Dynamics of two-level systems beyond the rotating-wave approximation

We study the dynamics of quantum discord and entanglement in a two-qubit system coupled to the same quantized field without rotating-wave approximation. In the absence of initial correlations, we show that maximal quantum discord (entanglement) can be obtained in the strong coupling regime. Analytical result corresponding to an effective Hamiltonian is given. In a deep strong coupling regime, sudden death and sudden birth of entanglement are observed, while the peak value of quantum discord is reached periodically. The results of our investigation also suggest that some special quantum state with non-zero quantum discord may be created.     

Spin Squeezing and Fixed-Point Bifurcation

We study spin squeezing and classical bifurcation in a nonlinear bipartite system. We show that the spin squeezing can be associated with a fixed-point bifurcation in the classical dynamics, namely, it acts as an indicator of the classical bifurcation. For the ground state of a system with coupled giant spins, we find that the spin squeezing achieves its minimum value near the bifurcation point. We also study the dynamics of the spin squeezing, for an initial state corresponding to one of the fixed point, we find that in the stable regime, the spin squeezing exhibits periodic oscillation and always persists except at some fixed times, while in the unstable regime, the periodic oscillation phenomenon disappears and the spin squeezing survives for a short time. Finally, we show that the mean spin squeezing, which is defined to be averaged over time, attains its minimum value near the bifurcation point.     

Spin Squeezing and Fixed-Point Bifurcation

We study spin squeezing and classical bifurcation in a nonlinear bipartite system. We show that the spin squeezing can be associated with a fixed-point bifurcation in the classical dynamics, namely, it acts as an indicator of the classical bifurcation. For the ground state of a system with coupled giant spins, we find that the spin squeezing achieves its minimum value near the bifurcation point. We also study the dynamics of the spin squeezing, for an initial state corresponding to one of the fixed point, we find that in the stable regime, the spin squeezing exhibits periodic oscillation and always persists except at some fixed times, while in the unstable regime, the periodic oscillation phenomenon disappears and the spin squeezing survives for a short time. Finally, we show that the mean spin squeezing, which is defined to be averaged over time, attains its minimum value near the bifurcation point.     

Entanglement and Other Nonclassical Properties of Two Two-Level Atoms Interacting with a Two-Mode Binomial Field: Constant and Intensity-Dependent Coupling Regimes

In this paper, we consider the interaction between two two-level atoms and a two-mode binomial field with a general intensity-dependent coupling regime. The outlined dynamical problem has explicit analytical solution, by which we can evaluate a few of its physical features of interest. To achieve the purpose of the paper, after choosing a particular nonlinearity function, we investigate the quantum statistics, atomic population inversion and at last the linear entropy of the atom-field system which is a good measure for the degree of entanglement. In detail, the effects of binomial field parameters, in addition to different initial atomic states on the temporal behavior of the mentioned quantities have been analyzed. The results show that, the values of binomial field parameters and the initial state of the two atoms influence on the nonclassical effects in the obtained states through which one can tune the nonclassicality criteria appropriately. Setting intensity-dependent coupling function equal to 1 reduces the results to the constant coupling case. By comparing the latter case with the nonlinear regime, we will observe that the nonlinearity disappears the pattern of collapse-revival phenomenon in the evolution of Mandel parameter and population inversion (which can be seen in the linear case with constant coupling), however, more typical collapse-revivals will be appeared for the cross-correlation function in the nonlinear case. Finally, in both linear and nonlinear regime, the entropy remains less than (but close to) 0.5. In other words the particular chosen nonlinearity does not critically affect on the entropy of the system.     

