Persistence of the phase transition in the Dicke model with external fields and counter-rotating terms

We show that the addition of classical external fields to the Dicke model does not necessarily remove the phase transition if a mechanism is already present which destroys the gauge invariance of the model.     

A simple green function approach to the Dicke model with external fields

Using the technique of double-time temperature-dependent Green functions, the lack of phase transition in the Dicke model with external fields is proved.     

Rényi entropy and quantum phase transition in the Dicke model

The Rényi entropies of the Dicke model are presented. This quantum-optical model describes a single-mode bosonic field interacting with an ensemble of N two-level atoms. There is a quantum phase transition in the N→∞ limit. It is shown that there is an abrupt change in the Rényi entropy of order β at the transition point. Around the critical value of the coupling strength λc the Rényi entropy is proportional to the logarithm of the characteristic length and diverges as ln|λc−λ| for any order β. The pseudocapacity defined here in analogy with the heat capacity exhibits the phase transition. The critical exponent for the Dicke model is found to be 1 for any value of the parameter β.     

Entanglement and excited-state quantum phase transition in an extended Dicke model

We investigate the properties of entanglement and excited-state quantum phase transition (ESQPT) in a hybrid atom-optomechanical system in which an optomechanical quadratic interaction is introduced into a normal Dicke model. Interestingly, by preparing the ancillary mode in a coherent state, both the quantum entanglement and ESQPT can be realized in a relative weak-coupling condition. Moreover, the entanglement is immune to the A² term, and a reversed trend of the entropy is obtained when the A² term is included. Density of states (DoS) and Peres lattice are used to investigate ESQPTs. Compared to a normal Dicke model, the DoS enlarges exp(2r_α) times if the ancillary mode is prepared in a coherent state. This work is an extension of the ground-state quantum phase transition, which may inspire further exploration of the quantum criticality in many-body systems.     

Entanglement generated by a Dicke phase transition

We consider A atoms interacting dispersively with two cavity modes. We find that the entanglement between two modes of the electromagnetic field is created in a Dicke phase transition.     

Exploring symmetry breaking at the Dicke quantum phase transition

We study symmetry breaking at the Dicke quantum phase transition by coupling a motional degree of freedom of a Bose-Einstein condensate to the field of an optical cavity. Using an optical heterodyne detection scheme, we observe symmetry breaking in real time and distinguish the two superradiant phases. We explore the process of symmetry breaking in the presence of a small symmetry-breaking field and study its dependence on the rate at which the critical point is crossed. Coherent switching between the two ordered phases is demonstrated.     

Nonequilibrium quantum phase transitions in the Dicke model

We establish a set of nonequilibrium quantum phase transitions in the Dicke model by considering a monochromatic nonadiabatic modulation of the atom-field coupling. For weak driving the system exhibits a set of sidebands which allow the circumvention of the no-go theorem which otherwise forbids the occurrence of superradiant phase transitions. At strong driving we show that the system exhibits a rich multistable structure and exhibits both first- and second-order nonequilibrium quantum phase transitions.     

Fisher information,Rényi entropy power and quantum phase transition in the Dicke model

Fisher information, Rényi entropy power and Fisher–Rényi information product are presented for the Dicke model. There is a quantum phase transition in this quantum optical model. It is pointed out that there is an abrupt change in the Fisher information, Rényi entropy power, the Fisher, Shannon and Rényi lengths at the transition point. It is found that these quantities diverge as the characteristic length: |_λc−λ|^−1/4${|{\lambda }_c-\lambda |}^{-1/4}$ around the critical value of the coupling strength _λc${\lambda }_c$ for any value of the parameter β$\beta$.     

Phase transition in a generalized Dicke model of superradiance

By means of the use of the “gap equations”, we calculate the thermodynamic properties of a sufficiently general Dicke model. We obtain the general relations which correspond to the condition of second-order phase transition from the normal to the superradiant state.     

First order phase transition in the system of two coupled fields with different transition temperatures

It is shown that for the case of a strong field coupling in the system of two fields the low temperature phase may be stable in the fluctuation region of the high temperature phase.     

Phase transition in spontaneous coherent state in Dicke model and retarded potentials

In contrast with the results by Rzazewski, Wodkiewicz and Zakowicz who have taken only the A²-term, it is shown that addition of the retarted potentials to the Dicke Hamiltonian conserves the threshold condition of a phase transition.     

A one-dimensional model with phase transition

Two repellent particles are bound to occupy two among thek _n +1 adjacent sites 0=x ₀ ⁽ⁿ⁾ <x ₁ ⁽ⁿ⁾ <...<x _kn ⁽ⁿ⁾ =1, sayx _q ⁽ⁿ⁾ ,x _q+1 ⁽ⁿ⁾ . Define the Hamiltonian _q ⁽ⁿ⁾ =–ln(x _q+1 ⁽ⁿ⁾ –x _q ⁽ⁿ⁾ ) and the partition function     

A one-dimensional model with phase transition

A one-dimensional model is studied with nearest neighbor interaction and certain forbidden configurations. In this model it is possible to investigate the phase transition even on the microcanonical level, and it turns out that phases can coexist under certain circumstances.     

Layering transition in SOS model with external magnetic field

For the SOS model defined by the Hamiltonian , where _x , _x ,{1,2,...},h>0,x ^d ,d2 it is shown that in the low-temperature region an infinite sequence of first-order phase transitions takes place whenh»0 and the temperature is fixed.     

Instabilities of the Dicke model with field interactions

The instability in the Dicke model with a rotating-wave approximation for finite N atoms is investigated in terms of the Berry phase and the fidelity. It can be identify by the discontinuity of these quantities as a function of the atom-field coupling parameter. Involving an additional field interaction, it is observed that the instability is not eliminated even for strong interaction of the bosonic fields, contrarily to the previous results limited to the minimal coupling regions.     

Quantized fields in interaction with external fields

We consider a massive, charged, scalar quantized field interacting with an external classical field. Guided by renormalized perturbation theory we show that whenever the integral equations defining the Feynman or retarded or advanced interaction kernel possess non perturbative solutions, there exists anS-operator which satisfies, up to a phase, the axioms of Bogoliubov, and is given for small external fields by a power series which converges on coherent states. Furthermore this construction is shown to be equivalent to the one based on the Yang-Källen-Feldman equation. This is a consequence of the relations between chronological and retarded Green's functions which are described in detail.     

Out-of-time-ordered correlation in the anisotropic Dicke model

Out-of-time-ordered correlation (OTOC) functions have been used as an indicator of quantum chaos in a lot of physical systems. In this work, we numerically demonstrate that zero temperature OTOC can detect quantum phase transition in the anisotropic Dicke model. The phase diagram is given with OTOC. The finite-size effect is studied. Finally, the temperature effect is discussed.