Two-state system coupled to a boson mode: Quantum dynamics and classical approximations

The relation between classical and quantum mechanical integrability is investigated for a boson mode coupled to a two-level system. Different semi-classical approximations of this system are considered which are obtained by (i) factorization of expectation values of the two-state variable and the boson, (ii) making a WKB-type approximation, (iii) replacing the boson by a classical field of constant amplitude and fixed frequency and (iv) putting the boson into a self-consistent coherent state. The results vary considerably and include cases of non-integrable and integrable classical dynamics. Quantum mechanically the system is found to satisfy a criterion of quantum mechanical integrability, which we formulate, but the separated Hamiltonian of the boson alone does not have a well-defined classical limit. Numerical results for the energy spectrum and expectation values are obtained, which show a high degree of regularity but also display overlapping avoided crossings usually associated with non-integrable Hamiltonians. The exact dynamics of the occupation probabilities of the two levels is also analysed numerically. The dependence of quantum mechanical recurrence effects (in quantum optics known as revivals) on coupling strength, frequency detuning and initial conditions is studied. The revivals are found to disappear in the case of strong coupling. The Fourier spectra of the dynamical expectation values are also calculated     

Quantum dynamics of a mechanical resonator driven by a cavity

We explore the quantum dynamics of a mechanical resonator whose position is coupled to the frequency of an optical (or microwave) cavity mode. When the cavity is driven at a frequency above resonance the mechanical resonator can gain energy and for sufficiently strong coupling this results in limit-cycle oscillations. Using a truncated Wigner function approach, which captures the zero-point fluctuations in the system, we develop an approximate analytic treatment of the resonator dynamics in the limit-cycle regime. We find that the limit-cycle oscillations produced by the cavity are associated with rather low levels of energy fluctuations in the resonator. Compared to a resonator at the same temperature which is driven by a pure harmonic drive to a given average energy, the cavity-driven oscillations can have much lower energy fluctuations. Furthermore, at sufficiently low temperatures, the cavity can drive the resonator into a non-classical state which is number-squeezed.     

Solvable dynamics of N driven two-level atoms coupled to a dissipative cavity mode

We solve exactly the dynamics of N strongly driven two-level atoms equally coupled on resonance to a dissipative cavity mode. Analytical results are derived on decoherence, entanglement, purity, atomic correlations and cavity field mean photon number. Decoherence-free subspaces are predicted for the whole system and the N-qubit subsystem. Multi-partite entangled states and cavity cat-like states can be conditionally generated. The decay of quantum coherence and purity can be monitored by joint measurements on atomic populations. Atoms prepared in states invariant under permutation of any two components evolve within the subspace spanned by the completely symmetric Dicke states. Applications to N = 3, 4 are discussed.     

Correlated squeezed-state approach for the ground state of strongly correlated electrons coupled to local Holstein phonons

Summary In the present work we have applied the correlated squeezed-state approach to investigate the ground state of the extended Hubbard model which is coupled to local Holstein phonons. Our study begins with decoupling the electron and phonon subsystems approximately by introducing a variational correlated squeezed-state ansatz for the phonons. Then assuming the renormalized intersite electron correlation of the effective electronic Hamiltonian to be attractive and the renormalized on-site correlation repulsive, we have applied the generalized Hartree-Fock approximation to obtain the ground state of the system, which is a superconducting state with intersite pairing. With optimal values of the variational parameters the correlated squeezed-state approach will by construction yield a ground-state energy lower than those obtained in previous studies. This means that our variational ansatz is more stable as the ground state of the system. Furthermore, our variational study shows that in the correlated squeezed state the polaronic reduction effect of phonons is much more alleviated, and thus the mass enhancement inherent to the polaron effect is noticeably weakened. This weakening of the reduction effect should, in turn, significantly affect other physical properties of the system.     

Average dynamics of a driven set of globally coupled excitable units

We investigate the behavior of the order parameter describing the collective dynamics of a large set of driven, globally coupled excitable units. We derive conditions on the parameters of the system that allow to bound the degree of synchrony of its solutions. We describe a regime where time dependent nonsynchronous dynamics occurs and, yet, the average activity displays low dimensional, temporally complex behavior.     

Strongly correlated two-photon transport in a one-dimensional waveguide coupled to a two-level system

We show that two-photon transport is strongly correlated in one-dimensional waveguide coupled to a two-level system. The exact S matrix is constructed using a generalized Bethe-ansatz technique. We show that the scattering eigenstates of this system include a two-photon bound state that passes through the two-level system as a composite single particle. Also, the two-level system can induce effective attractive or repulsive interactions in space for photons. This general procedure can be applied to the Anderson model as well.     

与Ising链耦合的中心双量子比特系统的量子关联

通过对双量子比特系统分别独自与Ising链耦合情形下的关联问题的研究, 推导出了量子失协和量子关联几何度量的演化规律. 在弱耦合相互作用情况下Ising链的临界点附近, 量子关联存在突变. 此外本文发现在某段时间内的演化过程中几何量子关联度保持不变. 关键词： 量子关联 量子失协 量子关联几何度量     

Supersolidity for hard-core-bosons coupled to optical phonons

The coexistence of diagonal long-range order (DLRO) and off-diagonal long-range order (ODLRO), manifested in some systems, is still a theoretical enigma. Here, we present a novel microscopic mechanism for supersolidity or the homogeneous coexistence of charge-density-wave state (an example of DLRO) and superfluidity/superconductivity (a realization of ODLRO). We derive an effective d-dimensional Hamiltonian for a system of hard-core-bosons coupled to optical phonons in a lattice. At non-half-fillings, a superfluid/superconductor to a supersolid transition occurs at intermediate boson–phonon couplings, while at strong-couplings the system phase separates. We demonstrate explicitly that the presence of next-nearest-neighbor hopping and nearest-neighbor repulsion leads to supersolidity.     