Entanglement and Other Nonclassical Properties of Two Two-Level Atoms Interacting with a Two-Mode Binomial Field: Constant and Intensity-Dependent Coupling Regimes

In this paper, we consider the interaction between two two-level atoms and a two-mode binomial field with a general intensity-dependent coupling regime. The outlined dynamical problem has explicit analytical solution, by which we can evaluate a few of its physical features of interest. To achieve the purpose of the paper, after choosing a particular nonlinearity function, we investigate the quantum statistics, atomic population inversion and at last the linear entropy of the atom-field system which is a good measure for the degree of entanglement. In detail, the effects of binomial field parameters, in addition to different initial atomic states on the temporal behavior of the mentioned quantities have been analyzed. The results show that, the values of binomial field parameters and the initial state of the two atoms influence on the nonclassical effects in the obtained states through which one can tune the nonclassicality criteria appropriately.Setting intensity-dependent coupling function equal to 1 reduces the results to the constant coupling case. By comparing the latter case with the nonlinear regime, we will observe that the nonlinearity disappears the pattern of collapse-revival phenomenon in the evolution of Mandel parameter and population inversion(which can be seen in the linear case with constant coupling), however, more typical collapse-revivals will be appeared for the cross-correlation function in the nonlinear case. Finally, in both linear and nonlinear regime, the entropy remains less than(but close to) 0.5. In other words the particular chosen nonlinearity does not critically affect on the entropy of the system.     

Sudden death and robustness of quantum correlations in the weak- or strong-coupling regime

We study the dynamics of quantum discord and entanglement of two entangled two-level atoms within two isolated and dissipative cavities in the weak- or strong-coupling regime. The quantum entanglement are measured by concurrence and relative entropy. The quantum discord of two atoms based on quantum mutual information and relative entropy are also calculated. In the weak-coupling regime, the sudden death of quantum discord and entanglement of two atoms can occur simultaneously within a short interaction time. When the interaction time is long, quantum discord and entanglement of two atoms could be partially preserved due to the long-lived nature of quantum discord and entanglement. However, in the strong-coupling regime, there is no sudden death of quantum discord though the entanglement sudden death phenomenon occurs. In addition, we observe that entanglement and discord will be destroyed eventually when the atom-field interactions are strong. We also address the issue of experimental realization briefly.     

Resonant enhancement and dissipation in nonequilibrium van der Waals forces

Dispersion forces between molecules that are in relative motion, coupled to baths at different temperatures, or in excited states, are calculated using a Green function Liouville space expansion that extends the celebrated McLachlan response theory to the nonlinear regime. Our dynamical theory is applicable to systems that may be in any initial nonequilibrium state and that are subject to an arbitrary time-dependent coupling. In contrast to equilibrium forces which are attractive, nonequilibrium forces may be attractive or repulsive, exhibit chemically specific resonances, are far stronger, and may be nonconservative (with either positive or negative dissipation).     

Tavis-Cummings模型中的几何量子失协特性

采用几何量子失协的计算方法,通过改变两原子初始状态、腔内光子数和偶极-偶极相互作用强度,研究了Tavis-Cummings模型中的几何量子失协特性.结果表明:几何量子失协都是随时间周期性振荡的,选取适当的初态可以使两原子一直保持失协状态,增加腔内光子数和偶极相互作用对几何量子失协有积极的影响.     

Growth and Nonlinear Saturation of Fluctuations in a Nonlinear Oscillator at the Threshold of a Bifurcation of Spontaneous Symmetry Breaking

We consider the phenomenon of prebifurcation noise amplification in a nonlinear oscillator at the threshold of a bifurcation of spontaneous symmetry breaking. The studies are based on the model of a nonlinear oscillator in which the potential relief transforms from monostable to symmetric bistable and the noise acting on the system is assumed Gaussian and short-correlated. The fluctuation variance as a function of the regime of the system and the rate at which the bifurcation threshold is reached are examined. Our analytical estimates are in good agreement with the results of numerical simulation for both the linear growth and the nonlinear saturation of fluctuations. It is noted that in the case of fast bifurcation transitions, a loop of noise-dependent hysteresis and breaking of probability symmetry of stable final states are observed in the nonlinear oscillator. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 5, pp. 425–435, May 2005.     

