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Physical Review A

Creating macroscopic quantum superpositions with Bose-Einstein condensates

Dan Gordon, Craig M. Savage

Published Jun 1, 1999• 132 citations
Publisher

Abstract

We use a simple two-mode model to investigate the quantum state dynamics of a two-species Bose-Einsten condensate, such as that produced in recent experiments, undergoing weak Josephson coupling. We find that in certain parameter regimes the quantum state of the system evolves into a macroscopic superposition of two states which differ in the atom number difference between the two species. The ``size'' of the macroscopic superposition created by such a method can be varied by adjusting the Josephson coupling coefficient, and is found to be near maximal for a certain critical value of this coefficient.

DOI
10.1103/physreva.59.4623

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We use a simple two-mode model to investigate the quantum state dynamics of a two-species Bose-Einsten condensate, such as that produced in recent experiments, undergoing weak Josephson coupling. We find that in certain parameter regimes the quantum state of the system evolves into a macroscopic superposition of two states which differ in the atom number difference between the two species. The ``size'' of the macroscopic superposition created by such a method can be varied by adjusting the Josephson coupling coefficient, and is found to be near maximal for a certain critical value of this coefficient.
We present a scheme to prepare generalized coherent states in a system with two species of Bose-Einstein condensates. First, within the two-mode approximation, we demonstrate that a Schrodinger cat-like can be dynamically generated and, by controlling the Josephson-like coupling strength, the number of coherent states in the superposition can be varied. Later, we analyze numerically the dynamics of the whole system when interspecies collisions are inhibited. Variables such as fractional population, Mandel parameter and variances of annihilation and number operators are used to show that the evolved state is entangled and exhibits sub-Poisson statistics.
We give a theoretical analysis of the experimental scheme for creating macroscopic superpositions of different superfluid flow states with Bose-Einstein condensates trapped in an optical lattice [J. Dunningham et al., Phys. Rev. A 74, 023601 (2006)]. It is shown that a class of macroscopic superposition states can be created for an arbitrary number of particles by dynamical evolution with a properly prepared initial state. When the number of particles is a multiple of 3, such states are exactly reduced to macroscopic superpositions of different superfluid flow states.
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.
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.
We present a straightforward scheme for creating macroscopic superpositions of different superfluid flow states of Bose-Einstein condensates trapped in optical lattices. This scheme has the great advantage that all the techniques required are within the reach of current experiments. Furthermore, the relative difficulty of creating superpositions scales favorably with the size of the state. This means that this scheme may be well suited to creating superpositions involving large numbers of particles. Such states may have interesting technological applications such as making quantum-limited measurements of angular momentum.