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Enrique J. Galvez
The last ten years have seen the development of new advanced physics laboratories that emphasize a new array of topics not touched by previous laboratories: fundamentals of quantum mechanics. The labs involve quantum optics experiments. They use a modern source of light brought in by technological advances and current research in quantum computing: correlated photon pairs. The experiments are table-top and do not require an optical table or large and expensive lasers. They incorporate a number of techniques both in terms of optics hardware (alignment of optical beams and interferometers) and electronics (photon counting and coincidence timing), but their real strength is in the physics they convey. In fact, the physics of the experiments is so compelling that the labs have been adopted at a number of levels, from introductory, to intermediate, to advanced, and as a laboratory component for a quantum mechanics course (see Ref. 1 and references therein).
In addition, the experiments address fundamental topics of quantum mechanics that are sometimes sidestepped in instruction in favor of more mechanical treatments of quantum mechanics. In experiments performed one photon at a time the physics of the experiments concentrates on the quantum mechanics of a single quantum, precisely the type of approach used in introducing the principles of quantum mechanics. The experiments can touch on misconceptions about what photons are, wave-particle duality riddles, and on more fundamental tenets of quantum mechanics such as non-realism and non-locality. Finally, in an era very enthusiastic about quantum information and the prospects of quantum computing, the experiments can provide non-physics beginners a more vivid demonstration of quantum superposition, the fundamental pillar of this new technology.
There are two types of experiments that can be performed with this apparatus. Both use a unique light source whose output is a pair of photons. These photons can be used in two ways. In a first way, one photon does something, and is "heralded" by its partner. That is, one partner announces the presence of the other in the apparatus. Each experiment then requires that both photons be detected. Since both photons are created simultaneously then coincidence detection is part of the data acquisition apparatus. This heralded-photon setup is critical in making this source quantum mechanical. As such the source of light is non-classical. An attenuated source of light (e.g., a laser) behaves as a "classical" source, and so all experiments done with it can be explained by a classical treatment. A non-classical source requires a quantum mechanical explanation. Below we describe an experiment that distinguishes between the two.
A second way of using the source treats both photons of a pair as equals. Both photons are born together and thus carry correlations that can be shown to be quantum mechanical, and in many situations they behave as one, and are thus called "biphotons." The ultimate correlation of biphotons is the entangled state, which can be straight-forwardly produced!2 Various implementations of this method result in undergraduates doing a measurement of a violation of Bell inequalities in one afternoon’s laboratory.
In this article I give an overview of the general apparatus used in these experiments and the types of experiments that have been developed for undergraduates.
The source of light relies on the process of spontaneous parametric down conversion; it consists of the generation of two photons from one pump photon. Energy and momentum are conserved in the process, so if we consider the pair to have the same energy then they have a wavelength that is twice the wavelength of the original (pump) photon. This puts certain restrictions on the wavelength of the pump beam, because the photon pairs have to be detected individually with reasonable efficiency. For this reason, inexpensive photomultipliers are unfortunately not suitable. These are efficient in the mid visible range or lower wavelengths, but then they would require ultraviolet pump sources. The best compromise today is avalanche photodiodes, which have reasonable detection efficiency in the near infra-red. With these detectors the pump photons have a wavelength in the blue wavelength range of the visible.
Today the source is quite inexpensive because of the proliferation of Bluray video players, which carry a 405-nm GaN diode laser. A number of web sources already sell intense blue diode laser pointers (unsafe to use as such) for as low as $20! With a little bit of technology these diode lasers can be made temperature and current stable and be suitable for research well beyond undergraduate laboratories. The parametric down-conversion to low energy pairs is done with a non-linear crystal that costs about $500. The source has a low efficiency: 10-8, and after wavelength selection filtering and other losses, the final efficiency can be as low as 10-10. However, with a 20 mW pump source delivering 4 x 1016 photons per second, we still have plenty of pairs for photon counting experiments. More details on this source can be found in Ref. 4.
The photons then go through an apparatus that has optical hardware. These involve interferometer components (beam splitters and mirrors), polarizing optics (waveplates and polarizers), and detection components (filters and optical fibers). Our prototypes mount all of this hardware on a 2x5 ft optical breadboard. The components can be taken from equipment at hand. The only technique to avoid troubles with interference is to keep the optical beams low on the table and the size interferometers as small as possible. Since the light is broad-band the interferometer needs to be carefully aligned.4 Figure 1 shows a schematic accompanied with photos of our setup at Colgate University. More details of the hardware, setups and methods are given in our website.5
The detectors are currently the expensive component of the apparatus, at about $8000 for two detectors. A group of members of the physics education community has been in contact with vendors of these detectors to make more inexpensive options, so there is hope that these prices will come down. The detectors produce 5-volt square (TTL) pulses per detected photon. The pulses have to then go through a system of pulse electronics for pulse counting and coincidence detection. This can be accomplished by either using standard NIM modules4 or integrated interface cards.6
As mentioned earlier we have two types of experiments: heralded-photon experiments and biphoton experiments. In heralded-photon experiments we send one photon directly to a detector, and the other one through an interferometer and then to a detector. There are a number of experiments that can be done with this setup (the same as the one in Fig. 1). In a first experiment we just send the light through the interferometer. The probability that the photon passes through the interferometer is ½ (1 + cosδ), where δ is the phase due to the path length difference. The data gives lots of counts per second when the phase is a multiple of 2π and a minimum near zero when the phase is an odd multiple of π. One can understand this experiment as a single quantum (the photon) leaving the interferometer in a superposition of having traveled both paths. It is a fundamental principle of quantum mechanics, and what distinguishes it from classical mechanics. The discrete nature of the counts underscores Dirac’s famous quote that in going through an interferometer each photon interferes with itself and not with other photons. The mystery is augmented by putting a beam splitter after the interferometer, which does not show that the photons split at that splitter.
