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arXiv:1008.0314 · Physical Review A

Reproducible mesoscopic superpositions of Bose-Einstein condensates and mean-field chaos

Bettina Gertjerenken, Stephan Arlinghaus, Niklas Teichmann, Christoph Weiß

Published Aug 30, 2010• 14 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.82.023620

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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.
A Bose-Einstein condensate in a tilted double-well potential under the influence of time-periodic potential differences is investigated in the regime where the mean-field (Gross-Pitaevskii) dynamics become chaotic. For some parameters near stable regions, even averaging over several condensate oscillations does not remove the differences between mean-field and N-particle results. While introducing decoherence via piecewise deterministic processes reduces those differences, they are due to the emergence of mesoscopic entangled states in the chaotic regime.
For a Bose–Einstein condensate in a double-well potential, time-periodic shaking can lead to the emergence of non-classical mesoscopic superpositions on very short timescales. It is suggested to experimentally detect these deviations from mean-field (Gross–Pitaevskii) behaviour by investigating both the variance of the particle number and the interference pattern. The disappearance of the interference pattern followed by its reappearance a short time later could serve as an experimental signature of mesoscopic entanglement.
The properties of an atomic Bose-Einstein condensate in a double-well potential are investigated through a two-mode analysis. An analytic solution for the semiclassical tunnelling and self-trapping dynamics is compared with numerical simulations of the quantum dynamics, which exhibit collapses and revivals for a closed system. A continuous non-destructive measurement technique to monitor the Josephson tunnelling oscillations is presented, in which the condensate in one well dispersively shifts the phase of a coherent probe beam in proportion to atom-number. The evolution of the resulting homodyne photocurrent and Bloch Q distributions shows that oscillations develop even when the initial state possesses phase symmetry. The conditional dynamics of the condensate which result from measurement back-action also appear in certain semiclassical formulations. The homodyne measurement technique is incorporated into a proposed weak-force detector. A maximally entangled initial state, which is the ground state for a double condensate with strong attractive atomic interactions, enables a high-precision measurement. The dynamics of quantum many-body multimode systems of interacting bosons are simulated using phase-space methods. The use of the Wigner technique predicts novel noise effects in fibre solitons. The positive-P representation is used to simulate the formation of mesoscopic Bose-Einstein condensates via evaporative cooling in three dimensional atom traps. The results indicate highly non-classical behaviour near the critical point, and provide evidence for the spontaneous formation of vortices. Comparisons with corresponding mean-field calculations reveal large differences between the semiclassical and fully quantum results. Finally, the possibility of future progress with alternative phase-space methods is considered.
We present a quantum phase-space model of the Bose-Einstein condensate (BEC) in a double-well potential. In a quantum two-mode approximation we examine the eigenvectors and eigenvalues and find that the energy correlation diagram indicates a transition from a delocalized to a fragmented regime. Phase-space information is extracted from the stationary quantum states using the Husimi distribution function. We show that the mean-field phase-space characteristics of a nonrigid physical pendulum arises from the exact quantum states, and that only 4--8 particles per well are needed to reach the semiclassical limit. For a driven double-well BEC, we show that the classical chaotic dynamics is manifest in the dynamics of the quantum states. Phase-space analogy also suggests that a $\ensuremath{\pi}$ phase-displaced wave packet put on the unstable fixed point on a separatrix bifurcates to create a superposition of two pendulum rotor states---a macroscopic superposition state of BEC. We show that the choice of initial barrier height and ramping, following a $\ensuremath{\pi}$ phase imprinting on the condensate, can be used to generate controlled entangled number states with tunable extremity and sharpness.