Dynamics of quantum discord for two correlated qubits in two independent reservoirs at finite temperature

We investigate dynamics of quantum discord (QD) for two initially-correlated qubits in two independent Ohmic reservoirs at finite temperature. It is indicated that the QD changes from a constant regime to a decaying regime when the two qubits are initially prepared in X-type quantum states. In the QD constant regime, the initial QD can be preserved despite decoherence in the system. It is found that temperature difference between two reservoirs significantly affects the preservation duration (PD) of the initial QD. We show that it is possible to enhance the preservation duration by properly choosing system parameters of the two qubits and reservoir parameters. Physically, it is found that the PD of the QD can reflect the temperature inhomogeneity of the non-equilibrium system which consists of the two qubits and their reservoirs.     

The Dynamics of Quantum Correlations in Mixed Classical Environments

We present a comparative study of the dynamics of entanglement and quantum discord in a bipartite system in the presence of mixed classical noises. In particular, the joint effects of three different types of classical noises, namely, random telegraphic noise (RTN), Ornstein–Uhlenbeck noise (OU), and static noise, are studied by combining them in two different ways. In each case, one marginal system is coupled with random telegraphic noise, and the other marginal system is coupled with either OU or static noise. We make a comparison between the behaviors of both correlations in the two setups. In the weak coupling regime, the qualitative behavior of entanglement is unaffected by switching the coupling of only one marginal system from OU to static noise, and vice versa. However, the behavior of quantum discord strongly depends on whether it is coupled with OU or static noise. On the other hand, in the strong coupling regime, the static noise is more fatal to the survival of both correlations as compared to the other two noises.     

量子关联与原子间相互作用距离关系的研究

本文将两个二能级原子注入一个腔中,用共生纠缠的方法来度量两原子之间的纠缠并推出它们之间的量子失协,还给出了原子与环境之间的共生纠缠与量子失协的计算公式,讨论了原子自发衰变率的变化对量子纠缠及失协的影响,及不同的初始状态情况下,纠缠及失协随原子距离的演化情况。结果表明：原子自发衰变率减小,原子与环境之间的量子纠缠及失协增加;选择不同的初态,可以控制原子间出现纠缠死亡的现象或量子失协为零的状态。     

量子关联与原子间相互作用距离关系的研究

本文将两个二能级原子注入一个腔中,用共生纠缠的方法来度量两原子之间的纠缠并推出它们之间的量子失协,还给出了原子与环境之间的共生纠缠与量子失协的计算公式,讨论了原子自发衰变率的变化对量子纠缠及失协的影响,及不同的初始状态情况下,纠缠及失协随原子距离的演化情况。结果表明：原子自发衰变率减小,原子与环境之间的量子纠缠及失协增加;选择不同的初态,可以控制原子间出现纠缠死亡的现象或量子失协为零的状态。     

量子关联与原子间相互作用距离关系的研究

本文将两个二能级原子注入一个腔中,用共生纠缠的方法来度量两原子之间的纠缠并推出它们之间的量子失协,还给出了原子与环境之间的共生纠缠与量子失协的计算公式,讨论了原子自发衰变率的变化对量子纠缠及失协的影响,及不同的初始状态情况下,纠缠及失协随原子距离的演化情况.结果表明:原子自发衰变率减小,原子与环境之间的量子纠缠及失协增加;选择不同的初态,可以控制原子间出现纠缠死亡的现象或量子失协为零的状态.     

Reentrant and whirling hexagons in non-Boussinesq convection

We review recent computational results for hexagon patterns in non-Boussinesq convection. For sufficiently strong dependence of the fluid parameters on the temperature we find reentrance of steady hexagons, i.e. while near onset the hexagon patterns become unstable to rolls as usually, they become again stable in the strongly nonlinear regime. If the convection apparatus is rotated about a vertical axis the transition from hexagons to rolls is replaced by a Hopf bifurcation to whirling hexagons. For weak non-Boussinesq effects they display defect chaos of the type described by the two-dimensional (2D) complex Ginzburg–Landau equation. For stronger non-Boussinesq effects the Hopf bifurcation becomes subcritical and localized bursting of the whirling amplitude is found. In this regime the coupling of the whirling amplitude to (small) deformations of the hexagon lattice becomes important. For yet stronger non-Boussinesq effects this coupling breaks up the hexagon lattice and strongly disordered states characterized by whirling and lattice defects are obtained.     

