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arXiv:1006.2556 · Molecular Physics

Dynamical studies of macroscopic superposition states: phase engineering of controlled entangled number states of Bose–Einstein condensates in multiple wells

Mary Ann Leung, Khan W. Mahmud, William P. Reinhardt

Published May 9, 2012• 6 citations
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Abstract

We provide an experimentally viable scheme for the generation of entangled number states of Bose–Einstein condensates in multiple wells with cyclic pairwise connectivity. The condensate ground state in a multiple well trap can self-evolve, when appropriately phase engineered with specific phase differences between the neighbouring wells, to a macroscopic superposition state with controllable entanglement – as for example the multiple well generalization of double well NOON states. We demonstrate, through numerical simulations, the creation of entangled states of small numbers of particles in three and four wells and then explore the creation of entangled states where there are larger numbers of particles or a larger number of wells. In the four well case we study a novel, initially unexpected, type of entanglement produced as the particle numbers, or interaction strengths, increase.

DOI
10.1080/00268976.2012.681309

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We provide an experimentally viable scheme for the generation of entangled number states of Bose–Einstein condensates in multiple wells with cyclic pairwise connectivity. The condensate ground state in a multiple well trap can self-evolve, when appropriately phase engineered with specific phase differences between the neighbouring wells, to a macroscopic superposition state with controllable entanglement – as for example the multiple well generalization of double well NOON states. We demonstrate, through numerical simulations, the creation of entangled states of small numbers of particles in three and four wells and then explore the creation of entangled states where there are larger numbers of particles or a larger number of wells. In the four well case we study a novel, initially unexpected, type of entanglement produced as the particle numbers, or interaction strengths, increase.
We provide a scheme for the generation of controlled entangled number states of Bose-Einstein condensates in multiple wells, and also provide a novel method for the creation of squeezed states without severe adiabatic constraints on barrier heights. The condensate in a multiple well trap can be evolved, starting with a specific initial phase difference between the neighboring wells, to a tunable entangled state or a squeezed state. We propose a general formula for the initial phase difference between the neighboring wells that is valid for any number of wells, even and odd.
We propose a model for the creation of entangled number states (Schrödinger cat states) of a Bose–Einstein condensate in a double well through simple phase engineering. We show that a π-phase imprinted condensate in a double well evolves, with a simultaneous change of barrier height, to number states with well defined and controlled entanglement. The cat state generation is understood in terms of the underlying classical phase space dynamics of a π-phase displaced coherent state put at the hyperbolic fixed point of the separatrix of a physical pendulum. The extremity and sharpness of the final cat state is determined by the initial barrier height and the rate at which it is ramped during the evolution.
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We consider how macroscopic quantum superpositions may be created from arrays of Bose–Einstein condensates. We study a system of three condensates in Fock states, all with the same number of atoms and show that this has the form of a highly entangled superposition of different quasi-momenta. We then show how, by partially releasing these condensates and detecting an interference pattern where they overlap, it is possible to create a macroscopic superposition of different relative phases for the remaining portions of the condensates. We discuss methods for confirming these superpositions.