Quantum phase transition and Berry phase of the Dicke model in the presence of the Stark-shift

2017 ◽  
Vol 31 (12) ◽  
pp. 1750091 ◽  
Author(s):  
A. S. Abdel-Rady ◽  
Samia. S. A. Hassan ◽  
Abdel-Nasser A. Osman ◽  
Ahmed Salah
Keyword(s):  
Phase Transition ◽  
Energy Surface ◽  
Berry Phase ◽  
Optical Cavity ◽  
Mean Field ◽  
Single Mode ◽  
Stark Shift ◽  
Einstein Condensate ◽  
Level Atom ◽  
Dicke Model

In this paper, we employ the energy surface method to study a system of a two-level atom Bose–Einstein condensate coupled to a high-finesse optical cavity interacting with a single-mode electromagnetic field in the presence of the Stark-shift. The energy surface, the Phase transitions and the Berry phase of the two-level atom in Dicke model are obtained. Employing the Holstein–Primakoff representation of the angular momentum Lie algebra, the coupling line separation of the normal phase and the superradiant phase which occurs in a collection of fluorescent emitters (such as atoms), between a state containing few electromagnetic excitations are studied and a mean field description of the Dicke model is presented. We notice that in the thermodynamic limit, the energy surface takes a simple form for a direct description of the phase transition. Moreover, we show that the Stark-shift parameters and the atom–atom interactions can strongly affect the phase transition point. The results in the absence of the Stark-shift agree precisely with those obtained by Li, Liu and Zhou, who studied the same model using a different method.

scholarly journals Dynamical phase transition in the open Dicke model

2015 ◽  
Vol 112 (11) ◽  
pp. 3290-3295 ◽  
Author(s):  
Jens Klinder ◽  
Hans Keßler ◽  
Matthias Wolke ◽  
Ludwig Mathey ◽  
Andreas Hemmerich
Keyword(s):  
Phase Transition ◽  
Optical Cavity ◽  
Mean Field ◽  
Einstein Condensate ◽  
Dynamical Phase Transition ◽  
Dynamical Phase ◽  
Loop Area ◽  
Dicke Model ◽  
Many Body Systems ◽  
Infinite Range Interactions

The Dicke model with a weak dissipation channel is realized by coupling a Bose–Einstein condensate to an optical cavity with ultranarrow bandwidth. We explore the dynamical critical properties of the Hepp–Lieb–Dicke phase transition by performing quenches across the phase boundary. We observe hysteresis in the transition between a homogeneous phase and a self-organized collective phase with an enclosed loop area showing power-law scaling with respect to the quench time, which suggests an interpretation within a general framework introduced by Kibble and Zurek. The observed hysteretic dynamics is well reproduced by numerically solving the mean-field equation derived from a generalized Dicke Hamiltonian. Our work promotes the understanding of nonequilibrium physics in open many-body systems with infinite range interactions.

ENTANGLEMENT OF A TWO-LEVEL ATOM INTERACTING WITH A NEW STRUCTURE OF A GENERALIZED NONLINEAR STARK SHIFT VIA Ξ CONFIGURATION

2011 ◽  
Vol 25 (19) ◽  
pp. 2621-2636 ◽  
Author(s):  
E. M. KHALIL ◽  
M. M. A. AHMED ◽  
A.-S. F. OBADA
Keyword(s):  
Optical Cavity ◽  
Center Of Mass ◽  
Single Mode ◽  
Stark Shift ◽  
Mass Motion ◽  
Shift Parameter ◽  
Atomic Inversion ◽  
Level Atom ◽  
Quantized Field ◽  
Q Function

The problem of a two-level atom interacting with single mode cavity field is considered, however, the optical cavity is filled with new structure of a generalized nonlinear Stark shift via Ξ configuration. One starts with a three-level trapped atom interacting with the quantized field of center of mass motion thus a Hamiltonian for one-phonon process with nonlinearities is derived. Through the elimination of the intermediate level by using the adiabatic elimination method, we generate a new structure of effective Hamiltonian for a two-level atom with a nonlinear Stark shift. The temporal evolution of the atomic inversion is studied, we introduce that in the presence of the Stark shift parameter the atom leaves in a maximal entangled sate. We use the von Neuman entropy to measure the degree of entanglement between the atom and the field. After adding the nonlinear Stark shift the system never reaches the pure state. Also we study the Q-function for obtaining more information in phase space for this system. These aspects are sensitive to changes in the Stark shift parameter. The results shows that the effect of the nonlinearity in the Stark shift changes the quasiperiod of the field entropy and hence the entanglement between the particle and the field.

scholarly journals Basic Properties of a Mean Field Laser Equation

2019 ◽  
Vol 26 (03) ◽  
pp. 1950015 ◽  
Author(s):  
Franco Fagnola ◽  
Carlos M. Mora
Keyword(s):  
Master Equation ◽  
Regular Solution ◽  
Optical Cavity ◽  
Mean Field ◽  
Single Mode ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Nonlinear Operator Equation ◽  
Quantum Master Equation ◽  
The Mean

We study the nonlinear quantum master equation describing a laser under the mean field approximation. The quantum system is formed by a single mode optical cavity and two level atoms, which interact with reservoirs. Namely, we establish the existence and uniqueness of the regular solution to the nonlinear operator equation under consideration, as well as we get a probabilistic representation for this solution in terms of a mean field stochastic Schrödinger equation. To this end, we find a regular solution for the nonautonomous linear quantum master equation in Gorini–Kossakowski–Sudarshan–Lindblad form, and we prove the uniqueness of the solution to the nonautonomous linear adjoint quantum master equation in Gorini–Kossakowski–Sudarshan–Lindblad form. Moreover, we obtain rigorously the Maxwell–Bloch equations from the mean field laser equation.

Sign in / Sign up

Export Citation Format

Share Document