A popular extension of the interferometer is the quantum eraser, whereby using polarization optics we can eliminate the interference. This setup can be used to underscore a more conceptual aspect of superposition: that it exists provided that the paths leading to it are indistinguishable. Conversely, when the paths are distinguishable superposition (and interference) disappear. Manipulation of the polarization allows making the path information distinguishable or not. The "eraser" is a polarizer placed after the interferometer that, in the case when the path information is distinguishable, it erases the distinguishing information. We offer a laboratory experience on the quantum eraser to the first-year students that take our course on introductory modern physics (the first course in our physics sequence).7 The data that they take is divided into three sections, as shown in Fig. 2. In a first section the paths of the interferometer are distinguishable and so we see interference. The horizontal scale is proportional to the voltage sent to a device that changes the path length of one of the arms of the interferometer. It can be seen that coincident photon counts oscillate between maxima and minima, one photon at a time. In a middle portion the paths are made distinguishable by rotating the polarization of the light in one of the arms, making the paths distinguishable. The data is flat showing no interference (the probability is ½ in this section). In a third section we put a polarizer after the interferometer with its axis such that the polarizations of the two arms project equally. Past the polarizer the light has the same polarization regardless which path the light took. As a consequence, the light contains no path information; the polarizer erased the path information. The data for this section shows oscillations again. The detection probability is ¼ (1 + cosδ ).
This exercise also underscores a more general view of interference, where one does not need to disturb the system to wash out the interference – a legacy of the Bohr-Einstein dialogues. Instead, the key concept is whether the path information is available or not.
An interesting variation of the eraser is the manipulation of the coherence length of the light.5,8 One can view the coherence length as the length of the photon wave packet. Then interference would disappear when the path length difference of the interferometer is greater than the coherence length, a well known aspect of classical interferometry. However, in terms of photons one can understand this by picturing that interference disappears when the photons arrive to the detector at measurably distinct times that depend on the path that they took in the interferometer. The information can be erased by increasing the coherence length to values greater than the path-length difference via filters put before either detector.
As mentioned earlier, all of these experiments can be combined with sending the signal photon to a beam splitter and putting detectors at both output ports of the beam splitter. This allows doing a recreation of the Hanbury-Brown-Twiss test and a measurement of the degree of second-order correlation.9 This test basically amounts to showing that a photon exists because it does not split like a wave at a beam splitter into two half photons of the same wavelength as the incident photon, something predicted for a classical wave.
There are a number of interesting experiments that can be done with biphotons. We have done much work in developing experiments where two collinear photons go through an interferometer, producing an interesting pattern of interference that involves multiple paths.1 The experiments can also be used to show that some of the interference is due to the bosonic symmetry of the photon wavefunction.5
Finally, the ultimate experiment is the one that can be used to prepare photon pairs in polarization entangled states. One can use this setup to understand the difference between entangled and mixed states (the realistic view).1 A culmination of this is a measurement of a violation of a Bell inequality.3 The setup is now well developed, and can be used to test other interesting variations of the inequalities.10 All of these experiments test students’ understanding of the quantum mechanical algebra but also of its fundamental philosophical underpinnings.
In summary, I presented here a brief description of a relatively new set of experiments that open the door for new laboratory explorations at the undergraduate level. Due to their cost the experiments are slowly being adopted, but in time with the availability of lower cost components, these experiments could become a staple of modern advanced laboratories.
This work was funded by two grants from the National Science Foundation (in 1999 and 2004) and internal funds from Colgate University.References
1. E.J. Galvez, Am. J. Phys. 78, 510 (2010).
2. P.G. Kwiat, E. Waks, A.G. White, I. Appelbaum, and P.H. Eberhard, Phys. Rev. A 60, 773 (1999).
3. D. Dehlinger and M.W. Mitchell, Am. J. Phys. 70, 903 (2002).
4. E.J. Galvez, C.H. Holbrow, M.J. Pysher, J.W. Martin, N. Courtemanche, L. Heilig, and J. Spencer, Am. J. Phys. 73, 1210 (2004).
5. URL: departments.colgate.edu/physics/pql.htm
7. Modern Introductory Physics, C.H. Holbrow, J.N. Lloyd, J.C. Amato, E.J. Galvez, and M.E. Parks (2nd Ed., Springer-Verlag, New York, 2010).
8. P.G. Kwiat, A.M. Steinberg, and R.Y. Chiao, Phys. Rev. A 45, 7729 (1992).
9.J.J. Thorn, M.S. Neel, V.W. Donato, G.S. Bergreen, R.E. Davies, and M. Beck, Am. J. Phys. 72, 1210 (2004).
10.J.A. Carlson, D.M. Olmstead, and M. Beck, Am. J. Phys. 74, 180 (2006).
Enrique "Kiko" Galvez is a Professor of Physics and Astronomy at Colgate University. His research interests are in optical physics and in physics education. He was co-Chair of the 2010 GRC meeting.