Evolution of squeezed states under the Fock-Darwin Hamiltonian

Details Evolution of squeezed states under the Fock-Darwin Hamiltonian Evolution of squeezed states under the Fock-Darwin Hamiltonian

2009-05-21

arxiv.org/abs/0905.3547v1

Phys. Rev. A 80, 053401 (2009)

Physics

Condensed Matter

Quantum Gases

Scientific paper

10.1103/PhysRevA.80.053401

We develop a complete analytical description of the time evolution of squeezed states of a charged particle under the Fock-Darwin Hamiltonian and a time-dependent electric field. This result generalises a relation obtained by Infeld and Pleba\'nski for states of the one-dimensional harmonic oscillator. We relate the evolution of a state-vector subjected to squeezing to that of state which is not subjected to squeezing and for which the time-evolution under the simple harmonic oscillator dynamics is known (e.g. an eigenstate of the Hamiltonian). A corresponding relation is also established for the Wigner functions of the states, in view of their utility in the analysis of cold-ion experiments. In an appendix, we compute the response functions of the FD Hamiltonian to an external electric field, using the same techniques as in the main text.

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