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arXiv:1311.5940 · Entropy

Genuine Tripartite Entanglement and Nonlocality in Bose-Einstein Condensates by Collective Atomic Recoil

Samanta Piano, Gerardo Adesso

Published May 17, 2013• 7 citations
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Abstract

We study a system represented by a Bose-Einstein condensate interacting with a cavity field in presence of a strong off-resonant pumping laser. This system can be described by a three-mode Gaussian state, where two are the atomic modes corresponding to atoms populating upper and lower momentum sidebands and the third mode describes the scattered cavity field light. We show that, as a consequence of the collective atomic recoil instability, these modes possess a genuine tripartite entanglement that increases unboundedly with the evolution time and is larger than the bipartite entanglement in any reduced two-mode bipartition. We further show that the state of the system exhibits genuine tripartite nonlocality, which can be revealed by a robust violation of the Svetlichny inequality when performing displaced parity measurements. Our exact results are obtained by exploiting the powerful machinery of phase-space informational measures for Gaussian states, which we briefly review in the opening sections of the paper.

DOI
10.3390/e15051875

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We study a system represented by a Bose-Einstein condensate interacting with a cavity field in presence of a strong off-resonant pumping laser. This system can be described by a three-mode Gaussian state, where two are the atomic modes corresponding to atoms populating upper and lower momentum sidebands and the third mode describes the scattered cavity field light. We show that, as a consequence of the collective atomic recoil instability, these modes possess a genuine tripartite entanglement that increases unboundedly with the evolution time and is larger than the bipartite entanglement in any reduced two-mode bipartition. We further show that the state of the system exhibits genuine tripartite nonlocality, which can be revealed by a robust violation of the Svetlichny inequality when performing displaced parity measurements. Our exact results are obtained by exploiting the powerful machinery of phase-space informational measures for Gaussian states, which we briefly review in the opening sections of the paper.
We study a system represented by a Bose-Einstein condensate interacting with a cavity field in presence of a strong off-resonant pumping laser. This system can be described by a three-mode Gaussian state, where two are the atomic modes corresponding to atoms populating upper and lower momentum sidebands and the third mode describes the scattered cavity field light. We show that, as a consequence of the collective atomic recoil instability, these modes possess a genuine tripartite entanglement that increases unboundedly with the evolution time and is larger than the bipartite entanglement in any reduced two-mode bipartition. We further show that the state of the system exhibits genuine tripartite nonlocality, which can be revealed by a robust violation of the Svetlichny inequality when performing displaced parity measurements. Our exact results are obtained by exploiting the powerful machinery of phase-space informational measures for Gaussian states, which we briefly review in the opening sections of the paper.
We investigate the genuine multipartite nonlocality of three-mode Gaussian states of continuous variable systems. For pure states, we present a simplified procedure to obtain the maximum violation of the Svetlichny inequality based on displaced parity measurements, and we analyze its interplay with genuine tripartite entanglement measured via Rényi-2 entropy. The maximum Svetlichny violation admits tight upper and lower bounds at fixed tripartite entanglement. For mixed states, no violation is possible when the purity falls below 0.86. We also explore a set of recently derived weaker inequalities for three-way nonlocality, finding violations for all tested pure states. Our results provide a strong signature for the nonclassical and nonlocal nature of Gaussian states despite their positive Wigner function, and lead to precise recipes for its experimental verification.
We present a quantum description of the interaction between a Bose-Einstein condensate and a single-mode quantized radiation field in the presence of a strong far-off-resonant pump laser. In the linear regime, the atomic medium is described approximately by two momentum states coupled to the radiation mode. We calculate the evolution of the operators in the Heisenberg picture and their expectation values, such as average and variance of the occupation numbers, atom-atom and atom-field correlations, and two-mode squeezing parameters. Then, we disentangle the evolution operator and obtain the exact evolution of the state vector in the linear regime. This allows us to demostrate that the system can be atom-atom or atom-field thermally entangled. We define the quasiclassical and the quantum recoil limits, for which explicit expressions of the average population numbers are obtained.
We propose a novel scheme to generate and manipulate bipartite and tripartite entanglement and Bell nonlocality in a closed-loop three-mode optomechanical system, where two optical modes are simultaneously coupled to a mechanical mode via typical optomechanical interactions and also coupled to each other through field transmission. This configuration gives rise to a phase-sensitive coupling, in which the relative phase directly controls the population distribution between two optical modes, enabling coherent redistribution of quantum correlations. By tuning this relative phase, we achieve deterministic switching of bipartite entanglement between two optical-mechanical pairs, as well as tunable genuine tripartite entanglement among three modes. Employing the displaced-parity measurement, we construct both the bipartite and tripartite Bell inequalities in phase space and observe maximal violations of approximately 2.322.322.32 and 333, respectively, which coincide exactly with the values achievable for ideal bipartite and tripartite Einstein-Podolsky-Rosen states. Counterintuitively, we find that the tripartite Bell nonlocality can persist even when the genuine tripartite entanglement is absent, providing deeper insight into the relationship between these two types of quantum correlations. Furthermore, we systematically analyze the effects of mechanical dissipation and thermal noise, identifying the parameter regions where Bell violation survives under realistic experimental conditions. Our results establish a comprehensive framework for generating, controlling, and verifying multipartite quantum correlations, paving the way towards phase-tunable quantum networks and noise-resilient tests of quantum foundations.