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Moscow University Physics Bulletin

Specific features of interference of photons and other quantum particles

Aleksandr V. Belinsky, V. B. Lapshin

Published May 1, 2016• 2 citations
Publisher

Abstract

Specific features of the behavior of quantum particles in different experimental situations are considered. The variants of two-beam interference of single photon and other quantum particles, as well as their ability to form “standing” and “progressive” waves with the interference minima, i.e., “dead” zones in the propagation path, are studied. We also consider some type of quantum particle teleportation in an unconventional understanding of this word, where elementary particles overcome regions of the space where they cannot be, or rather the borders where the probability of finding them is zero. At these boundaries there is no pulse impact of particles on anything, it is as if they are unobservable. When observing three-beam interference, it turns out that all three modes should be present simultaneously in the light field prior to photodetection. If each mode involves a photon, it contradicts the energy conservation law, it is indicative of the fact that the observed quantity (number of photons in the field) has no any particular value prior to the measurement (a priori) unless the quantum system is in the eigen state of a measured value (Fock state).

DOI
10.3103/s0027134916030036

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•Jul 1, 2019•0 citations
Specific features of the behavior of quantum particles in different experimental situations are considered. The variants of two-beam interference of single photon and other quantum particles, as well as their ability to form “standing” and “progressive” waves with the interference minima, i.e., “dead” zones in the propagation path, are studied. We also consider some type of quantum particle teleportation in an unconventional understanding of this word, where elementary particles overcome regions of the space where they cannot be, or rather the borders where the probability of finding them is zero. At these boundaries there is no pulse impact of particles on anything, it is as if they are unobservable. When observing three-beam interference, it turns out that all three modes should be present simultaneously in the light field prior to photodetection. If each mode involves a photon, it contradicts the energy conservation law, it is indicative of the fact that the observed quantity (number of photons in the field) has no any particular value prior to the measurement (a priori) unless the quantum system is in the eigen state of a measured value (Fock state).
The peculiarities of the behavior of photons in various experimental situations are considered. Variants of double-beam interference of a single photon and the possibility of forming a standing wave by this photon are analyzed; three-beam interference is also discussed. The effects observed in this case prove the absence of particular values of the measured quantities up to the moment of measurement; in the latter case, the number of photons in the field does not a priori have a certain value, in spite of the fact that the system is in the energy state. An experiment is also considered that proves the absence of a certain phase and the phase difference of photons in the Fock state, which makes it possible to treat different types of theories of hidden parameters, including nonlocal ones, more critically.
How can we construct a picture of the photon from the wealth of observation material available to us? The photon appears to have a split personality: it is neither a wave nor a particle but something else which, depending on the experimental situation, exhibits a wave- or a particle-like behavior. In other words, in the photon (as in material particles such as the electron) the particle–wave dualism becomes manifest. Whereas classically the wave and the particle pictures are separate, quantum mechanics accomplishes a formal synthesis through a unified mathematical treatment. Let us look first at the wave aspect familiar from classical electrodynamics, which seems to be the most natural description. It makes all the different interference phenomena understandable, such as the “interference of the photon with itself” on the one hand and the appearance of spatial and temporal intensity correlations in a thermal radiation field on the other (which are obviously brought about by superposition of elementary waves emitted independently from different atoms). It might come as a surprise (at least for those having quantum mechanical preconceptions) that the classical theory is valid down to arbitrarily small intensities: the visibility of the interference pattern does not deteriorate even for very small intensities – the zero point fluctuations of the electromagnetic field advocated by quantum mechanics do not have a disturbing effect – and is valid not only for conventional interference experiments but also for interference between independently generated light beams (in the form of laser light).
