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arXiv:quant-ph/0507281

Dirac's principle in multimode interference of independent sources

Pedro Sancho

Published Jul 29, 2005• 0 citations
arXivHTMLPDF

Abstract

The extended Dirac's principle describes the interference between different particles as an effect of the multiparticle system with itself. In this paper we present a novel example, based on the detection of particles emitted in multimode states by independent sources, which illustrates in a simple way the necessity of extending the original Dirac's criterion.

DOI
10.48550/arxiv.quant-ph/0507281

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The extended Dirac's principle describes the interference between different particles as an effect of the multiparticle system with itself. In this paper we present a novel example, based on the detection of particles emitted in multimode states by independent sources, which illustrates in a simple way the necessity of extending the original Dirac's criterion.
Multimode two-particle systems show interference effects in one-particle detections when both particles have common modes. We explore the possibility of extending the usual concepts of distinguishability and visibility to these types of systems. Distinguishability will refer now to the balance between common and different modes of a two-particle system, instead of the standard definition concerning available alternatives for a one-particle system. On the other hand, the usual concept of visibility is not suitable for our problem and must be replaced with that of contrast, measuring the ratio of detection probabilities with and without interference effects. Finally, we show that for the type of states considered in the paper there is a complementarity relation between distinguishability and contrast for two-boson states. In contrast, there is no two-fermion counterpart.
IT is well known from experiment, as well as from classical theory, that strictly monochromatic light waves originating from different sources do interfere.' An example in which the waves are nearly monochromatic is found in the case of radio waves, and it is known that radio waves from two stations that have the same frequency show an interference effect. We may describe the phenomenon quantum mechanically if we represent the light quanta emitted by both sources by waves in Schroedinger configuration space. So long as we consider the quanta emitted by one source as different from those emitted by the other, the total wave function will be the product of the wave functions corresponding to the quanta emanating from both sources, and there will be no interference effect. In the present paper, we will see how things are changed when we symmetrize or antisymmetrize the wave function, i.e. assume either Bose or Fermi statistics for the particles. In the simple quantum mechanical picture that we will use here, we will assume a definite number of photons coming out from each source, and this implies that the phase relations will be undetermined.2 As a result, even the symmetrized wave functions must be expected to give, at any point in space, the same density of quanta that classical theory determines, when the intensity is averaged over the phase differences between the two sources. This implies that no interference is observed between the waves from the two sources. If we want to look for an interference effect when dealing with a quantum picture in which we have a definite number of photons, we must look for a phenomenon whose classical description should be independent of the phase. We shall make use of the fact that, in classical theory,
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.
We extend and generalize previous work on the interference of light from independent cavities that began with the suggestion of Pfleegor and Mandel [Phys. Rev. 159, 1084 (1967)] that their observed interference of laser beams should not be associated too closely with particular states of the beams but more with the detection process itself. In particular we examine how the detection of interference induces a nonrandom-phase difference between internal cavity states with initial random phases for a much broader range of such states than has previously been considered. We find that a subsequent interference measurement should give results consistent with the induced phase difference. The inclusion of more cavities in the interference measurements enables the construction in principle of a laboratory in the sense used by Aharonov and Susskind, made up of cavity fields that can serve as frames of phase reference. We also show reasonably simply how intrinsic phase coherence of a beam of light leaking from a single cavity arises for any internal cavity state, even a photon number state. Although the work presented here may have some implications for the current controversy over whether or not a typical laboratory laser produces a coherent state, it is not the purpose of this paper to enter this controversy; rather it is to examine the interesting quantum physics that arises for cavities with more general internal states.