The Quantum Josephson Hamiltonian In The Phase Representation

J. R. Anglin; P. Drummond; A. Smerzi

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arXiv · cond-mat/0011440

The Quantum Josephson Hamiltonian In The Phase Representation

J. R. Anglin·P. Drummond·A. Smerzi

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Abstract

The quantum Josephson Hamiltonian of two weakly linked Bose-Einstein condensates is written in an overcomplete phase representation, thus avoiding the problem of defining a Hermitian phase operator. We discuss the limit of validity of the standard, non-rigorous Mathieu equation, due to the onset of a higher order $\cos 2 ϕ$ term in the Josephson potential, and also to the overcompleteness of the representation (the phase $ϕ$ being the relative phase between the two condensates). We thereby unify the Boson Hubbard and Quantum Phase models.

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J. R. Anglin, P. Drummond, A. Smerzi. 2000-11-26. The Quantum Josephson Hamiltonian In The Phase Representation. https://arxiv.org/abs/cond-mat/0011440

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