Universal occurrence of the phase-flip bifurcation in time-delay coupled systems

Recently, the phase-flip bifurcation has been described as a fundamental transition in time-delay coupled, phase-synchronized nonlinear dynamical systems. The bifurcation is characterized by a change of the synchronized dynamics from being in-phase to antiphase, or vice versa; the phase-difference between the oscillators undergoes a jump of pi as a function of the coupling strength or the time delay. This phase-flip is accompanied by discontinuous changes in the frequency of the synchronized oscillators, and in the largest negative Lyapunov exponent or its derivative. Here we illustrate the phenomenology of the bifurcation for several classes of nonlinear oscillators, in the regimes of both periodic and chaotic dynamics. We present extensive numerical simulations and compute the oscillation frequencies and the Lyapunov spectra as a function of the coupling strength. In particular, our simulations provide clear evidence of the phase-flip bifurcation in excitable laser and Fitzhugh-Nagumo neuronal models, and in diffusively coupled predator-prey models with either limit cycle or chaotic dynamics. Our analysis demonstrates marked jumps of the time-delayed and instantaneous fluxes between the two interacting oscillators across the bifurcation; this has strong implications for the performance of the system as well as for practical applications. We further construct an electronic circuit consisting of two coupled Chua oscillators and provide the first formal experimental demonstration of the bifurcation. In totality, our study demonstrates that the phase-flip phenomenon is of broad relevance and importance for a wide range of physical and natural systems.     

Steady-State Discord Between Two Qubits Coupled Collectively to a Thermal Reservoir

We study the dynamics of quantum discord between two qubits coupled collectively to a thermal reservoir. For comparison, we also consider the dynamics of quantum entanglement. It is shown that we can obtain a stable quantum discord induced by the thermal environment when the discord of the initial state is zero. The thermal environment can also induce a stable amplification of the initially prepared quantum discord for certain X-type states. It is very valuable that the quantum discord is more resistant against the thermal environment than quantum entanglement. And, we have demonstrated that the sudden death of discord in a Markovian regime is impossible even at high temperature. It provides us a feasible way to create and protect quantum correlation in the case of a high-temperature thermal environment for various physical system such as trapped ions, quantum dots or Josephson junctions.     

Internal mode mechanism for collective energy transport in extended systems

We study directed energy transport in homogeneous nonlinear extended systems in the presence of homogeneous ac forces and dissipation. We show that the mechanism responsible for unidirectional motion of topological excitations is the coupling of their internal and translation degrees of freedom. Our results lead to a selection rule for the existence of such motion based on resonances that explain earlier symmetry analysis of this phenomenon. The direction of motion is found to depend both on the initial and the relative phases of the two harmonic drivings, even in the presence of noise.     

High-order subharmonic parametric resonance of nonlinearly coupled micromechanical oscillators

This paper studies parametric resonance of coupled micromechanical oscillators under periodically varying nonlinear coupling forces. Different from most of previous related works in which the periodically varying coupling forces between adjacent oscillators are linearized, our work focuses on new physical phenomena caused by the periodically varying nonlinear coupling. Harmonic balance method (HBM) combined with Newton iteration method is employed to find steady-state periodic solutions. Similar to linearly coupled oscillators studied previously, the present model predicts superharmonic parametric resonance and the lower-order subharmonic parametric resonance. On the other hand, the present analysis shows that periodically varying nonlinear coupling considered in the present model does lead to the appearance of high-order subharmonic parametric resonance when the external excitation frequency is a multiple or nearly a multiple (≥3) of one of the natural frequencies of the oscillator system. This remarkable new phenomenon does not appear in the linearly coupled micromechanical oscillators studied previously, and makes the range of exciting resonance frequencies expanded to infinity. In addition, the effect of a linear damping on parametric resonance is studied in detail, and the conditions for the occurrence of the high-order subharmonics with a linear damping are discussed.