Collapses and revivals of entanglement in phase space in an optomechanical cavity
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Collapses and revivals of entanglement in phase space in an optomechanical cavity J. Rodríguez-Lima, L. M. Arévalo Aguilara Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Apartado postal 1152, 7200 Puebla, Pue., Mexico Received: 20 November 2019 / Accepted: 15 April 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract We analyse the dynamics of an optomechanical cavity considering two modes of the electromagnetic field and a mechanical resonator. As a result of this interaction, the initial non-entangled state evolves into a final entangled state. In this work, we use the Q(α) function to observe the behavior of the system in the phase space, finding that such entanglement is a function of time showing collapses and revivals. To carry out this analysis, we use the generalization of the single-party Q(α) function towards three-party systems Q(α, μ, ν) and we ascertain that the entanglement perfectly maps into the Q(α, μ, ν) function because it becomes non-separable too. To prove that the Q function accurately certifies entanglement, we compare its behaviour with the plots of the van Loock inequalities. Additionally, as the optomechanical systems were proposed to carry out quantum information tasks, we investigate the kind of phase gate that is produced when we keep the Kerr term that arises in the evolution operator.
1 Introduction Quantum entanglement has generated great interest and significance due to its implications for the development of quantum physics and its potential applications in the field of quantum information and quantum computing [1,2]. Nowadays, the quantification of entanglement for bipartite discrete variables systems has been developed to such extent that currently there are many well-understood entanglement measures, for both pure and mixed states, like the concurrence [3]. However, for three and more systems the quantification and properties of entanglement become more complex and unfortunately there is not a fully fledged theory yet, especially for mixed states, although some important advances have been reached [4]. One of the first issues about the entanglement of three systems was whether or not system 1 which is entangled with system 2 could share any entanglement with a third system, and this has opened the possibility to introduce the concept of residual entanglement and the 3-tangle measure, √ which assigns a maximum entanglement for the GHZ states (|G H Z = (|000+|111)/ 2) √ and paradoxically assigns zero for the W states (|W = (|001+|010+|100)/ 3) [4]. This result shows the complexity and problems that arise when using well-developed entanglement
a e-mail: [email protected] (corresponding author)
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measures for two-party system on three-party systems. If we consider continuous variables, the complexity raises considerably. Moreover, the generation of entanglement in new physical systems is an activ
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