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Journal of Physics B Atomic Molecular and Optical Physics

Probe dispersion and quantum coherence

Lars Bojer Madsen, Knud Taulbjerg

Published Jun 28, 1997• 0 citations
Publisher

Abstract

The dispersion of the initial state of a probe system, be it a quantum object or a macroscopic system in a classical interference experiment, is in general an essential element in the analysis of quantum interference phenomena. The general situation is discussed briefly with particular reference to generic cases in two-colour atomic-physics experiments. The effect of dispersion is, at first sight, somewhat counter-intuitive: if the probe is dispersion-free there is no interference except in special cases, while quantum interference gains full weight in the classical limit , where the dispersion is large. We propose experiments in which a continuous transition between the two regimes may be observed.

DOI
10.1088/0953-4075/30/12/001

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The dispersion of the initial state of a probe system, be it a quantum object or a macroscopic system in a classical interference experiment, is in general an essential element in the analysis of quantum interference phenomena. The general situation is discussed briefly with particular reference to generic cases in two-colour atomic-physics experiments. The effect of dispersion is, at first sight, somewhat counter-intuitive: if the probe is dispersion-free there is no interference except in special cases, while quantum interference gains full weight in the classical limit , where the dispersion is large. We propose experiments in which a continuous transition between the two regimes may be observed.
Optical interference is regarded as a classical phenomenon and is usually completely described in classical terms, in which optical fields are represented by classical waves. Does it mean that optical interference, which is fundamentally ascribable to the phenomenon of a superposition of wave amplitudes, cannot be applied to test quantum phenomena? The superposition principle is at the heart of quantum physics and one could expect that it should distinguish the quantum nature of light from thewave nature. Our experience based on extensive theoretical analysis and experimental observations shows that classical and quantum theories of optical interference readily explain the presence of an interference pattern resulting from the first-order coherence. However, there are interference effects involving the higher order (second-order) coherence that distinguish the quantum (photon) nature of light from the wave nature. Quantum interference has recently returned to prominence because of its utility in manipulating spontaneous emission and other radiative properties of atomic systems. In this chapter, we present elementary concepts and definitions of both the classical and quantum theory of optical interference and discuss similarities and differences between these two approaches [80].
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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
Abstract One of the common conceptions of nature, typically derived from the experiences with classical systems, is that attributes of the matter coexist with the substance. In the quantum regime, however, the quantum particle itself and its physical property may be in spatial separation, known as the quantum Cheshire cat effect. While there have been several reports to date on the observation of the quantum Cheshire cat effect, all such experiments are based on first-order interferometry and destructive projection measurement, thus allowing simple interpretation due to measurement-induced disturbance and also subject to trivial interpretation based on classical waves. In this work, we report an experimental observation of the quantum Cheshire cat effect with noninvasive weak quantum measurement as originally proposed. The use of the weak-measurement probe has allowed us to identify the location of the single photon and that of the disembodied polarization state in a quantum interferometer. The weak-measurement probe based on two-photon interference makes our observation unable to be explained by classical physics. We furthermore elucidate the quantum Cheshire cat effect as quantum interference of the transition amplitudes for the photon and the polarization state which are directly obtained from the measurement outcomes or the weak values. Our work not only reveals the true quantum nature of Cheshire cat effect but also sheds light on a comprehensive understanding for the counter-intuitive quantum phenomena.
The fundamental indication of the departure of quantum mechanics from the classical world is the so-called quantum coherence.Typically, we define it as the characteristic of systems which are in a superposition of states yielding interference patterns in certain kinds of experiments.In addition to its captivating philosophical implications, quantum coherence turned out to be a valuable tool in different areas, ranging from quantum information to biology, where it was used to describe several fundamental processes.Here, we go one step further to study how classical uncertainties in a mixture of similar states reduce quantum coherence in quantum scattering theory.To this end, we deal with different examples, all of them with roots in the widely studied Feynman's two-slit thought experiment.We finally propose an operational and intuitive definition of the concept of coherence length whose implications largely transcend the simplicity of the corresponding mathematical development, as it is demonstrated when applied to the analysis of some recent atomic and molecular processes.