激光驱动下腔与玻色-爱因斯坦凝聚中的量子相变

Dicke模型中的量子相变在三十多年前已被预言,该模型描述的是N个二能级原子与单模腔场集体耦合的系统.在标准Dicke模型的基础上加入原子光的非线性相互作用和含时外场驱动,使用含时幺正变换和Holstein-Primafoff变换方法从理论上推导出基态能量表达式.并且给出了丰富的相图,而且这些性质最近已有文献从实验上验证.本文主要呈现了非线性相互作用和外场驱动对量子相变的影响.     

Influence of omitting the A2 term in the conventional photon-matter-Hamiltonian on the photon-field equation

It is shown that the conventional Hamiltonian without the A² term leads to the incorrect wave equation for the radiation field. The consequence of this is to allow the linear instability. The condition of the occurence of the linear instability is shown to be the same as the strong coupling condition for the supperradiant phase transition in the Dicke model to occur.     

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.     

Ising model with a new class of four-spin interactions

The Ising model on a Union-Jack lattice, described by a Hamiltonian with second-neighbor pair-pair, four-spin, infinite-range interactions is considered. The model is solved exactly and the results are compared with MFA predictions. Within the exact treatment two new classes of phase transitions are obtained. The first one includes transitions from a disordered to a metastable, ordered and then to a stable and ordered phase with decreasing temperature. The metastable phase does not appear if the temperature is increased. The second one contains transitions between ordered and partialy ordered, partialy frustrated phases.     

New ordered phases in a class of generalized XY models

It is well known that the 2D XY model exhibits an unusual infinite order phase transition belonging to the Kosterlitz-Thouless (KT) universality class. Introduction of a nematic coupling into the XY Hamiltonian leads to an additional phase transition in the Ising universality class [D. H. Lee and G. Grinstein, Phys. Rev. Lett. 55, 541 (1985)]. Using a combination of extensive Monte Carlo simulations and finite size scaling, we show that the higher order harmonics lead to a qualitatively different phase diagram, with additional ordered phases originating from the competition between the ferromagnetic and pseudonematic couplings. The new phase transitions belong to the 2D Potts, Ising, or KT universality classes.     

Lack of phase transition in the Dicke model with external fields

We show that the addition of external fields to the Dicke Hamiltonian removes the critical behaviour of the model. We analyse this result in terms of order parameter and conjugated field and compare with recent papers.     

Ginzburg-Landau theory for higher order phase transition

Ginzburg-Landau theory for studying phase transitions of higher order has been derived using coarse graining and lattice formulation within Ehrenfest thermodynamics. Our developed Hamiltonian leads directly to the functional of the system. We studied the evolution of the order parameter using our developed model equations for third and fourth order phase transitions. The periodic nature of the system can be likened to spatially varying periodic soliton/antisoliton lattice of holes in condensate. This is different from what one observes for any conventional solitary wave in the second order phase regime.     

光腔中两组分玻色-爱因斯坦凝聚体的受激辐射特性和量子相变

研究了单模光腔中两组分玻色-爱因斯坦凝聚的基态性质和相关的量子相变.通过利用自旋相干态变换将等效赝自旋哈密顿算符对角化并求得基态能量泛函.基态能量泛函对其经典场变量进行变分并取极小值,得到光子数解和相边界曲线.通过稳定性讨论发现系统除了出现正常相和超辐射相之外,还得到了多稳的宏观量子态;受激辐射来自于原子数反转的集体态,单组分的Dicke系统中并没有此现象;受激辐射只能从一组分的原子中产生,而另外的仍保持在普通超辐射状态.通过调整相关的原子-场耦合强度和频率失谐,超辐射和受激辐射态的顺序可以在原子的两个组分之间互换.     

Possible condensation of Frenkel exciton polaritons in an organic nanofiber

We theoretically investigate a phase transition of Frenkel exciton polaritons in an organic nanofiber. Assuming a phenomenological Hamiltonian, we derive a mean field equation for the condensation after finding an effective action for the phenomenon using the functional integral method and stationary phase analysis. From a solution of the mean field equation, we construct a phase diagram for the condensation and highlight features that distinguish J- and H-aggregates. We also detail a connection with the superradiant phase transition, which has been studied using the Dicke model.     

Crystal geometry and phenomenological models of reconstructive phase transitions

The basic concepts of the phenomenological theory of reconstructive phase transitions are presented. The nonlinear order parameter concept is introduced and the connection between the classical form of the Landau theory and a density wave approach to phase transitions is given. This new phenomenological approach is applied both to standard examples of reconstructive phase transformations (BCC-HCP, BCC-FCC, HCP-FCC, BCC-w) and to new problems like the formation of quasicrystals.     

