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Decoherence and fluctuations in quantum interference experiments

Angelo Mariano, Paolo Facchi A, Saverio Pascazio

Published Jan 1, 2001• 15 citations
Publisher

Abstract

We analyze the notion of quantum coherence in an interference experiment. We let the phase shifts fluctuate according to a given statistical distribution and introduce a decoherence parameter, defined in terms of a generalized visibility of the interference pattern. One might naively expect that a particle ensemble suffers a greater loss of quantum coherence by interacting with an increasingly randomized distribution of shifts. As we shall see, this is not always true. Decoherence is an interesting phenomenon and a topic that attracts widespread attention [1]. However, it is not easy to give a quantitative definition of decoherence [2]. All attempts at defining it always depend on the experimental configuration and on the authors ’ taste. An interesting related quantity is the

DOI
10.1002/1521-3978(200110)49:10/11<1033::aid-prop1033>3.0.co;2-u

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Decoherence is the main process behind the quantum to classical transition. It is a purely quantum mechanical effect by which the system loses its ability to exhibit coherent behavior. The recent experimental observation of diffraction and interference patterns for large molecules raises some interesting questions. In this context, we identify possible agents of decoherence to take into account when modeling these experiments, and study their visible (or not) effects on the interference pattern. We thereby present an analysis of matter wave interferometry in the presence of a dynamic quantum environment, and study how much the visibility fringe is reduced and in which timescale the decoherence effects destroy the interference of massive objects. Finally, we apply our results to the experimental data reported on fullerenes and cold neutrons. © World Scientific Publishing Company.

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We analyze the notion of quantum coherence in an interference experiment. We let the phase shifts fluctuate according to a given statistical distribution and introduce a decoherence parameter, defined in terms of a generalized visibility of the interference pattern. One might naively expect that a particle ensemble suffers a greater loss of quantum coherence by interacting with an increasingly randomized distribution of shifts. As we shall see, this is not always true. Decoherence is an interesting phenomenon and a topic that attracts widespread attention [1]. However, it is not easy to give a quantitative definition of decoherence [2]. All attempts at defining it always depend on the experimental configuration and on the authors ’ taste. An interesting related quantity is the
We analyze some interesting and peculiar phenomena that appear both in the well-known classical domain and in the quantum domain, related to the behavior of the visibility in interference experiments. One can show that, according to its usual definition, the visibility is not a monotonic function of appropriate quantities, such as the optical path difference. In the quantum domain, the visibility can be used to infer the quantum mechanical coherence properties of a quantum particle, like for example a neutron, interacting with a fluctuating environment. In some cases the wave function is more coherent even though it has interacted with a more disordered medium. We will refer to these results as anomalous, because they are against naive expectations.
We analyse the coherence properties of neutron wavepackets, after they have interacted with a phase shifter undergoing different kinds of statistical fluctuation. We give a quantitative (and operational) definition of decoherence and compare it to the standard deviation of the distribution of the phase shifts. We find that in some cases the neutron ensemble is more coherent, even though it has interacted with a wider (i.e. more disordered) distribution of shifts. This feature is independent of the particular definition of decoherence: this is shown by proposing and discussing an alternative definition, based on the Wigner function, that displays a similar behaviour. We briefly discuss the notion of entropy of the shifts and find that, in general, it does not correspond to that of decoherence of the neutron.
A model for intrinsic decoherence in quantum mechanics is proposed, based on a simple modification of unitary Schr\"odinger evolution. On sufficiently small time scales the system evolves by a random sequence of unitary phase changes generated by the Hamiltonian. The Schr\"odinger equation is obtained to zeroth order in the expansion parameter. Higher-order corrections lead to a loss of coherence in the energy basis. The rate of coherence loss becomes very large as the energy scale of the system is increased. The expansion parameter determines an uncertainty in the time step on very short times scales. A number of testable consequences are derived including anomalous dispersion of a free particle, decay of oscillatory systems, destruction of interference-fringe visibility, and a phase shift of interference fringes.
The problem of quantum interference in the presence of an environment is considered by two approaches. One treats the problem from the point of view of the trace left by the interfering particle on its environment. The other regards the phase accumulation of the interfering waves as a statistical process, and explains the loss of interference in terms of uncertainty in the relative phase. The equivalence of the two approaches is proven for the general case. The two approaches are applied to dephasing of electron interference by photon modes in coherent and thermal states, and to dephasing by electromagnetic fluctuations in metals.
Decoherence is the main process behind the quantum to classical transition. It is a purely quantum mechanical effect by which the system loses its ability to exhibit coherent behavior. The recent experimental observation of diffraction and interference patterns for large molecules raises some interesting questions. In this context, we identify possible agents of decoherence to take into account when modeling these experiments, and study their visible (or not) effects on the interference pattern. We thereby present an analysis of matter wave interferometry in the presence of a dynamic quantum environment, and study how much the visibility fringe is reduced and in which timescale the decoherence effects destroy the interference of massive objects. Finally, we apply our results to the experimental data reported on fullerenes and cold neutrons. © World Scientific Publishing Company.