Video recording true single-photon double-slit interference
Reuben S. Aspden and Miles J. Padgett∗ SUPA, Department of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom
Gabriel C. Spalding Department of Physics, Illinois Wesleyan University, Bloomington, IL 61701, United States (QuantIC Collaboration) (Dated: March 16, 2016) As normally used, no commercially available camera has a low-enough dark noise to directly produce video recordings of double-slit interference at the photon-by-photon level, because readout noise significantly contaminates or overwhelms the signal. In this work, noise levels are significantly reduced by turning on the camera only when the presence of a photon has been heralded by the arrival, at an independent detector, of a time-correlated photon produced via parametric down- conversion. This triggering scheme provides the improvement required for direct video imaging of Young’s double-slit experiment with single photons, allowing clarified versions of this foundational demonstration. Further, we introduce variations on this experiment aimed at promoting discussion of the role spatial coherence plays in such a measurement. We also emphasize complementary aspects of single-photon measurement, where imaging yields (transverse) position information, while diffrac- tion yields the transverse momentum, and highlight the roles of transverse position and momentum correlations between down-converted photons, including examples of “ghost” imaging and diffrac- tion. The videos can be accessed at http://sun.iwu.edu/~gspaldin/SinglePhotonVideos.html online.
I. INTRODUCTION tions, and is rooted in an inherent uncertainty associated with the particle itself. To a great many, the word photon brings to mind a In terms of the philosophical debate, rather than the picture of a particle-like ball (or, perhaps, a ray that de- “which slit” question it is the mechanism by which the scribes the ball’s trajectory). Such a photon cannot exist. extended photon wavefunction is collapsed (or projected) Yet these notions are so widespread that they have led to into a specific location in any one of the many sinusoidal suggestions that physicists ought to receive special train- far-field fringes that is most contentious (the “measure- ing and a license before being allowed to use the word ment problem of quantum mechanics”). Whereas Ein- “photon.”1 Such training would undoubtedly center upon stein raised3 key questions about the outcome of such an discussion of Young’s double slit experiment, which falls experiment, i.e. whether or not “hidden variables” con- into a small class of experiments that have a special place tained information about which fringe the photon would in both the history and development of physics. Generi- be observed in, the mainstream contemporary interpreta- cally, illumination of a double slit with spatially coherent tion is that the outcome remains a probabilistic distribu- light (usually an expanded laser beam) creates sinusoidal tion until (at least) the moment of irreversible interaction fringes in the far field. These fringes persist even when with the detector.4 Yet this notion that a single-photon the illumination light source is reduced in intensity such event remains indefinitely in a superposition of different that no more than one photon is present within the re- fringes until the moment of detection presents challenges gion of the slits at any time, providing the archetypal to our conventional understanding. In the case to be example of single-particle interference and wave-particle presented here, using spatially separated detectors for duality. an entangled pair of photons, the nature of wavefunction collapse becomes even more interesting to consider, as the arXiv:1602.05987v2 [quant-ph] 15 Mar 2016 As enshrined in the uncertainty principle, duality is characterized by an intrinsic incompatibility of simul- consequences of this collapse can be taken, incorrectly, to taneously defined position and momentum for a single imply a nonlocal cause and effect! particle. Whereas knowledge of which slit the photon Despite the central conceptual role in modern physics is transmitted through defines the photon’s transverse that is played by single-photon interference, there have position in the plane of the slits, knowledge of the pho- been few visualizations of actual data presented for ton’s position in the far field (i.e., within the interfer- Young’s double-slit interference experiment. Indeed, ence pattern) gives its transverse momentum. However, none of these previous examples have included direct physically configuring the experiment in such a way as 2D video imaging of the distribution of single-photon to provide knowledge of which slit the photon passes detection events. The videos supplementing this arti- through prevents observation of an interference pattern.2 cle, which are intended for classroom use, aim to address The mainstream contemporary interpretation of quan- this need, and can be found at
No. of photons=19 No. of photons=203 No. of photons=5067
Increasing no. of photons source Reduced coherence
No. of photons=304 No. of photons=1921 No. of photons=494067
FIG. 1. Sample frames illustrating single-photon double-slit diffraction. The sequence along the top is for a case where spatial coherence has been experimentally enhanced, by only accepting photons associated with a single mode, as discussed in the text. For comparison, the multi-modal case is shown at bottom.
