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arXiv:quant-ph/0612163

Uncoupling Which-Way Information from Interference: A Novel Interference Experiment using a Super-Focused Laser Beam

J. Wulleman

Published Dec 19, 2006• 0 citations

Abstract

The generally accepted view in quantum theory is that information about which way the quantum system traveled and interference visibility are complementary. In all which-way experiments, however, an intervention takes place in the interference process in order to determine which way the quantum system took. This intervention can imply the tagging of a which-way marker to a quantum system or, for instance, blocking off one of the paths in a Mach-Zehnder interferometer so that one indirectly knows that the quantum system took the other (open) path. It is, however, this intervention that destroys the interference. In this paper a novel two-slit which-way interference experiment will be discussed and proposed for implementation that provides maximum which-way information without intervening in the interference process so that simultaneously maximum interference visibility remains preserved. This, in fact, implies an uncoupling of which-way information from interference and consequently also entails violating the duality relation P^2+V^2<1. Basically, the purpose of the proposed experiment and of this paper is to scrutinize this duality relation. The experiment makes use of a super-focused laser beam that is launched into only one of the two slits of the two-slit interference experiment.

DOI: 10.48550/arxiv.quant-ph/0612163

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The generally accepted view in quantum theory is that information about which way the quantum system traveled and interference visibility are complementary. In all which-way experiments, however, an intervention takes place in the interference process in order to determine which way the quantum system took. This intervention can imply the tagging of a which-way marker to a quantum system or, for instance, blocking off one of the paths in a Mach-Zehnder interferometer so that one indirectly knows that the quantum system took the other (open) path. It is, however, this intervention that destroys the interference. In this paper a novel two-slit which-way interference experiment will be discussed and proposed for implementation that provides maximum which-way information without intervening in the interference process so that simultaneously maximum interference visibility remains preserved. This, in fact, implies an uncoupling of which-way information from interference and consequently also entails violating the duality relation P^2+V^2<1. Basically, the purpose of the proposed experiment and of this paper is to scrutinize this duality relation. The experiment makes use of a super-focused laser beam that is launched into only one of the two slits of the two-slit interference experiment.

In the conventional interpretation of quantum mechanics the interference of particles in a two-beam interferometer is closely related to the problem of which-way information. One of the mysteries of quantum mechanics relies on the assumption that the wavefunction of each photon propagates simultaneously along both classically allowed paths, and that interference arises as a consequence of the indistinguishability of those paths. Any attempt to obtain which-way information by putting individual labels on the photons in each pathway inevitably destroys interference. However, even in cases in which the photons carry which-way labels, it is possible to erase those labels after the particle has left the interferometer. The erasing process (partly or completely) destroys the which-way information, and thereby restores interference. This phenomenon is known as quantum erasing. Here we present a lecture demonstration experiment of quantum erasing based on a Mach–Zehnder interferometer operated with single photons.

The issue of interference and which-way information is addressed in the context of three-slit interference experiments. A new path distinguishability |

\mathcal {D}_{Q}

| is introduced, based on unambiguous quantum state discrimination. An inequality connecting the interference visibility and path distinguishability, |

\mathcal {V} + {2\mathcal {D}_Q\over 3- \mathcal {D}_Q} \le 1

|⁠, is derived which puts a bound on how much fringe visibility and which-way information can be simultaneously obtained. It is argued that this bound is tight. For two-slit interference, we derive a new duality relation which reduces to Englert's duality relation and the Greenberger–Yasin duality relation, in different limits.

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We have developed a which-way experiment using visible light that is completely analogous to a recent experiment involving which-way measurement in atom interference. This simple experiment, easily accessible to undergraduate students and the resources of undergraduate departments, facilitates the examination of the key elements of which-way measurement, quantum erasure, and related mysteries of quantum measurement. The experiment utilizes a Mach–Zehnder interferometer, and visually demonstrates the loss of interference fringes when a which-way measurement is imposed, and the restoration of that pattern when the which-way information is destroyed. This device is also sensitive enough to observe interference fringes arising from single photons. We present a simple analysis of the interference appropriate for the coherent classical field limit and the single photon limit at a level accessible to undergraduates. We also briefly mention related issues on the nature of the photon.

For a particle travelling through an interferometer, the trade-off between the available which-way information and the interference visibility provides a lucid manifestation of the quantum mechanical wave–particle duality. Here we analyse this relation for a particle possessing an internal degree of freedom such as spin. We quantify the trade-off with a general inequality that paints an unexpectedly intricate picture of wave–particle duality when internal states are involved. Strikingly, in some instances which-way information becomes erased by introducing classical uncertainty in the internal degree of freedom. Furthermore, even imperfect interference visibility measured for a suitable set of spin preparations can be sufficient to infer absence of which-way information. General results are illustrated with a proof-of-principle single-photon experiment. Quantum mechanics dictates that the interference pattern cast by particles after passing through a double slit depends on how much information it is possible to know about which slit they went through. Banaszek et al. show how this behaviour extends to a system’s internal degrees of freedom.