A scheme is proposed for experimentally achieving the famous two-slit gedanken experiment using photons. A particle’s quantum pathways can interfere to produce fringes in the probability for the particle to be found at some location. If the path taken by the particle is experimentally determined, the complementarity principle says that the fringes must disappear. To carry out this experiment with photons is difficult because normally the act of determining a photon’s location destroys it. We propose to overcome this by putting a type-II optical parametric amplifier (OPA) in each arm of a Mach-Zehnder interferometer and observing fringes at the output. An OPA responds to an input photon by increasing its probability to produce a pair of photons, one having polarization orthogonal to the input photon.
A scheme is proposed for experimentally achieving the famous two-slit gedanken experiment using photons. A particle’s quantum pathways can interfere to produce fringes in the probability for the particle to be found at some location. If the path taken by the particle is experimentally determined, the complementarity principle says that the fringes must disappear. To carry out this experiment with photons is difficult because normally the act of determining a photon’s location destroys it. We propose to overcome this by putting a type-II optical parametric amplifier (OPA) in each arm of a Mach-Zehnder interferometer and observing fringes at the output. An OPA responds to an input photon by increasing its probability to produce a pair of photons, one having polarization orthogonal to the input photon.
We propose a scheme to realize the famous two-slit gedanken experiment using photons. Measurements using optical parametric amplifiers (OPAs) are proposed to infer the probabilities that the input photon has taken a particular path in a Mach-Zehnder interferometer, without destroying the photon. Using information theory and Bayes' theorem, we find that the visibility of ensemble averaged interference fringes is inversely related to the which-path information that is made available by the OPAs. This is in agreement with the complementarity principle. A method is found to erase partially the which-path information before it is recorded; then by making conditional measurements the fringe visibility can be partially restored.
We present an analysis of a quantum nondemolition (QND) measurement, which determines which of the two possible paths a photon follows through a Mach-Zehnder interferometer. The measurement is effected by the nonlinear Kerr effect. If a photon traverses the arm of the interferometer containing the Kerr medium, it shifts the phase of a probe beam and then continues through to the interferometer output. The measurement does not destroy the photon but does disturb its phase. Using various probe states, we show how such phase disturbances reduce fringe visibility and enforce a principle of complementarity; the more accurately the QND measurement determines the path of the photon, the lower is the fringe visibility. We determine the appropriate parameters to optimize the observation of the two complementary quantities.
In optical experiments involving a single photon that takes alternative paths through an optical system and ultimately interferes with itself (e.g., Young's double-slit experiment, Mach-Zehnder interferometer, Sagnac interferometer), there exist fundamental connections between the linear and angular momenta of the photon on the one hand, and the ability of an observer to determine the photon's path through the system on the other hand. This paper examines the arguments that relate the photon momenta (through the Heisenberg uncertainty principle) to the "which path" (German: welcher Weg) question at the heart of quantum mechanics. We show that the linear momenta imparted to apertures or mirrors, or the angular momenta picked up by strategically placed wave-plates in a system, could lead to an identification of the photon's path only at the expense of destroying the corresponding interference effects. We also describe a thought experiment involving the scattering of a circularly-polarized photon from a pair of small particles kept at a fixed distance from one another. The exchange of angular momentum between the photon and the scattering particle in this instance appears to provide the "which path" information that must, of necessity, wipe out the corresponding interference fringes, although the fringe-wipe-out mechanism does not seem to involve the uncertainty principle in any obvious way.
Over the past several decades, single photon-based path interference in double-slit experiment has been well demonstrated for the particle nature of photons satisfying complementarity theory, where the quantum mechanical interpretation of the single photon interference fringe is given by Born rule for complex amplitudes in measurements. Unlike most conventional methods using entangled photon pairs, here, a classical coherent light source is directly applied for the proof of the same self-interference phenomenon. Instead of double slits, we use a Mach-Zehnder interferometer as usual, where the resulting self-interference fringe of coherent single photons is exactly the same as that of the coherent photon ensemble of the laser, demonstrating that the classical coherence based on the wave nature is rooted in the single photon self-interference. This unexpected result seems to contradict our common understanding of decoherence phenomena caused by multi-wave interference among bandwidth distributed photons in coherence optics.
Bohr's complementarity notion is at the heart of quantum physics. It suggests that quantum systems are observed as waves or particles depending on the type of measurement, i.e., the experimental arrangement, they are subjected to. For instance, sending single photons to an open or closed Mach-Zehnder interferometer (MZI) leads to the observation of particle or wave behaviours, respectively. In 1984, Wheeler proposed a "Gedanken" delayed-choice experiment in which the interferometer configuration is chosen at will by the experimentalist only after the photon has already passed the input beam-splitter (BS_in) of the device. This experiment was realized using a single photon source and showed that Bohr's complementarity notion was still obeyed.It was recently proposed to take Wheeler's experiment one step further by employing an output "quantum beam-splitter" (QBS), i.e.,preparing BS_out in a coherent superposition of being absent and present. This allows choosing the type of measurement, i.e., wave or particle, only after having determined the state of the QBS, which can be (in principle) infinitely delayed.We realized such an experiment by exploiting the resource of entanglement, in this case pairs of polarization entangled photons. The behaviour of one of the paired photons, called the test photon, is analysed using a MZI having a QBS at its output. This QBS is enabled by entanglement and made of a polarization dependent beam-splitter. The other photon, called the corroborative photon, allows determining the state of the QBS, and consequently, which test photon behaviour (wave, particle, or both) is observed.By manipulating the corroborative photon polarization state, we demonstrate a continuous morphing of the test photon from wave to particle behaviour. This refutes simple models of single photons behaving exclusively as waves or particles. The state of the QBS is determined via the measurement of the corroborative photon only after the test photon has already been detected. The space-like separation between the two measurements invalidates local-hidden variable models associated with pre-existing information about the measurement outcomes. In other words, when the test photon is detected, no information is available about the type of measurement it underwent. These results still perfectly obey Bohr's complementarity notion and its extension.
Atom interferometers are powerful tools for the study of fundamental issues in quantum mechanics. This paper describes the use of our atom interferometer [1] for an experimental realization of Feynman's gedanken experiment in which the observation of photons scattered off of particles emerging from a double slit is used to obtain which path information. This determination, in principal, of the particle's path, destroys any interference effects downstream. The interference can be regained by observing only those particles which scatter a photon into a small range of final directions.