It is essential that compelling experimental data be made available for the purpose of introducing students to foundational phenomena, especially when those phe- nomena differ markedly from expectations based upon common experience, as is often the case with quantum physics. Quantum Physics is one of the conceptual pil- lars of the physics curriculum, and is the required frame- work for understanding (and teaching) a broad range of FIG. 2. Down-conversion: ~ωpump = ~ω1 + ~ω2. A single topics. For example, Intel has released chipsets based 355 nm photon can be absorbed and re-emitted as a pair of upon 14 nm components, and is in pre-production of quantum mechanically entangled photons, each with wave- 10 nm-linewidth designs; at such scales, classical rules length 710 nm, chosen because it is the wavelength of peak of conduction are superseded, and so any student think- quantum efficiency for the detectors used. However, even if ing of becoming an electrical engineer should be intro- pump beam is well collimated, the output is not. duced, at some level, to quantum principles. Similarly, teaching Materials Physics often requires establishing a foundational understanding of basic quantum mechan- II. CORRELATED PHOTONS ics. Students are fascinated by the potential for quantum technologies to enable secure transmission of data (quan- In this paper, critical use is made of pairs of photons tum encryption), and to revolutionize computing archi- that are produced by parametric down-conversion within tectures (quantum computing). Connections to such ar- β-barium borate crystals (hereafter “BBO”). There are a eas of opportunity can motivate student engagement, but number of introductions to downconversion,5,6 but here abstract formalism and simulation are not, alone, suffi- we highlight several constraints placed upon the down- cient: pedagogical discussions about experimental obser- conversion process. First, down-conversion replaces one vations can help to assure students that the dialog is well photon with two new photons. The energies of the emit- grounded. ted pair of photons must, according conservation of en- ergy, add up to the energy of the incident pump pho- ton: ~ωpump = ~ω1 + ~ω2. This implies that the pair of photons must have been emitted from the same spatial position within the crystal where the first photon is ab- sorbed. Moreover, the momenta of the emitted pair of 3 photons must add up to the momentum of the incident photon. These constraints upon position and momentum might seem to challenge the uncertainty principle which, Imaging/ as noted above, states that position and momentum can- diffraction not be simultaneously well-defined for any single photon. lenses However, because the conservation principles only con- Heralding detector strain the summed properties of the two down-converted ICCD camera Delay line photons, they cannot be described individually, but only Double as an “entangled” two-particle wavefunction. For exam- slit ple, though the fact that the sum of their momenta is BBO crystal fixed means that their transverse momenta must add to zero, the momentum of each individual photon is not de- fined; the two-particle wavefunction itself contains a su- perposition of individual momentum values for each pho- FIG. 3. Simplified schematic. Following a beamsplitter, two ton. In a similar fashion, properties such as the energy, collection arms can detect the correlated photons emerging angular momentum, and polarization of each individual from the BBO crystal. The signal-to-noise ratio is improved photon in the pair can be engineered, depending upon by using the heralding detector to only trigger the time-gated the experimental design, to have no definite values until intensified CCD (ICCD) camera when a time-correlated pho- a measurement is made.7,8 (Entanglement persists over ton is due to arrive. The two slits used here were each 100 mi- the length scales probed by our experiments.9,10) crons wide, with a center-to-center separation of 500 microns. While the two well-defined rays sketched in Fig. 2 might suggest that the down-converted photons should emerge at well-defined angles, experiments show that mode optical fiber to limit what light makes it into the light emitted from the down-conversion process always heralding detector, and exploit the fact that the camera has an angular range. In our experiment, the light emit- will only detect