Exact dynamics of an infinite-atom Dicke maser model

We study the dynamics of the Dicke maser model in the limit as the number of atoms becomes infinite and the coupling constant between the atoms and the radiation field goes to zero. We find that the limiting Hamiltonian is integrable and obtain an explicit closed form for the unitary time evolution operators. As a corollary we show that in the limit the radiation emitted by the model is coherent in the sense by Glauber.     

Phase transitions in four-dimensional AdS black holes with a nonlinear electrodynamics source

In this work we consider black hole solutions to Einstein's theory coupled to a nonlinear power-law electromagnetic field with a fixed exponent value. We study the extended phase space thermodynamics in canonical and grand canonical ensembles, where the varying cosmological constant plays the role of an effective thermodynamic pressure. We examine thermodynamical phase transitions in such black holes and find that both first- and second-order phase transitions can occur in the canonical ensemble while, for the grand canonical ensemble, Hawking–Page and second-order phase transitions are allowed.     

Hamiltonian Formulation of Statistical Ensembles and Mixed States of Quantum and Hybrid Systems

Representation of quantum states by statistical ensembles on the quantum phase space in the Hamiltonian form of quantum mechanics is analyzed. Various mathematical properties and some physical interpretations of the equivalence classes of ensembles representing a mixed quantum state in the Hamiltonian formulation are examined. In particular, non-uniqueness of the quantum phase space probability density associated with the quantum mixed state, Liouville dynamics of the probability densities and the possibility to represent the reduced states of bipartite systems by marginal distributions are discussed in detail. These considerations are used to study ensembles of hybrid quantum-classical systems. In particular, nonlinear evolution of a single hybrid system in a pure state and unequal evolutions of initially equivalent ensembles are discussed in the context of coupled hybrid systems.     

Nonlinear supersymmetry,quantum anomaly and quasi-exactly solvable systems

The nonlinear supersymmetry of one-dimensional systems is investigated in the context of the quantum anomaly problem. Any classical supersymmetric system characterized by the nonlinear in the Hamiltonian superalgebra is symplectomorphic to a supersymmetric canonical system with the holomorphic form of the supercharges. Depending on the behaviour of the superpotential, the canonical supersymmetric systems are separated into the three classes. In one of them the parameter specifying the supersymmetry order is subject to some sort of classical quantization, whereas the supersymmetry of another extreme class has a rather fictive nature since its fermion degrees of freedom are decoupled completely by a canonical transformation. The nonlinear supersymmetry with polynomial in momentum supercharges is analysed, and the most general one-parametric Calogero-like solution with the second order supercharges is found. Quantization of the systems of the canonical form reveals the two anomaly-free classes, one of which gives rise naturally to the quasi-exactly solvable systems. The quantum anomaly problem for the Calogero-like models is “cured” by the specific superpotential-dependent term of order ℏ². The nonlinear supersymmetry admits the generalization to the case of two-dimensional systems.     

Quantum chaos triggered by precursors of a quantum phase transition: the dicke model

We consider the Dicke Hamiltonian, a simple quantum-optical model which exhibits a zero-temperature quantum phase transition. We present numerical results demonstrating that at this transition the system changes from being quasi-integrable to quantum chaotic. By deriving an exact solution in the thermodynamic limit we relate this phenomenon to a localization-delocalization transition in which a macroscopic superposition is generated. We also describe the classical analogs of this behavior.     

Uniform uniaxial anisotropic systems with coupled vector order parameters

Phase transitions in magnets, described by two coupled, m-component vector order parameters, having uniform uniaxial anisotropies are studied. Using a phenomenological model, it is shown that when both order parameters are anisotropic, phase transitions are always second order, in either the uniaxial or the (m???1)-isotropic phase. This is contrary to the isotropic case of two coupled order parameters, for which phase transitions are fluctuation-induced first order. The transitions are still continuous into the m-isotropic phase even when the only anisotropic order parameter is the one with the lowest mean-field critical temperature. New discontinuous transitions still occur in either the uniaxial or the (m???1)-isotropic phase, when the only anisotropic order parameter has the highest mean-field critical temperature.     

Picturing quantum phase transitions

We discuss the quantum phase transitions (QPT) in N-spin chains from the point of view of collective observables. We show that the measurement space representation is a convenient tool for the analysis of phase transitions, allowing the determination of an appropriate set of macroscopic order parameters (for a given Hamiltonian). Quantum correlations in the vicinity of the critical points are analyzed both in the ground states and low temperature thermal states.