Evolution of squeezed states under the Fock-Darwin Hamiltonian
arXiv:0905.3547 · doi:10.1103/PhysRevA.80.053401
Abstract
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 Plebański 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.
References in corpus (7)
- The Quantum Internet
- Squeezing as an irreducible resource
- Dense Coding for Continuous Variables
- Quantum engineering of squeezed states for quantum communication and metrology
- Quantum Benchmark for Teleportation and Storage of Squeezed States
- Orbital Magnetism and Current Distribution of Two-Dimensional Electrons under Confining Potential
- Coherent-State Approach to Two-dimensional Electron Magnetism