down-converted photons that are highly ted at ω1 and the light emitted at ω2 are essentially correlated with those detected by the heralding detector: collinear, but there remains a spread in the angular dis- essentially, it is as if the slits were being illuminated by tribution that arises due to geometric effects associated a single-mode source. with the length of the down-conversion crystal.11 (For Some further details of this experimental apparatus the experiments shown here, we used a 3 mm thick BBO may be of interest. In our experiment we use type- crystal.) Because the light spreads more quickly than I spontaneous parametric downconversion (SPDC) in a would be the case for a Gaussian mode, the BBO crystal collinear regime, which is why we require a beamsplit- must be considered a multi-modal source. However, as ter to separate the output photons. This separation oc- demonstrated below, production of an interference pat- curs in a probabilistic manner: separation efficiency at tern with high-contrast fringes requires the high degree of the beamsplitter is only 50%. However, as this loss is spatial coherence associated with a single-mode source. before the photons interact with the object it does not affect the heralding efficiency of the system. The down- converted photon pairs are separated from the remain- III. EXPERIMENTAL SETUP ing pump beam after the BBO crystal by use of a “cold mirror,” which is the term used for a standard, commer- Fig. 3, illustrating our basic experimental approach, cially available dielectric mirror that reflects short wave- features a pump laser at far right, followed by the BBO lengths while very efficiently transmitting infrared wave- crystal, from which we extract down-converted photon lengths. The reflected pump beam was sent to a beam pairs (and block any transmitted light at the pump fre- dump, while the transmitted light was filtered by a 10 nm quency). The time-gated, intensified CCD (ICCD) cam- bandwidth high transmission interference filter centered era at far left is capable of detecting the down-converted on 710 nm to ensure that only the down-converted pho- photons but, to reduce noise, needs to be time gated: tons are present in our system. The slits used here were that’s the purpose of the beamsplitter and the heralding 100 microns wide, with a center-to-center separation of arm. The camera will only record data in those instances 500 microns. The heralding detector we have used is a where one photon takes the path to the heralding detec- fiber-coupled single-pixel, single-photon avalanche diode tor, which provides the trigger signal to the camera’s (“SPAD”) with quantum efficiency at 710 nm of approx- gate, while the other member of the down-converted pair imately 65%. Detection of a photon produces a short goes on to be detected by the camera. Along the way to (15 ns) TTL pulse that is used to trigger the camera. An the camera, this photon encounters the slits. In order to optical delay line added to the camera arm compensates produce a high-contrast interference pattern, there needs for the electronic delay associated with this triggering. to be some workaround for the fact that the BBO crys- Measured dark-count rates for this SPAD were roughly tal is a multi-modal source, and so lacks the required 100 per second, but these would normally only result in degree of spatial coherence. The key is to use a single- a blank image at the camera. Crucially, the gating time 4 on the camera is limited to a 5 ns coincidence window, so the contribution of noise from the camera photocathode Vertical cross sections is also minimal. The photon flux used for this experiment Young's double slit was such that the camera detects only the single, corre- Coherent source lated photon in each coincidence window. The signals 180 from multiple coincidence windows can be accumulated on the CCD chip over a longer exposure period before 120 the frame is read out. Individual frames may therefore