The photon in the interferometer This chapter introduces many of the ideas of quantum theory by exploring three specific “case studies” of quantum systems. Each is an example of a qubit , a generic name for the simplest type of quantum system. The concepts we develop will be incorporated into a rigorous mathematical framework in the next chapter. Our business here is to provide some intuition about why that mathematical framework is reasonable and appropriate for dealing with the quantum facts of life. Interferometers In Section 1.2 we discussed the two-slit interference experiment with a single photon. In that experiment, the partial waves of probability amplitude were spread throughout the entire region of space beyond the two slits. It is much easier to analyze the situation in an interferometer , an optical apparatus in which the light is restricted to a finite number of discrete beams . The beams may be guided from one point to another, split apart or recombined as needed, and when two beams are recombined into one, the result may show interference effects. At the end of the interferometer, one or more sensors can measure the intensity of various beams. (A beam is just a possible path for the light, so there is nothing paradoxical in talking about a beam of zero intensity.) Figure 2.1 shows the layout of a Mach–Zehnder interferometer , which is an example of this kind of apparatus.
The wave aspect of light is observed experimentally through interference phenomena, and in a certain sense such observations always require a division of the given (initial) light field into two or more space-time parts. The division can only be done by introducing matter (massive particles) in the field region, and the light-matter interaction inevitably changes the initial state of the field. Not least when one is dealing with single and few-photon interference, it is good to remember again a central point of Niels Bohr, namely that no elementary phenomenon is a phenomenon until it is a registered (observed) phenomenon. It turns out that it is possible to observe interference with a quantized electromagnetic field which contains only one photon. Since the irreversible final detection destroys the photon, it is in practice necessary to repeat the experiment starting from the same initial (given) conditions. Below we shall discuss the basics of single-photon interference in the simplest terms.
Since the wavefunction of a photon only describes the probability of photon detection in time and space, it is impossible to derive uniquely defined trajectories describing the path taken by the photon between emission and detection. However, it is possible to test whether a particular set of trajectories is consistent with the statistics observed at different times for photons in the same initial state. Recently, I have shown that quantum interference effects between position and momentum can result in a violation of inequalities associated with motion along straight lines. Here, I present a more detailed analysis on the origin of the effect and its relation with other experimentally observable aspects of quantum statistics such as weak measurements and quantum tomography. It is shown that the interference pattern between a quantum state component of well-defined position and a quantum state component of well-defined momentum describes a modified causality relation between the positions detected at different times. The phase of the interference pattern is identified with the classical action of particle motion and the relation between uncertainty and causality is considered. The specific case of single photon wavefunctions is used to explain the possibilities and limitations of control at the ultimate quantum limit.
Quantum interference constitutes one of the sharpest divides between our classical intuition and the weirdness of the quantum world. Whenever there are multiple paths leading to the same outcome, it is the interplay of associated probability amplitudes that determines measurement results. In the double slit experiment, wave-like interference governs the distribution of particles on a detection screen. Extending to multiple particles allows behaviour that cannot be described by a classical wave, such as the bunching of photon pairs in Hong-Ou-Mandel interference. In both these examples, the ability to distinguish the interfering paths leads to degradation of interference and a return to behaviour described by probabilities. Understanding how this transition evolves for larger multiparticle quantum systems is of fundamental interest and also vital for developing photonic quantum technologies that rely on many-photon interference. In this thesis we investigate the role of distinguishability in the interference of three and four independent photons by using polarisation and time delays. For three photons, a new type of collective distinguishing phase appears that goes beyond a pairwise description of the similarity of quantum states. We use nonlinear photon sources and a fibre interferometer to experimentally demonstrate the ability to tune and isolate this phase in interference statistics. Extending to four photons we show that, contrary to intuition from two-photon experiments, the interference of photons prepared in distinguishable states is possible due to a four-particle phase. This is confirmed experimentally using a bulk four-mode interferometer. We then extend our study to include the effects of state impurity in the interference of three photons. New properties of this interference enable diagnosis of realistic experimental imperfections and characterisation tasks impossible using only two photons. Finally, we link discussions of state distinguishability to the group representations underpinning the exchange symmetry of multiparticle wavefunctions.