Quantum state of two trapped Bose-Einstein condensates with a Josephson coupling

TL;DR

This paper analyzes the quantum state of two coupled Bose-Einstein condensates, revealing how atom number and phase squeezing depend on physical parameters, with implications for quantum control and entanglement.

Contribution

It introduces a novel representation of the two-condensate quantum state using a Wigner-like distribution on the Bloch sphere and explores phase squeezing regimes.

Findings

Number of atoms affects squeezing in the number difference.

Phase squeezing occurs for weaker interactions in negative scattering length regimes.

Asymmetric traps also exhibit phase squeezing.

Abstract

We consider the precise quantum state of two trapped, coupled Bose Einstein condensates in the two-mode approximation. We seek a representation of the state in terms of a Wigner-like distribution on the two-mode Bloch sphere. The problem is solved using a self-consistent rotation of the unknown state to the south pole of the sphere. The two-mode Hamiltonian is projected onto the harmonic oscillator phase plane, where it can be solved by standard techniques. Our results show how the number of atoms in each trap and the squeezing in the number difference depend on the physical parameters. Considering negative scattering lengths, we show that there is a regime of squeezing in the relative phase of the condensates which occurs for weaker interactions than the superposition states found by Cirac et al% (quant-ph/9706034, 13 June 1997). The phase squeezing is also apparent in mildly asymmetric trap configurations.