiments see the link at the bottom of the web page
When measuring photons, we must define what is considered to be 'simultaneous'. To measure anything our detectors must observe over a non-zero period of time. The observation time, also called the coincidence window because any two photons measured within one observation period are considered simultaneous and therefore a coincidence, is on the order of 10 nanoseconds and is called τc. Further complications arise when we consider the poissonian nature of photons. When travelling through space, the exact position of each photon is ill-defined, and instead of being a single point each photon exists as a poissonian probability density. This leads to an unexpectedly high rate of 'simultaneous' counts as the photons observed locations overlap causing false coincidental counts. These counts are called accidental counts.
Theory:
We created single, correlated photons using a beta-barium borate crystal (BBO). This is an optics instrument that consists of two non-linear dielectrics pressed against each other. The dielectrics and their orientation are manufactured in such a way as to facilitate the process of SPDC to create our correlated single photons from a 405 nm pump laser. SPDC is a process wherein a photon is absorbed by the crystals, and two photons are emitted. These photons have half the energy of the original one, therefore, by conservation of energy, our 405 nm photons are broken into 810 nm photons in this non-linear process. The down converted photons are then emitted on opposite sides of two cones so that momentum is conserved (Figure 1).
Figure 1: This shows the cone of possible outputs the correlated photons from SPDC take.
Each correlated photon is emitted on one of the two rings made by the cones such that
if the pair's momentum were added, the resulting vector would be along the red laser beam. [1]
In the case of our setup, these two cones have an angle of separation of 3o. We defined a parameter called the anti-correlation coefficient, α as:
[2]
There are three possible cases for this parameter:
(i) If Rcoincidence >> Raccidental then we have a value greater than 1. This means that our events are correlated, meaning that we get always detect photons on both detectors.
(ii) If Rcoincidence = Raccidental then we have a value equal to 1. This means that our events are not correlated, meaning that all we are detecting are the accidental counts caused by the poissonian noise inherent in our system.
(iii) If Rcoincidence << Raccidental then we have a value less than 1. This means that our events are anti-correlated, meaning that we never get counts at both detectors at the same time.
Our photons are created through a process called spontaneous parametric down conversion. This is a non-linear process facilitated by our BBO, which is itself a non-linear dielectric, in which a photon is absorbed by the crystal and two are emitted. Due to conservation of energy these photons have half the energy, and therefore double the wavelength, of our original photon. Because of this, we go from a 405 nm pump laser to two 810 nm photons. To put it simply, our photons go from one end of the visible spectrum, straight through the other and into the infrared. Because of this, we used a HeNe laser for much of the alignment (as talked about below).
Correlation Proof:
To prove that our photons were correlated, we had two detectors setup at opposite sides of the two cones coming from our BBO, and we calculated the anti-correlation coefficient between the two. We expected it to fall into the regime of case (i), because this would mean that our photons truly do exist as pairs travelling out from our BBO. We emphasize that these photons are not proven to be entangled, but correlated. To measure entanglement we would have had to measure the polarization, which we did not have the equipment or time to do.
Single Photon Proof:
To prove we had single photons, we added a beam splitter into the path of one of the photons and placed a third detector in this newly created path. This allowed us to calculate the anti-correlation coefficient between the three detectors instead of just two. If we have single photons, then we expect that when a photon reaches the beam splitter, then it would have to go either to detector B or C but cannot go to both, and so we expect the anti-correlation coefficient to fall into the regime of case (iii).
This could theoretically be done with only two detectors, however to beat the poissonian noise (which would cause detectors B and C to fall under case ii) we would have to greatly lower our laser's intensity. However, thermal noise caused by the detectors themselves would completely drown out this signal. Because of that, we instead used three detectors, and when we found a photon at detector A then and only then did we check for a coincidence between the other two. This is what allowed us to get an anti-correlation coefficient within case iii.
Apparatus:
We had a 405 nm pump laser mirror walked into a half-wave plate. The mirrors allowed us to fine-tune the adjustment of the laser, and the HWP allowed us to adjust the polarization such that it aligned with what the BBO preferred. The BBO was next, splitting the single beam path into two. There were then two 810 nm filters, one in front of each collimating lens. One of these filters had to be tilted significantly from being parallel with the lens face for reasons unknown. The collimated light was then fed through a fiber-optic cable, into a cage assembly, through another cable and into a single photon counting module. The signals from these modules were then fed through an FPGA which handled our data collection and analysis before sending data to our computer. A LabVIEW script was written by previous students to facilitate data collection.
