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Physical Review Letters

Complementarity Enforced by Random Classical Phase Kicks

Alfredo Luis, Luis Lorenzo Sánchez-Soto

Published Nov 9, 1998• 34 citations
Publisher

Abstract

Quantum phase difference is used to analyze which-path detectors in which the loss of interference predicted by complementarity cannot be attributed to classical momentum transfer between the interfering particle and the measuring apparatus. It is shown that the dynamics of the measurement disturbs the interference via random classical phase shifts.

DOI
10.1103/physrevlett.81.4031

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arXiv:quant-ph/9910037•Journal of Modern Optics•Oct 1, 2000•16 citations
Quantum phase difference is used to analyze which-path detectors in which the loss of interference predicted by complementarity cannot be attributed to classical momentum transfer between the interfering particle and the measuring apparatus. It is shown that the dynamics of the measurement disturbs the interference via random classical phase shifts.
Two-slit interference experiment with a which-way detector has been a topic of intense debate. Scientific community is divided on the question whether the particle receives a momentum kick because of the process of which-way measurement. It is shown here that the same experiment can be viewed in two different ways, depending on which basis of the which-way detector states one chooses to look at. In one view, the loss of interference arises due to the entanglement of the two paths of the particle with two orthogonal states of the which-way detector. In another view, the loss of interference can be interpreted as arising from random momentum kicks of magnitude h/2dh/2dh/2d received by the particle, ddd being the slit separation. The same scenario is shown to hold for a three-slit interference experiment. The random momentum kicks for the three-slit case are of two kinds, of magnitude ±h/3d\pm h/3d±h/3d. The analysis is also generalized to the case of n-slit interference. The two alternate views are described by the same quantum state, and hence are completely equivalent. The concept of "local" versus "nonlocal" kicks, much discussed in the literature, is not needed here.
Interference results when a quantum particle is free to choose among a few indistinguishable paths. A canonical example of Bohr's complementarity principle [1] is a two-path interferometer with an external detector coupled to one of the paths. Then, interference between the two paths vanishes (i.e. dephasing) if one is able to detect, even in principle, the path taken by the particle. This type of which path (WP) experiment was already executed with photons, cooled atoms, neutrons, solitons, and more recently with electrons in a mesoscopic system [2]. In the latter experiment path determination was provided by inducing a change in the current flowing through the detector. In the present experiment we perform a more intriguing WP determination: only a phase change is being induced in the detector while the current remains unaffected. We show that such detector-interferometer interaction can be understood both, from the WP information obtained by the detector, or alternatively by understanding the disturbance in the interferometer caused by the detector. Moreover, we address the subtle role of detector coherency and point out difficulties in the intuitive interpretation of the experiment.
Interference effects are usually observed by intensity measurement. Path indistinguishability by the quantum complementarity principle requires projection of the interfering fields into a common indistinguishable mode before detection. On the other hand, the essence of wave interference is the addition of amplitudes of the interfering fields. Therefore, if amplitudes can be directly measured and added, interference can occur even though the interfering fields are in well-distinguishable modes. Here, we make a comprehensive study in both theory and experiment of a technique by homodyne measurement of field amplitudes to reveal interference. This works for both classical and quantum fields even though there exists distinguishability in the interfering paths of light. This directly challenges the complementarity principle. We present a resolution of this issue from the viewpoint of measurement that emphasizes either particle or wave. This technique is particularly useful for recovering interference in unbalanced interferometers with path imbalance beyond a coherence length of the input field and can be applied to remote sensing to extend the applicable range. Since the amplitude-based interference phenomena studied here are fundamentally different from the traditional intensity-based interference phenomena, our approach leads to a new paradigm to study coherence between optical fields.