Entanglement in an expanding toroidal Bose-Einstein condensate

Abstract

Recent experiments have employed rapidly expanding toroidal Bose-Einstein condensates (BECs) to mimic the inflationary expansion in the early universe. One expected signature of the expansion in such experiments is spontaneous particle creation (of phonons) which is observable in density-density correlations. We study entanglement of these particles, which are known to result in a two-mode squeezed state. Using techniques for Gaussian states of continuous variable systems, we quantify the entanglement generated in this system, including effects such as decoherence and the use of an initially squeezed state, which can suppress and enhance entanglement, respectively. We also describe a protocol to experimentally measure the correlations entering the covariance matrix, allowing an experimental quantification of the entanglement properties of the inflationary BEC.

arXiv comment20 pages, 11 figures

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• Toward the Observation of Entangled Pairs in BEC analogue Expanding Universes
• Entanglement and correlations between local observables in de Sitter spacetime
• Analog Unruh effect of inhomogeneous one-dimensional Dirac fermions
• Mechanical cosmology: simulating scalar fluctuations in expanding Universes using synthetic mechanical lattices
• Quantum entanglement of Hawking-Partner modes in expanding cavities
• Uncertainty, von Neumann Entropy, and Squeezing in a Bipartite State of Two-Level Atoms
• Phonon Dynamics in Spherically-Curved Analog-Gravity Bose-Einstein Condensates