Correlation Proof:
We setup a ruler roughly 40 inches away from the BBO that was perpendicular to the beam path (this was done by placing two screws into the optics table and using them to ensure the ruler was straight and perpendicular). We then placed one detector a few inches from the center and used the count of that detector to find a point on the cone of photons from the BBO. A second detector was then placed equidistant from the center, and then we used the coincidental count rates between the two detectors to ensure that the two were on opposite sides of their respective cones. The ruler allowed us to adjust the position without changing the distance from the BBO. In the case of the second detector, we also used the count rates, but only to ensure we were on the cone itself. Watching the count rates change as we moved the detector allowed us to get an idea of the size of the cone, and work along the outer edge of it. Steps taken from [3].
Single Photon Proof:
We placed a polarizing beam splitter in the path of the second detector and then put a third detector in the newly created path. Once again, coincidental counts were used to find the exact position required. A half wave plate was also utilized before the beam splitter, to ensure all the photons were going to our third detector, making the coincidental counts more apparent. We used a Helium Neon (HeNe) laser to mimic the path of the infrared photons to aid with alignment. This was done using, at first, an extra collimating lens that then was connected to the collimating lens of a detector so that the light from the HeNe went back towards the BBO. A pick-off mirror was then placed in front of the BBO, and another to reflect the light back into the HeNe. We then removed the extra lens, and allowed the light from the HeNe to be reflected off of the two mirrors and into the collimator. This allowed us to accurately place our beam splitter. Steps taken from [3]
Results:
The data below conclusively proves that we had both single and correlated photons. The anti-correlation coefficient in the first table is much larger than 1, meaning that we are in the field of the first case discussed above and therefore proving correlation. Meanwhile the data in the second shows an anti-correlation coefficient less than 1, meaning we fall into case three, anti-correlation. This is exactly what we were looking for, as discussed previously. This means we have single correlated photons. There are however some discrepancies between our values and those of Pearson and Jackson (the sources of the 'accepted values'). For the correlation proof, we attenuated our laser more than they did. This causes a drop in the count rates at both detectors and a drop in the accidental count rate as they are proportional to one another. This in turn increases our anti-correlation coefficient above the value of Pearson and Jackson's as the anti-correlation coefficient is inversely proportional to the accidental count rate. The single photon discrepancies however, are more nuanced. Part of the difference can be accounted for by the same difference in attenuation, as seen by the difference in our count rates at A, as seen in table 3. However, we experienced a strange phenomenon wherein our counts at detectors B and C were significantly lower than half the counts at A, or even half the counts that we received at B during the correlation proof. There are a plethora of reasons that this could occur, including accidental and unaccounted for adjustments to some alignment, imperfect alignment of the beam splitter caused by the HeNe laser not being perfectly mimicking the infrared path, and likely more that we can not account for. Despite this, our data still conclusively shows that we were observing single photons.
Conclusion:
This method of creating single, correlated photons using a beta-barium borate crystal to facilitate spontaneous parametric down conversion is a useful, but non-trivial process with many applications. Having conclusively proven correlated photons, we would like to set out to demonstrate some quantum mechanical interference effects such as the Hong-Ou-Mandel effect first demonstrated in 1987 or the Hardy's test. We also recommend further study into the reasoning behind tilting the A detector's 810 nm filter. While we believe that a co-linear BBO used to replace the 3o separation BBO should make the experiments much easier to do, we did not have time to construct a working setup with this new crystal, and so also recommend future experiments studying it.
References:
These experiments were based on those outlined in Pearson and Jackson's Paper "A hands-on introduction to single photons and quantum mechanics for undergraduates " [2]
[1] “Spontaneous Parametric down-Conversion.” Wikipedia, Wikimedia Foundation, 16 Mar. 2019, en.wikipedia.org/wiki/Spontaneous_parametric_down-conversion.
[2] Pearson, Brett J. “A Hands-on Introduction to Single Photons and Quantum Mechanics for Undergraduates.” Am. J. Phys., by David P. Jackson, vol. 78, no. 5, May 2010, pp. 471–484.
[3] King, Brendan, and Kevin Booth. “Single Photon Quantum Interference Lab.” Google Sites, 2016, sites.google.com/a/umn.edu/mxp/advanced-experiments/SPQI.