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arXiv:quant-ph/0011006 · Journal of Optics B Quantum and Semiclassical Optics

Entanglement of coherent states and decoherence*

Radim Filip, Jaroslav Řeháček, Miloslav Dušek

Published Sep 27, 2001• 12 citations
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Abstract

The possibility of producing entangled superpositions of strong coherent states is discussed. A recent proposal by Howell and Yeazell (2000 Phys. Rev. A 62 012102) of a device that entangles two strong coherent states is modified. It is shown that the modified scheme can generate non-classical states that violate Bell inequality. Moreover, a detailed analysis of the effect of losses and decoherence on the degree of entanglement is accomplished. It reveals the high sensitivity of the device to any disturbances and the fragility of generated states.

DOI
10.1088/1464-4266/3/5/310

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The possibility of producing entangled superpositions of strong coherent states is discussed. A recent proposal by Howell and Yeazell (2000 Phys. Rev. A 62 012102) of a device that entangles two strong coherent states is modified. It is shown that the modified scheme can generate non-classical states that violate Bell inequality. Moreover, a detailed analysis of the effect of losses and decoherence on the degree of entanglement is accomplished. It reveals the high sensitivity of the device to any disturbances and the fragility of generated states.
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We review entangled coherent state research since its first implicit use in 1967 to the present. Entangled coherent states are important to quantum superselection principles, quantum information processing, quantum optics and mathematical physics. Despite their inherent fragility, entangled coherent states have been produced in a conditional propagating-wave quantum optics realization. Fundamentally the states are intriguing because they entangle the coherent states, which are in a sense the most classical of all states of a dynamical system. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Coherent states: mathematical and physical aspects'.
The Talbot effect in quantum physics is known to produce intricate patterns in the probability distribution of a particle, known as ``quantum carpets,'' corresponding to the revival and replication of the initial wave function. Recently, it was shown that one can encode a DDD-level qudit in such a way that the Talbot effect can be used to process the DDD-dimensional quantum information [Far\'{\i}as et al., Phys. Rev. A 91, 062328 (2015)]. Here we introduce a scheme to produce free-propagating ``entangled quantum carpets'' with pairs of photons produced by spontaneous parametric down-conversion. First we introduce an optical device that can be used to synthesize arbitrary superposition states of Talbot qudits. Sending spatially entangled photon pairs through a pair of these devices produces an entangled pair of qudits. As an application, we show how the Talbot effect can be used to test a DDD-dimensional Bell inequality. Numerical simulations show that violation of the Bell inequality depends strongly on the amount of spatial correlation in the initial two-photon state. We briefly discuss how our optical scheme might be adapted to matter wave experiments.