Two-mode generalization of the Jaynes-Cummings and Anti-Jaynes-Cummings models

Abstract

We introduce two generalizations of the Jaynes-Cummings (JC) model for two modes of oscillation. The first model is formed by two Jaynes-Cummings interactions, while the second model is written as a simultaneous Jaynes-Cummings and Anti-Jaynes-Cummings (AJC) interactions. We study some of its properties and obtain the energy spectrum and eigenfunctions of these models by using the tilting transformation and the Perelomov number coherent states of the two-dimensional harmonic oscillator. Moreover, as physical applications, we connect these new models with two important and novelty problems: The relativistic non-degenerate parametric amplifier and the relativistic problem of two coupled oscillators.

arXiv comment16 pages

References in corpus (22)

• Quantum simulation of the Dirac equation
• 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
• Ultrafast Quantum Gates in Circuit QED
• Quantum Simulations with Cold Trapped Ions
• Chirality Quantum Phase Transition in the Dirac oscillator
• Exact solution of the two-dimensional Dirac oscillator
• Relativistic quantum mechanics with trapped ions
• Two-photon entanglement in multi-qubit bi-directional waveguide QED
• Three-dimensional Dirac oscillator in a thermal bath
• Quantum phase transitions in the noncommutative Dirac Oscillator
• How Nonlinear Optical Effects degrade Hong-Ou-Mandel Like Interference
• Quantum phase transitions of the Dirac oscillator in a minimal length scenario
• The SU(1,1) Perelomov number coherent states and the non-degenerate parametric amplifier
• Graphene physics via the Dirac oscillator in (2+1) dimensions
• A generalized Jaynes-Cummings model: The relativistic parametric amplifier and a single trapped ion
• Coherent states for the two-dimensional Dirac-Moshinsky oscillator coupled to an external magnetic field
• Mapping of the 2+1 q-deformed Dirac oscillator onto the q-deformed Jaynes-Cummings model: It's non-relativistic limit and Zitterbewegung effect
• The calculation of the thermal properties of graphene under a magnetic field via the two-dimensional Dirac oscillator
• $SU(1,1)$ and $SU(2)$ Perelomov number coherent states: algebraic approach for general systems
• Quantum phase transition in the chirality of the (2+1)-dimensional Dirac oscillator

Cited by in corpus (10)

• Phase-space representation of Landau and electron coherent states for uniaxially strained graphene
• Algebraic solution and coherent states for the Dirac oscillator interacting with a topological defect
• Exploring Supersymmetry: Interchangeability Between 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
• Algebraic approach and Berry phase of a Hamiltonian with a general $SU(1,1)$ symmetry
• $Sp(4,R)$ algebraic approach of the most general Hamiltonian of a two-level system in two-dimensional geometry
• Modular Operators and Entanglement in Supersymmetric Quantum Mechanics
• 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