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

Abstract

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.

Enhancing quantum phase transitions in the critical point of Extended TC-Dicke model via Stark effect

“…We find that the QPTs are affected by the atom coupling strength and the Stark shift parameters. Compared with our work 25 , we notice that some of the properties for QPTs are changing under the consideration of a new coherent state.…”

“…The number of atoms is assumed to be conserved by all processes. Inserting Ψ into the second quantized form, we can obtain the many-body Hamiltonian as follow 25 where ω is the effective frequency of the cavity field 17 , γ 1 ( γ 2 ) is describe the intensity-dependent Stark-shift 25 , χ is the nonlinear coupling strength, which is satisfies, χ = χ 1 = χ 2 = − χ 12 , from equation ( 4 ), we obtain …”

“…When increasing the collective coupling strength, this model exhibits a second-order quantum phase transition from a normal state to a superradiant state 22 – 24 . More recently, we study a system of a two-level atom BEC coupled to a high-finesse optical cavity interacting with a single mode electromagnetic field in the presence of the Stark-shift employing the energy surface method and the QPTs as well as Berry phase for this system is obtained 25 . Also, we obtain a simple expression for the energy surface of the Dicke Hamiltonian using as the Heisenberg-Weyl coherent states for the tensor product of matter and field components 26 .…”

Influence of Stark-shift on quantum coherence and non-classical correlations for two two-level atoms interacting with a single-mode cavity field

“…(1). This Stark effect induces the splitting and shifting of spectral energy levels due to the presence of an electromagnetic cavity field [55][56][57]. In this picture, the total Hamiltonian of the system is given by ( = 1)…”

Dicke States Generation via Selective Interactions in Dicke-Stark Model

“…The Stark term plays an important role in dynamical selectivity. This nonlinear coupling term was also added to the Dicke model [32][33][34][35], which is a fundamental model of quantum optics to describe the interactions between light and matter [36][37][38][39][40]. The existence of Stark term in the Dicke-Stark (DS) model can be used to create nonlinear energy levels, which will be used to generate entangled states selectively.…”