contain multiple photon events, although the accumu- Photons 60 lation time was always such that there was statistically much less than one photon per pixel in any frame. For 0 presentation purposes, during post-processing the videos 650 2600 4550 6500 x distance (µm) have been recompiled such that the photon arrival rate increases exponentially as the video progresses. Partially coherent source Except for the camera, which is an (Andor iStar gen 1600 III) intensified CCD, hundreds of institutions already 1200 have all of the elements of the set-up shown, in under- graduate instructional labs. For example, educationally 800 priced SPADs are available from the Advanced Labora- Photons 400 tory Physics Association (ALPhA).12 Regardless, any in- stitution may make use of the video data provided with 0 650 2600 4550 6500 this article. x distance (µm) As possible extensions of this work, we note that it is possible to perform similar studies, with compromised FIG. 4. Top: Diffraction pattern for a case where spatial co- spatial resolution and loss of 2D information, by using herence has been experimentally enhanced, by only accepting multiple SPADs arrayed along a line rather than a two- photons associated with a single mode. For comparison, the dimensional ICCD camera.13 Such experiments could multi-modal case is shown at bottom. (Insets show the full be performed even more affordably by using a single, 2D datasets.) scanning-fiber detector in place of the ICCD camera. However, when using a scanning detector, each image would have to be built up from exposures taken with the gle photons passing through the slits. Again, without detector in N different locations, yielding N distinct pix- such heralding, the readout noise associated with any els in the reconstructed image. The detection efficiency of commercially available camera would significantly cor- the imaging system would fundamentally be limited to a rupt or completely swamp the single-photon signal of maximum of 1/N, thus increasing the collection time by a interest.19,20 factor of N. Here, this limitation is overcome by replacing The optics following the BBO crystal re-images the the scanning detector by a two-dimensional ICCD cam- down-converted light onto the double slits. So, when the era, thereby detecting all photons irrespective of their camera is located in an image plane of the BBO crystal position within the image, an approach which opens up (as is the case when using the optics represented by the many opportunities.14,15 All of this begs the question: lenses shown in orange in Fig. 3) we capture an image, what is the minimum number of photons required to form one photon at time, of the slits, rather than the inter- an image? With conventional cameras, of order 1012 pho- ference pattern produced by those slits. Conversely, by tons would be collected for each image.16 For a megapixel substituting the 500 mm lens shown in green in Fig. 3 camera, this corresponds to 106 photons per pixel. Our for the two 250 mm lens shown in orange, we can in- paper describes two distinct imaging modes, each utiliz- stead capture the double-slit interference pattern (also ing the same components: heralded imaging and ghost one photon at a time). 17 imaging. In both configurations it is possible to pro- To promote discussion of the role of spatial coherence, duce high-quality images from an average of much fewer we show the effects of replacing the single-mode opti- 18 than one detected photon per image pixel. cal fiber that couples light into our heralding detector with multi-mode fiber. Accepting this broader range of heralded photons means that the slits themselves are ef- IV. HERALDED MEASUREMENTS fectively being illuminated with a multi-mode source. As a consequence the diffraction patterns are largely erased, In our heralded imaging system, we exploit the strong as shown in Fig. 4, while imaging is far less affected, temporal correlations between the down-converted pho- as demonstrated in Fig. 5 (though the increased vertical tons to obtain photon-by-photon measurements of an im- spread of the detected signal should be noted, as it is age of a double slit and, in a separate experiment, we indicative of the multi-modal illumination). capture the diffraction pattern obtained from the sin- Simply put, imaging tells us about the transverse (hori- 5
Vertical cross sections Image of a double slit Coherent source Imaging/ 600 diffraction lenses Heralding 500 detector 400 ICCD camera 300 Delay line Double 200
Photons slit 100 BBO crystal 0 650 2600 4550 6500 x distance (µm) Partially coherent source FIG. 6. Ghost imaging schematic. The slits are no longer in 1600 the same arm as the camera, yet when data collected by the camera is triggered only by arrival of a correlated photon at 1200 the heralding detector, the results contain information about 800 the slits.
