A generalized Jaynes-Cummings model: The relativistic parametric amplifier and a single trapped ion

Abstract

We introduce a generalization of the Jaynes-Cummings model and study some of its properties. We obtain the energy spectrum and eigenfunctions of this model by using the tilting transformation and the squeezed number states of the one-dimensional har- monic oscillator. As physical applications, we connect this new model to two important and novelty problems: the relativistic parametric amplifier and the quantum simulation of a single trapped ion.

This paper was published onder the title "A generalized Jaynes-Cummings model: The relativistic parametric amplifier and a single trapped ion"

References in corpus (4)

• Progressive field-state collapse and quantum non-demolition photon counting
• Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion
• Exact Mapping of the 2+1 Dirac Oscillator onto the Jaynes-Cummings Model: Ion-Trap Experimental Proposal
• The SU(1,1) Perelomov number coherent states and the non-degenerate parametric amplifier

Cited by in corpus (10)

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• Two-mode generalization of the Jaynes-Cummings and Anti-Jaynes-Cummings models
• Matrix diagonalization and exact solution of the k-photon Jaynes-Cummings model
• Algebraic approach to the Tavis-Cummings model with three modes of oscillation
• $Sp(4,R)$ algebraic approach of the most general Hamiltonian of a two-level system in two-dimensional geometry
• Algebraic approach and Berry phase of a Hamiltonian with a general $SU(1,1)$ symmetry
• Mapping of the 2+1 Dirac-Moshinsky Oscillator Coupled to an External Isospin Field onto Jaynes-Cummings Model
• Berry phase of the Tavis-Cummings model with three modes of oscillation
• Exact solution of the isotropic and anisotropic Hamiltonian of two coupled harmonic oscillators