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arXiv:1907.04996 · Physical Review A

Decoherence and visibility enhancement in multipath interference

Sandeep Mishra, Anu Venugopalan, Tabish Qureshi

Published Oct 28, 2019• 31 citations
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Abstract

We theoretically analyze the observations reported in a four-path quantum interference experiment via multiple-beam Ramsey interference [Phys. Rev. Lett. 86, 559 (2001)]. In this experiment, a selective scattering of photons from just one interfering path causes decoherence. However, contrary to expectations, there is an increase in the contrast of the interference pattern, demonstrating that path selective decoherence can not only lead to a decrease but, under certain conditions, lead to an increase of the fringe contrast. Here we explain this seemingly counterintuitive effect based on a model for a multipath interference, with four to six slits, in the presence of decoherence. The effect of the environment is modeled via a coupling to a bath of harmonic oscillators. When decoherence is introduced in one of the multiple paths, an enhancement in fringe contrast is seen under certain conditions. A similar effect is shown to appear if instead of path-selective decoherence, a selective path detector is introduced. Our analysis points to the fact that while traditional fringe visibility captures the wave nature in the two-path case, it can fail in multipath situations. We explain the enhancement of fringe visibility and also show that quantum coherence based on the ${l}_{1}$ norm of coherence, in contrast to traditional visibility, remains a good quantifier of wave nature, even in such situations. The enhancement of fringe contrast in the presence of environmental decoherence underscores the limitations of traditional visibility as a good measure for wave nature in quantifying complementarity and also makes it an unlikely candidate for quantifying decoherence. Our analysis could lead to better insight in ways to quantify decoherence in multipath interference and in studies that seek to exploit quantum superpositions and quantum coherence for quantum information applications.

DOI
10.1103/physreva.100.042122

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We theoretically analyze the observations reported in a four-path quantum interference experiment via multiple-beam Ramsey interference [Phys. Rev. Lett. 86, 559 (2001)]. In this experiment, a selective scattering of photons from just one interfering path causes decoherence. However, contrary to expectations, there is an increase in the contrast of the interference pattern, demonstrating that path selective decoherence can not only lead to a decrease but, under certain conditions, lead to an increase of the fringe contrast. Here we explain this seemingly counterintuitive effect based on a model for a multipath interference, with four to six slits, in the presence of decoherence. The effect of the environment is modeled via a coupling to a bath of harmonic oscillators. When decoherence is introduced in one of the multiple paths, an enhancement in fringe contrast is seen under certain conditions. A similar effect is shown to appear if instead of path-selective decoherence, a selective path detector is introduced. Our analysis points to the fact that while traditional fringe visibility captures the wave nature in the two-path case, it can fail in multipath situations. We explain the enhancement of fringe visibility and also show that quantum coherence based on the l1{l}_{1}l1​ norm of coherence, in contrast to traditional visibility, remains a good quantifier of wave nature, even in such situations. The enhancement of fringe contrast in the presence of environmental decoherence underscores the limitations of traditional visibility as a good measure for wave nature in quantifying complementarity and also makes it an unlikely candidate for quantifying decoherence. Our analysis could lead to better insight in ways to quantify decoherence in multipath interference and in studies that seek to exploit quantum superpositions and quantum coherence for quantum information applications.
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.
It is well known that fringe contrast is not a good quantifier of the wave nature of a quanton in multipath interference. An alternative interference visibility, based on the Hilbert-Schmidt coherence is introduced. It is demonstrated that this visibility is a good quantifier of wave nature and can be experimentally measured. A generalized path predictability is introduced, which reduces to the predictability of Greenberger and Yasin for the case of two paths. In a multipath, which-way interference experiment, the new visibility, the predictability, and the III concurrence (quantifying the entanglement between the quanton and the path detector) are shown to follow a tight triality relation. It quantifies the essential role that entanglement plays in multipath quantum complementarity.
We have scattered photons from an interfering path of a multiple beam Ramsey interference experiment realized with a cesium atomic beam. It is demonstrated that in multiple beam interference the decoherence from photon scattering cannot only lead to a decrease but, under certain conditions, also to an increase of the Michelson fringe contrast. In all cases, the atomic quantum state loses information with photon scattering, as "which-path" information is carried away by the photon field. We outline an approach to quantify this which-path information from observed fringe signals, which allows for an appropriate measure of decoherence in multiple path interference.
We derive a generalized wave-particle duality relation for arbitrary multipath quantum interference phenomena. Beyond the conventional notion of the wave nature of a quantum system, i.e., the interference fringe visibility, we introduce a quantifier as the normalized quantum coherence, recently defined in the framework of quantum information theory. To witness the particle nature, we quantify the path distinguishability or the which-path information based on unambiguous quantum state discrimination. Then, the Bohr complementarity principle for multipath quantum interference can be stated as a duality relation between the quantum coherence and the path distinguishability. For two-path interference, the quantum coherence is identical to the interference fringe visibility, and the relation reduces to the well-known complementarity relation. The duality relation continues to hold in the case where mixedness is introduced due to possible decoherence effects.
The interference observed for a quanton, traversing more than one path, is believed to characterize its wave nature. Conventionally, the sharpness of interference has been quantified by its visibility or contrast, as defined in optics. Based on this visibility, wave-particle duality relations have been formulated for two-path interference. However, as one generalizes the situation to multi-path interference, it is found that conventional interference visibility is not a good quantifier. A recently introduced measure of quantum coherence has been shown to be a good quantifier of the wave nature. The subject of quantum coherence, in relation to the wave nature of quantons and to interference visibility, is reviewed here. It is argued that coherence can be construed as a more general form of interference visibility, if the visibility is measured in a different manner, and not as contrast. Quanta 2019; 8: 24–35.
Wave-particle duality in multipath interference is fraught with issues despite substantial progress in recent years. It was experimentally shown that in certain specific conditions, getting path information in a multipath experiment can actually increase the visibility of interference. As a result, it was argued that in multipath interference experiments, visibility of interference and which-path information are not always complementary observables. In the present paper, an alternative wave-particle duality relation is presented, based on a sum of visibilities of interference from individual pairs of paths. This relation is always respected, even in the kinds of specific situations mentioned above. This sum of visibilities turns out to be related to a recently introduced measure of coherence. As one of the consequences, it provides an alternative way of experimentally measuring coherence in a multipath interference experiment. As another consequence, this relation suggests a simple way of measuring path-distinguishability in multipath interference. In addition, it resolves several outstanding issues concerning wave-particle duality in multipath interference.