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Physical Review Letters

Decoherence due to the geometric phase in a ‘‘welcher-weg’’ experiment

Rajendra Bhandari

Published Dec 28, 1992• 14 citations
Publisher

Abstract

We describe a new version of the well-known gedanken experiments to determine which of the two paths a particle took in a two-beam interference experiment. In this version the presence of a geometric phase can be deduced from the requirement that the interference pattern must disappear as a result of the welcher-weg (which path) information.

DOI
10.1103/physrevlett.69.3720

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We describe a new version of the well-known gedanken experiments to determine which of the two paths a particle took in a two-beam interference experiment. In this version the presence of a geometric phase can be deduced from the requirement that the interference pattern must disappear as a result of the welcher-weg (which path) information.
We introduce a simple experiment involving a double-slit interferometer by which one can learn basic concepts of quantum interference such as which-path marking, quantum erasers, and geometric phases. Each of them exhibits seemingly mysterious phenomena in quantum physics. In our experiment, we use the double-slit interference of visible light with the polarization as an internal state to demonstrate the disappearance of fringes by which-path marking, recovery of interference using quantum erasers, and the rapid shifting of the fringe pattern induced by the geometric phase. We also present a simple theoretical analysis of an interferometer with an internal state.
Summary form only given. The transition between quantum and classical systems is usually ascribed to decoherence effects, which become increasingly important for larger size systems and tend to obscure the quantum behavior. Decoherence effects also come into play in the famous thought 'Gedanken' experiments on the wave-particle duality of matter. For example, in a double slit experiment with electrons, a wavepacket passes simultaneously through both slits and forms an interference pattern. However, if one attempts to keep track of the electron path, e.g., by scattering a photon from the electron, the resulting decoherence destroys the interference pattern and the particle behavior takes over. We report on the extension of such a which-path experiment to an arrangement with more than two interfering paths, which is realized using the interference of four internal states of the cesium atom. This two-qubits arrangement represents a more complex quantum system than a two-beam interferometer, which represents a single qubit system. While in a two-beam interference experiment the observation of a path will inevitable destroy the fringe signal, we demonstrate that the scattering of a photon on one of the path of a multiple path arrangement cannot only lead to a decrease of the contrast, but, under certain conditions, also lead to an increase of the fringe contrast.
As was demonstrated in the previous chapter, the process of observation and acquisition of information or at least the possibility of ‘knowing’ (whether or not we bother to ‘look’) can profoundly change the outcome of an experiment. For example, in the case of the micromaser which-path detector, we do not need to ‘look at’ or ‘interrogate’ the masers in order to lose the interference cross term; it is enough that we could have known. Experiments along these lines provide a dramatic example of the importance of which-path, or ‘Welcher-Weg’, information. The present chapter treats the Welcher-Weg quantum eraser problem from a different vantage. We first consider the interference of light as it is scattered from simple atomic systems consisting of single atoms located at two neighboring sites. From this simple model, we can gain a wealth of insight into such problems as complementarity, delayed choice, and the quantum eraser via field–field and photon–photon correlation functions, i.e., via G (1) ( r , t ) and G (2) ( r , r ′ t , t ′). The chapter concludes with a demonstration that such considerations can, in principle, even lead to new kinds of high-resolution spectroscopy.
We discuss complementarity and uncertainty in a gedanken Which-Way (Welcher-Weg) experiment in a Mach-Zehnder interferometer. Although a Welcher-Weg measurement can be performed with only a negligible amount of momentum change in the detector itself, the change in the interference pattern must correspond to a change in the momentum distribution of the particle. Entanglement between the Mach-Zehnder interferometer and the Welcher-Weg measurement introduces orthogonality that disables the interference of the particle, but simultaneously, it also generates a momentum transfer between the particle and other parts of the whole entangled system (including macroscopic parts). This analysis can be related to the Delayed Choice interpretation. We show where the momentum change takes place and we conclude that entanglement is the key to understand how complementarity (i.e. Which Way versus interference) and the position-momentum uncertainty relation are interwoven.