Photons 400
0 650 2600 4550 6500 the plane of the ghost image are conjugate image planes. x distance (µm) Yet, were it not for the heralded triggering employed, the complete set of photons hitting the ICCD camera would FIG. 5. Top: Image results when using single-mode fiber. reveal only the incident (Gaussian) beam shape. Nor Bottom: comparable results obtained from multi-mode fiber. could the data collected by the SPAD (which contains no spatial information), taken on its own, reveal an im- age. Rather, it is the correlation between the two data zontal) spatial location of photons within the plane of the sets that allows us to select out those photons required object being imaged. Because the location of the slits in for image construction. that object are the same, regardless of whether we use single-mode or multi-mode fiber, the imaging results can be roughly comparable. On the other hand, diffraction depends upon the transverse momenta of the photons as Vertical cross sections they exit those slits. Clearly, the diffraction pattern is "Ghost" image of a double slit sensitive to the degree of spatial coherence, while imag- Coherent source ing is robust. 3000 2500 2000 V. SPATIALLY CORRELATED GHOST 1500 1000 MEASUREMENTS Photons 500
Having discussed the importance of temporal correla- 0 650 2600 4550 6500 tions, we turn to another configuration, shown in Fig. 6, x distance (µm) designed to highlight the importance of nonlocal spatial Partially coherent source correlations. Specifically, we also took data when our slits 700 were placed into the arm that does not contain the cam- 600 era. Using this version of the set up, even though the 500 photons collected by the camera have never interacted 400 with the two slits, it is nevertheless possible to perform 300 200 experiments revealing information about either imaging Photons 100 or diffraction. Such experiments are referred to as ghost 0 imaging and ghost interference,21 with the word “ghost” 650 2600 4550 6500 referencing Einstein’s concern over “spooky action at a x distance (µm) distance.”3 For ghost imaging, illustrated Fig. 7, the key point is FIG. 7. Ghost imaging data. According to any classical that the down-converted photons pairs are not just tem- model, the photons used to construct this image have never porally correlated, but also spatially correlated. Here, interacted with the object imaged. An image is formed is due the plane containing the slits in the heralding beam and to the spatial correlation between entangled photons. 6
Opportunities for discussion are extended much fur- diffraction plane is simply the Fourier transform of the ther when we reconfigure our setup so as to examine amplitude of the distribution found in the ghost image the far field, where we expect (according to the classi- plane. Thus, the fringe spacing observed is determined cal schematic in Fig. 2) the photons to have diverged. by the effective focal length of the optics utilized. More- By inserting the optics represented by the lens shown in over, given the optical layout incorporated in the exper- green in Fig. 6, we capture the ghost far-field double-slit iments presented here, the ghost diffraction plane and interference pattern as shown in Fig. 8, rather than a the heralded diffraction plane are 1:1 equivalent planes. direct image of the object containing the slits. That is, in our observations the fringe spacing in ghost diffraction are the same as those observed in heralded diffraction. Students should be encouraged to compare
Vertical cross sections the observed fringe spacing to the theoretical prediction, "Ghost" Young's double slit which can be calculated to be fλ/d, where d is the center- Coherent source to-center distance between the slits, λ is the wavelength 150 of the down-converted light, and f is the 500 mm focal length of the lens which lies between the image plane of 100 the slits and the far-field interference pattern. Again, the
Photons 50 double slit used here had a center-to-center separation of 500 microns.
0 650 2600 4550 6500 x distance (µm) Partially coherent source VI. CONCLUSION
400 300 Quantum mechanics is full of counter-intuitive phe- 200 nomena. For this reason, we believe it to be
Photons useful that real experimental data be used to in- 100 troduce students to some of the foundational phe- 0 650 2600 4550 6500 nomena of quantum mechanics. The processed x distance (µm) video versions of the data described in this arti- cle are available at
∗ [email protected] 16 P. Llull, X. Liao, X. Yuan, J. Yang, D. Kittle, L. Carin, G. 1 W. E. Lamb, Jr., “Anti-photon,” Appl. Phys. B 60, 77–84 Sapiro, D. J. Brady, “Coded aperture compressive tempo- (1995). ral imaging,” Opt. Express 21, 10526–10545 (2013). 2 R. P. Feynman, The Character of Physical Law - part 6 17 J. H. Shapiro, R. W. Boyd, “The physics of ghost imaging,” probability and uncertainty, a series of lectures recorded Quantum Inf. Process. 11, 949–993 (2012). by the BBC at Cornell University.