Quantum dynamic behaviour in a coupled cavities system

The dynamic behaviour of the two-site coupled cavities model which is doped with ta wo-level system is investigated.The exact dynamic solutions in the general condition are obtained via Laplace transform.The simple analytical solutions are obtained in several particular cases,which demonstrate the clear and simple physical picture for the quantum state transition of the system.In the large detuning or hoppling case,the quantum states transferring between qubits follow a slow periodic oscillation induced by the very weak excitation of the cavity mode.In the large coupling case,the system can be interpreted as two Jaynes-Cummings model subsystems which interact through photon hop between the two cavities.In the case of λ≈△>> g,the quantum states transition of qubits is accompanied by the excitation of the cavity,and the cavity modes have the same dynamic behaviours and the amplitude of probability is equal to 0.25 which does not change with the variation of parameter.     

Intermittent lag synchronization in a driven system of coupled oscillators

We study intermittent lag synchronization in a system of two identical mutually coupled Duffing oscillators with parametric modulation in one of them. This phenomenon in a periodically forced system can be seen as intermittent jump from phase to lag synchronization, during which the chaotic trajectory visits a periodic orbit closely. We demonstrate different types of intermittent lag synchronizations, that occur in the vicinity of saddle-node bifurcations where the system changes its dynamical state, and characterize the simplest case of period-one intermittent lag synchronization.     

Critical dynamics of a localized moment system coupled to conduction electrons

We discuss the critical dynamics of a system of localized spins interacting with conduction electrons via an isotropic exchange coupling between the respective spin densities. It is shown that the elimination of the conduction electrons by an adiabatic approximation is not allowed for small wave vectors. The quantum mechanical Fokker-Planck equation derived in a previous paper is used to investigate the renormalization of the kinetic coefficients due to nonlinear mode coupling contributions.     

Quantum system driven by periodic external field

A quantum Floquet Theory for a periodically driven system is studied. For this purpose the periodic external fields are changed to have an increasing amplitude with exp(t), where is an infinitestimal positive number to be taken to be zero at the end. By using the expansions in terms of inverse powers of the driving frequency, periodic factors of the time evolution operator are factorized successively. Each step corresponds to a periodically driven system with different strength of external field. This approach produces a time-independent effective Hamiltonian. The effectiveness of the method is examined by applying it to simple models; 1) a forced harmonic oscillator, 2) a particle in the double-well potential, and 3) a hydrogen atom in an electric potential.     

Quantum field theory for a system of interacting photons,electrons, and phonons

A Lagrangian in (1 + 3)-dimensional space-time which describes the interaction of photons, electrons, and phonons is proposed. This is a generalization of Rodriguez-Nuñez' model. This Lagrangian is also singular in the sense of Dirac. The path-integral quantization of this system is performed with the aid of the Dirac formalism for a singular Lagrangian and the method of functional integration. The phase-space generating functional of the Green function of this system is deduced. The Ward identities in canonical formalism for local symmetries are derived, and the Ward identities of proper vertices for this system are obtained. The conserved charges at the quantum level are also obtained. The effective Lagrangian in configuration space for the present model is derived in the case = const. Thus, the Feynman rule can be deduced immediately.     

Quantum dynamics of electric-dipole coupled defect centers in solids

We investigate the quantum dynamics of two defect centers in solids,which are coupled by vacuum-induced dipole-dipole interactions.When the interaction between defects and phonons is taken into account,the two coupled electron-phonon systems make up two equivalent multilevel atoms.By making Born-Markov and rotating wave approximations,we derive a master equation describing the dynamics of the coupled multilevel atoms.The results indicate the concepts of subradiant and superradiant states can be applied to these systems and the population transfer process presents different behaviors from those of the two dipolar-coupled two-level atoms due to the participation of phonons.     

Quantum heat engine cycle working with a strongly correlated electron system

A new model of a quantum heat engine(QHE) cycle is established,in which the working substance consists of an interacting electrons system.One of our purposes is to test the validity of the second law of thermodynamics by this model,which is more general than the spin-1/2 antiferromagnetic Heisenberg model since it would recover the spin model when the on-site Coulomb interaction U is strong enough.On the basis of quantum mechanics and the first law of thermodynamics,we show no violation of the second law of thermodynamics during the cycle.We further study the performance characteristics of the cycle by investigating in detail the optimal relations of efficiency and dimensionless power output.We find that the efficiency of our engine can be expressed as η = 1 - t22/t12 in the large-U limit,which is valid even for a four sites QHE.     

关联白噪声驱动的具有时间延迟的Logistic系统

关联白噪声驱动的具有时间延迟的Logistic系统可更真实的反映肿瘤细胞的增长问题,本文通过小时间延迟近似方法对由关联白噪声驱动的具有时间延迟的Logistic系统进行了研究,得到了系统的稳态概率密度,并进一步分析了加性和乘性噪声强度,噪声关联时间和时间延迟对稳态概率密度的影响以及噪声诱导的非平衡相变现象. 关键词： Logistic系统 关联白噪声 时间延迟 非平衡相变