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arXiv:0707.4061 · Laser Physics Letters

Generation of mesoscopic superpositions of a binary Bose-Einstein condensate in a slightly asymmetric double well

Christoph Weiß, Niklas Teichmann

Published Sep 6, 2007• 9 citations
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Abstract

A previous publication [1] suggested to coherently generate mesoscopic superpositions of a two-component Bose-Einstein condensate in a double well under perfectly symmetric conditions. However, already tiny asymmetries can destroy the entanglement properties of the ground state. Nevertheless, even under more realistic conditions, the scheme is demonstrated numerically to generate mesoscopic superpositions.

DOI
10.1002/lapl.200710078

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A previous publication [1] suggested to coherently generate mesoscopic superpositions of a two-component Bose-Einstein condensate in a double well under perfectly symmetric conditions. However, already tiny asymmetries can destroy the entanglement properties of the ground state. Nevertheless, even under more realistic conditions, the scheme is demonstrated numerically to generate mesoscopic superpositions.
In a parameter regime for which the mean-field (Gross-Pitaevskii) dynamics becomes chaotic, mesoscopic quantum superpositions in phase space can occur in a double-well potential, which is shaken periodically. For experimentally realistic initial states, such as the ground state of some 100 atoms, the emergence of mesoscopic quantum superpositions in phase space is investigated numerically. It is shown to be reproducible, even if the initial conditions change slightly. Although the final state is not a perfect superposition of two distinct phase states, the superposition is reached an order of magnitude faster than in the case of the collapse-and-revival phenomenon. Furthermore, a generator of entanglement is identified.
A recent publication [Phys. Rev. Lett. 100, 140408 (2008)] shows that there is a relation between mean-field chaos and multi-particle entanglement for BECs in a periodically shaken double well. “Schrödingercat” like mesoscopic superpositions in phase-space occur for conditions for which the system displays mean-field chaos. In the present manuscript, more general highly-entangled states are investigated. Mean-field chaos accelerates the emergence of multi-particle entanglement; the boundaries of stable regions are particularly suited for entanglement generation.
We study analytically the generation of maximally entangled states (MESs) formed by a two-component Bose–Einstein condensate (BEC) trapped in an adiabatically driven single potential well. Under the condition of the linear interaction controlled by a driven field being much stronger than the effective nonlinear interaction between the components, MESs, as some particular cases of superpositions of spin coherent states (SSCS), may emerge periodically along with not only time evolution but also the equidifferent change of the linear coupling strength at a particular time.
We study mesoscopic superpositions of two component Bose-Einstein condensates. Atomic condensates, with long coherence times, are good systems in which to study such quantum phenomena. We show that the mesoscopic superposition states can be rapidly generated in which the atoms dispersively interact with the photon field in a cavity. We also discuss the production of compass states which are macroscopic quantum superposition states. The physical realization of mesoscopic states is important in studying decoherence and precision measurement.
We study the generation of two-mode entanglement in a two-component Bose-Einstein condensate trapped in a double-well potential. The dynamics of the system is shown to be equivalent to that of two coupled harmonic oscillators in the low excitation regime. Strong entanglement between the two components can be achieved if the interspecies interaction is sufficiently strong. In particular, the condensate constitutes a symmetric Gaussian system and hence its entanglement of formation can be measured directly by fluctuations in the quadratures of the two constituent components.