The Quantum Josephson Hamiltonian In The Phase Representation

Details The Quantum Josephson Hamiltonian In The Phase Representation The Quantum Josephson Hamiltonian In The Phase Representation

2000-11-26

arxiv.org/abs/cond-mat/0011440v1

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

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 $\cos 2 \phi$ term in the Josephson potential, and also to the overcompleteness of the representation (the phase $\phi$ being the relative phase between the two condensates). We thereby unify the Boson Hubbard and Quantum Phase models.

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