Nonlinear optical effects on the atom-field interaction based on the nonlinear coherent states approach

Abstract

In this paper, to study the effects of a nonlinear medium on the atom-field interaction, we use the nonlinear coherent states approach. For this purpose, we choose the two-mode cross-Kerr as the our nonlinear optical phenomena and with the use of it's algebra, we show that it can be described equivalently by a deformed oscillator algebra and also, by a deformed (su(2)) algebra. Then, we construct the associated coherent states and investigate their statistical properties. After that, as an example of applicability of the constructed two-mode nonlinear coherent states, we investigate the nonlinear effects of the medium on the dynamics of atom-field interaction within the framework of the coherent states. By using the time-dependent Schrödinger equation, we first obtain the atom-field state and then study the effect of the nonlinear medium on the occupation probabilities of the atomic levels. In the following, we consider the relation between the revival time of the atomic occupation probabilities and the nonlinear parameter of the medium. Then, to study the nonlinear effects on the dynamical properties of the cavity field, we consider photon distribution, correlation function, Mandel parameters of the field, the von Neumann entropy and the squeezing. Particularly, the nonlinearity of the media on the nonclassical properties of two modes is clarified.

arXiv comment13 pages, 17 figures

References in corpus (21)

• The Quantum Internet
• Measurement of conditional phase shifts for quantum logic
• A gravitational wave observatory operating beyond the quantum shot-noise limit: Squeezed light in application
• Quantum Imaging with Undetected Photons
• f-Oscillators and Nonlinear Coherent States
• Quantum Metrology for Gravitational Wave Astronomy
• Infrared Spectroscopy with Visible Light
• First Long-Term Application of Squeezed States of Light in a Gravitational-Wave Observatory
• Generation of Continuous Variable Einstein-Podolsky-Rosen Entanglement via the Kerr Nonlinearity in an Optical Fibre
• A symmetry analyser for non-destructive Bell state detection using EIT
• Spontaneous parametric down-conversion
• Realisation of the first sub shot noise wide field microscope
• Deterministic quantum nonlinear optics with single atoms and virtual photons
• Photon-added coherent states as nonlinear coherent states
• The Construction of Some Important Classes of Generalized Coherent states: The Nonlinear Coherent States Method
• Quantum Nonlinear Optics without Photons
• Cross Kerr Effect Induced by Coupled Josephson Qubits in Circuit Quantum Electrodynamics
• An Introduction to the Quantum Theory of Nonlinear Optics
• Geometric approach to nonlinear coherent states using the Higgs model for harmonic oscillator
• Finite temperature Casimir effect in the presence of nonlinear dielectrics
• Energy and momentum entanglement in parametric downconversion