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Physical Review A

Two-coherent-state interferometry

Dien A. Rice, Gregg S. Jaeger, Barry C. Sanders

Published Jun 6, 2000• 26 citations
Publisher

Abstract

We examine interference phenomena involving entangled pairs of quantum coherent states. Two-coherent-state interferometry, which can involve macroscopic numbers of photons, is shown to share several characteristics of two-particle quantum interferometry in such a macroscopic limit. These include the complementarity between one-system and two-system interference visibilities in the extreme cases of product and maximally entangled quantum states, and the violation of a Bell-type inequality.

DOI
10.1103/physreva.62.012101

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We examine interference phenomena involving entangled pairs of quantum coherent states. Two-coherent-state interferometry, which can involve macroscopic numbers of photons, is shown to share several characteristics of two-particle quantum interferometry in such a macroscopic limit. These include the complementarity between one-system and two-system interference visibilities in the extreme cases of product and maximally entangled quantum states, and the violation of a Bell-type inequality.
Neutron interferometry provides a powerful tool to investigate particle and wave features in quantum physics. Single particle interference phenomena can be observed with neutrons and the entanglement of degrees of freedom, i.e., contextuality can be verified and used in further experiments. Entanglement of two photons, or atoms, is analogous to a double slit diffraction of a single photon, neutron or atom. Neutrons are proper tools for testing quantum mechanics because they are massive, they couple to electromagnetic fields due to their magnetic moment, they are subject to all basic interactions, and they are sensitive to topological effects, as well. The 4π-symmetry of spinor wave functions, the spin-superposition law and many topological phenomena can be made visible, thus showing interesting intrinsic features of quantum physics. Related experiments will be discussed. Deterministic and stochastic partial absorption experiments can be described by Bell-type inequalities. Neutron interferometry experiments based on post-selection methods renewed the discussion about quantum non-locality and the quantum measuring process. It has been shown that interference phenomena can be revived even when the overall interference pattern has lost its contrast. This indicates a persisting coupling in phase space even in cases of spatially separated Schrödinger cat-like situations. These states are extremely fragile and sensitive against any kind of fluctuations and other decoherence processes. More complete quantum experiments also show that a complete retrieval of quantum states behind an interaction volume becomes impossible in principle, but where and when a collapse of the wave-field occurs depends on the level of experiment.
Progress in multiphoton interferometry allows us now to observe even six-photon interference of a very high contrast. Also, it is possible to observe interference of two photons originating from truly independent sources. Non-classical effects may violate Bell inequalities, or reveal quantum non-separability. Methods of producing non-classical states of few photons, and the detection of entanglement via Bell inequalities, or via nor-separability criteria will be presented. Implications of violations of Bell inequalities will be discussed, with a special stress on over-interpretations of this fact.
Entanglement of two photons, or atoms is a complementary situation to a double slit situation of a single photon, neutron or atom. With neutrons single particle interference phenomena can be observed and the “entanglement of degrees of freedom”, i.e. contextuality can be verified. In this respect, neutrons are proper tools for testing quantum mechanics because they are massive, they couple to electromagnetic fields due to their magnetic moment and they are subject to all basic interactions, and they are sensitive to topological effects, as well. Related experiments will be discussed. Deterministic and stochastic partial absorption experiments can be described by Bell‐type inequalities. Recent neutron interferometry experiments based on postselection methods renewed the discussion about quantum nonlocality and the quantum measuring process. It has been shown that interference phenomena can be revived even when the overall interference pattern has lost its contrast. This indicates a persisting coupling in phase space even in cases of spatially separated Schrödinger cat‐like situations. These states are extremely fragile and sensitive against any kind of fluctuations and other decoherence processes. More complete quantum experiments also show that a complete retrieval of quantum states behind an interaction volume becomes impossible in principle.
An approach has been proposed to calculate the coherence and interference characteristics of macroscopic quantum systems. A general method of the analysis of two-particle quantum systems based on the Schmidt decomposition has been presented to analyze quantum entanglement between the system and environment, as well as the coherence of interfering alternatives. Simple relations have been obtained between the coherence, interference visibility, and Schmidt number. The developed method has been applied to multimode quantum states of Schrödinger’s cat.