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.     

Path integral approach to the full Dicke model

The full Dicke model describes a system of N identical two level-atoms coupled to a single mode quantized bosonic field. The model considers rotating and counter-rotating coupling terms between the atoms and the bosonic field, with coupling constants g₁ and g₂, for each one of the coupling terms, respectively. We study finite temperature properties of the model using the path integral approach and functional methods. In the thermodynamic limit, N→∞, the system exhibits phase transition from normal to superradiant phase, at some critical values of temperature and coupling constants. We distinguish between three particular cases, the first one corresponds to the case of rotating wave approximation, where g₁≠0 and g₂=0, the second one corresponds to the case of g₁=0 and g₂≠0, in these two cases the model has a continuous symmetry. The last one, corresponds to the case of g₁≠0 and g₂≠0, where the model has a discrete symmetry. The phase transition in each case is related to the spontaneous breaking of its respective symmetry. For each one of these three particular cases, we find the asymptotic behaviour of the partition function in the thermodynamic limit, and the collective spectrum of the system in the normal and the superradiant phase. For the case of rotating wave approximation, and also the case of g₁=0 and g₂≠0, in the superradiant phase, the collective spectrum has a zero energy value, corresponding to the Goldstone mode associated to the continuous symmetry breaking of the model. Our analysis and results are valid in the limit of zero temperature, β→∞, in which, the model exhibits a quantum phase transition.     

Non-equilibrium Dynamics of an Optomechanical Dicke Model

Motivated by the experimental realization of Dicke model in optical cavities, we model an optomechanical system consisting of two-level BEC atoms with transverse pumping. We investigate the transition from normal and inverted state to the superradiant phase through a detailed study of the phase portraits of the system. The rich phase portraits generated by analytical arguments display two types of superradiant phases, regions of coexistence and some portion determining the persistent oscillations. We study the time evolution of the system from any phase and discuss the role of mirror frequency in reaching their attractors. Further, we add an external mechanical pump to the mirror which is capable of changing the mirror frequency through radiation pressure and study the impact of the pump on the phase portraits and the dynamics of the system. We find the external mirror frequency changing the phase portraits and even shifting the critical transition point, thereby predicting a system with controllable phase transition.     

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.     

Stability of symmetry breaking states in finite-size Dicke model with photon leakage

We investigate the finite-size Dicke model with photon leakage. It is shown that the symmetry breaking states, which are characterized by non-vanishing $〈\stackrel{?}{a}〉\ne 0$ and correspond to the ground states in the superradiant phase in the thermodynamic limit, are stable, while the eigenstates of the isolated finite-size Dicke Hamiltonian conserve parity symmetry. We introduce and analyze an effective master equation that describes the dynamics of a pair of the symmetry breaking states that are the degenerate lowest energy eigenstates in the superradiant region with photon leakage. It becomes clear that photon leakage is essential to stabilize the symmetry breaking states and to realize the superradiant phase without the thermodynamic limit. Our theoretical analysis provides an alternative interpretation using the finite-size model to explain results from cold atomic experiments showing superradiance with the symmetry breaking in an optical cavity.     

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$\beta$.     

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.     

Dicke模型的量子经典对应关系

非旋波近似条件下Dicke模型表现为量子混沌动力学特征.在详细考察Dicke模型经典相空间结构特点的基础上,采用经典-量子"一对多"的思想,即经典相空间中的一点对应于量子体系两个初始相干态的演化,利用对两个初态量子纠缠动力学演化取统计平均的方法,得到了与经典相空间对应非常好的量子相空间结构.数值计算结果表明:经典混沌有利地促进系统两体纠缠的产生,平均纠缠可以作为量子混沌的标识,利用平均纠缠可以得到一种较好的量子动力学与经典相空间的对应关系. 关键词： Dicke模型 非旋波近似 量子混沌 经典量子对应     

Out-of-Time-Order Correlators and Quantum Phase Transitions in the Rabi and Dicke Models

The out-of-time-order correlators (OTOCs) is used to study the quantum phase transitions (QPTs) between the normal phase and the superradiant phase in the Rabi and few-body Dicke models with large frequency ratio of the atomic level splitting to the single-mode electromagnetic radiation field frequency. The focus is on the OTOC thermally averaged with infinite temperature, which is an experimentally feasible quantity. It is shown that the critical points can be identified by long-time averaging of the OTOC via observing its local minimum behavior. More importantly, the scaling laws of the OTOC for QPTs are revealed by studying the experimentally accessible conditions with finite frequency ratio and finite number of atoms in the studied models. The critical exponents extracted from the scaling laws of OTOC indicate that the QPTs in the Rabi and Dicke models belong to the same universality class.     

Dicke模型中的偏态信息

利用Wigner-Yanase偏态信息的定义,通过Dicke模型研究了数态光场的信息向原子系综的动力学转移.研究表明多个二能级原子组成的系综具备存储并释放光场信息的功能,但是,通过该模型光场信息只是部分地向原子系综转移.通过增加原子个数,光场信息的残留可以得到一定程度的抑制.     

Dicke模型的量子混沌和单粒子相干动力学特性

量子化的Dicke模型在非旋波近似条件下表现为量子混沌动力学特征.利用单粒子一阶时间关联函数,通过数值计算详细考察了Dicke模型中单粒子相干动力学特性.结果表明:当初始相干态处在混沌区域时,一阶时间关联函数曲线衰减较快,而当初始相干态处在规则区域时,一阶时间关联函数曲线衰减较慢,单粒子相干动力学对初态具有较强的敏感性,经典混沌抑制量子相干.考察单粒子相干动力学在相空间的平均演化性质,得到一种较好的量子经典对应关系.最后研究了相空间单粒子相干的整体动力学性质,更好地揭示了相空间的混沌和规则结构.     

三量子比特Dicke模型中的两体和三体纠缠动力学

本文利用绝热近似方法和精确对角化方法研究三量子比特Dicke模型中的纠缠动力学.处于两种典型的纠缠态GHZ态和W态上的量子比特在时间演化过程中与辐射光场发生强耦合作用,在各种子系统间产生纠缠,通过分析这些纠缠的演化特性发现初始GHZ态的三体纠缠鲁棒性比W态强,这与旋波近似结论一致.与旋波近似下结果不同的是,两种态中任意...     

Quantum Chaos in the Extended Dicke Model

We systematically study the chaotic signatures in a quantum many-body system consisting of an ensemble of interacting two-level atoms coupled to a single-mode bosonic field, the so-called extended Dicke model. The presence of the atom–atom interaction also leads us to explore how the atomic interaction affects the chaotic characters of the model. By analyzing the energy spectral statistics and the structure of eigenstates, we reveal the quantum signatures of chaos in the model and discuss the effect of the atomic interaction. We also investigate the dependence of the boundary of chaos extracted from both eigenvalue-based and eigenstate-based indicators on the atomic interaction. We show that the impact of the atomic interaction on the spectral statistics is stronger than on the structure of eigenstates. Qualitatively, the integrablity-to-chaos transition found in the Dicke model is amplified when the interatomic interaction in the extended Dicke model is switched on.     

Nonclassical effects in a highly nonlinear generalized homogeneous Dicke model

An intensity dependent nonlinear coupling model of N two-level atoms (generalized Dicke model) interacting dispersively with a bimodal cavity field via two-photon transitions is investigated in a scenario where the rotating wave approximation is assumed. The model becomes homogeneous in the sense that the spin transition frequency is the same for all atoms and the coupling constants emerging from the collective interactions of the atomic system with the cavity field depend only on the particular radiation field mode. This allows us to represent the Dicke Hamiltonian entirely in terms of the total angular momentum J. It is assumed that, initially, the atomic system and the field are in a disentangled state where the field modes are in Glauber coherent states and the atomic system is a superposition of states |JM〉 (Dicke states). The model is numerically tested against simulations of normal squeezing variance of the field, squeezing factors based on the Heisenberg uncertainty principle, along with the statistical properties of the light leading to the possible production of nonclassical effects, such as degree of second-order coherence in the modes, degree of intermode correlation, as well as violation of the Cauchy–Schwartz inequality. Analytical expression of the total density operator matrix elements at t>0 shows the present nonlinear model to be strongly entangled, which is reflected in the time evolution of the linear entropy, where the superposition states are reduced to statistical mixtures. Thus, the present generalized Dicke model does not preserve the modulus of the Bloch vector. The computations, performed in the weak coupling and strong field limits, were conducted via second-order Dyson perturbative expansion of the time evolution operator matrix elements for the totality of the angular momentum states of the atomic system.     

单模光腔中N个二能级原子系统的有限温度特性和相变

本文研究单模光场中N个二能级原子Dicke模型的有限温度特性和相变. 把原子赝自旋转换为双模费米算符, 用虚时路径积分方法推导出系统的配分函数, 对作用量变分求极值得到系统的热力学平衡方程, 及原子布居数期待值和平均光子数随原子-光场耦合强度变化的解析表达式. 重点研究了在量子涨落起主导作用的低温区, 由耦合强度变化产生的从正常相到超辐射相的相变, 指出该相变遵从Landau连续相变理论, 平均光子数可作为序参数, 零值表示正常相, 大于零则为超辐射相. 在零温极限下本文的结果和量子相变理论完全符合. 另外, 本文也讨论了系统的热力学性质, 比较有限温度相变和量子相变的异同. 发现, 在强耦合区低温稳定态的光子数和平均能量都和绝对零度的值趋于一致, 而超辐射相的熵则随耦合强度的增强迅速衰减为零.     

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.     

The effect of the counter-rotating terms on the Rabi oscillations and squeezing in the Dicke model with cavity losses

The effect of the counter-rotating terms in the Dicke model with cavity losses is examined. Numerical results for the time evolutions of the atomic population inversion, dipole moment, mean-photon number and atomic and field squeezing parameters for an initial coherent field are presented for various numbers of atoms and different cavity dampings. As a consequence of the counter-rotating terms, the appearance of new steady states for atomic population inversion and the mean-photon number is pointed out.     

Thermal phase transition for some spin-boson models

In this work we study two different spin-boson models. Such models are generalizations of the Dicke model, it means they describe systems of N$N$ identical two-level atoms coupled to a single-mode quantized bosonic field, assuming the rotating wave approximation. In the first model, we consider the wavelength of the bosonic field to be of the order of the linear dimension of the material composed of the atoms, therefore we consider the spatial sinusoidal form of the bosonic field. The second model is the Thompson model, where we consider the presence of phonons in the material composed of the atoms. We study finite temperature properties of the models using the path integral approach and functional methods. In the thermodynamic limit, N→∞$N\to \infty$, the systems exhibit phase transitions from normal to superradiant phase at some critical values of temperature and coupling constant. We find the asymptotic behavior of the partition functions and the collective spectrums of the systems in the normal and the superradiant phases. We observe that the collective spectrums have zero energy values in the superradiant phases, corresponding to the Goldstone mode associated to the continuous symmetry breaking of the models. Our analysis and results are valid in the limit of zero temperature β→∞$\beta \to \infty$, where the models exhibit quantum phase transitions.