Quantum Correlations and Speed Limit of Central Spin Systems

In this article, single, and two-qubit central spin systems interacting with spin baths are considered and their dynamical properties are discussed. The cases of interacting and non-interacting spin baths are considered and the quantum speed limit (QSL) time of evolution is investigated. The impact of the size of the spin bath on the quantum speed limit for a single qubit central spin model is analyzed. The quantum correlations for (non-)interacting two central spin qubits are estimated and their dynamical behavior with that of QSL time under various conditions are compared. How QSL time could be availed to analyze the dynamics of quantum correlations is shown.     

Quantum communication in spin star configuration

This paper considers a generalized spin star system which can be solved exactly, with the central spin-1/2 system embedded in an outer ring of N spin-1/2 particles（denoted as spin bath）. In this model, in addition to the central-outer interaction, each pair of nearest neighbour of the bath interacts within themselves. The general expressions of the eigenstates as well as the eigenvalues of the model are derived with the use of the symmetries of system. It analyses the quantum state transfer and the dynamical behaviour of entanglement created during quantum communication. It also analyses the efficiency of the configuration regarded as quantum phase covariant clone or decoherence model. Some interesting results are discovered concerning the properties of quantum communication in this model.     

Entanglement Dynamics of Two Coupled Spins in a Spin Star Environment

We theoretically study the entanglement dynamics of two coupled spins in a spin star environment, whose elements are coupled to local bosonic baths. It is shown that the dynamics of the entanglement depends on the initial state of the system and the coupling strength between the two coupled central spins, the interactions between the central system and the environment, as well as interactions between the bath spin and the reservoir. We also investigate the effect of non-Markovian dynamics in contrast with the Markovian case. It is found that the non-Markovian dynamics has a significant effect on the disentanglement between the two central spins.     

The Dynamical Evolution of Quantum Correlations in the Two Isolate Spin Particles Coupled to a Common Bath

We study the dynamical evolution of quantum correlations between two central spins independently coupled to a common bath, which are represented by quantum entanglement and quantum discord. According to the results of the exact solution, we show that quantum discord is more robust and includes richer correlation than quantum entanglement due to the nonvanishing quantum correlation in the region of entanglement death, i.e., the separable states maybe contain nonclassical correlations. We discuss the effects of the intrinsic properties of the bath on quantum correlation between the two central spins in the XY and XXZ model baths. At the low temperature, the central system can keep the good quantum correlation. With the more spin number in the bath, the dynamical evolution of quantum correlation can be bounded with the small oscillation and finally approaches a stable value. In addition, we find that the interaction between the central spins and the bath in the z direction has the significant effects on quantum correlation of the central spin system.     

Restoring coherence lost to a slow interacting mesoscopic spin bath

For a two-state quantum object interacting with a slow mesoscopic interacting spin bath, we show that a many-body solution of the bath dynamics conditioned on the quantum-object state leads to an efficient control scheme to recover the lost quantum-object coherence through disentanglement. We demonstrate the theory with the realistic problem of one electron spin in a bath of many interacting nuclear spins in a semiconductor quantum dot. The spin language can be easily generalized to a quantum object in contact with a bath of interacting multilevel quantum units with the caveat that the bath is mesoscopic and its dynamics is slow compared with the quantum object.     

Quantum fidelity for Gaussian states describing the evolution of open systems

Using the expression of the fidelity for the most general Gaussian quantum states, the quantum fidelity is studied for the states of a harmonic oscillator interacting with an environment, in particular with a thermal bath. The time evolution of the considered system is described in the framework of the theory of open systems based on quantum dynamical semigroups. By taking a correlated squeezed Gaussian state as initial state, we calculate the quantum fidelity for both undisplaced and displaced states. The time evolution of the quantum fidelity is analyzed depending on the squeezing and correlation parameters characterizing the initial Gaussian state and on the dissipation constant and temperature of the thermal bath.     

Non-Gaussian noise in quantum spin glasses and interacting two-level systems

We study a general model for non-Gaussian 1/f noise based on an infinite range quantum Ising spin system in the paramagnetic state, or, equivalently, interacting two-level classical fluctuators. We identify a dilatation interaction term in the dynamics which survives the thermodynamic limit and circumvents the central limit theorem to produce non-Gaussian noise even when the equilibrium distribution is that of noninteracting spins. The resulting second spectrum ("noise of the noise") itself has a universal 1/f form which we analyze within a dynamical mean-field approximation.     

Ground-state and dynamical properties of a spin-S Heisenberg star

We generalize the Heisenberg star consisting of a spin-1/2 central spin and a homogeneously coupled spin bath modeled by the XXX ring [Richter J and Voigt A 1994 J. Phys. A: Math. Gen. 27 1139-1149] to the case of arbitrary central-spin size S < N/2, where N is the number of bath spins. We describe how to block-diagonalize the model based on the Bethe ansatz solution of the XXX ring, with the dimension of each block Hamiltonian ≤ 2S + 1. We obtain all the eigenenergies and explicit expressions of the sub-ground states in each l-subspace with l being the total angular momentum of the bath. Both the eigenenergies and the sub-ground states have distinct structures depending whether S ≤ l or l < S. The absolute ground-state energy and the corresponding l as functions of the intrabath coupling are numerically calculated for N = 16 and S = 1, 2, ⋯ ,7 and their behaviors are quantitatively explained in the weak and strong intrabath coupling limits. We then study the dynamics of the antiferromagnetic order within an XXX bath prepared in the Néel state. Effects of the initial state of the central spin, the value of S, and the system-bath coupling strength on the staggered magnetization dynamics are investigated. By including a Zeeman term for the central spin and the anisotropy in the intrabath coupling, we also study the polarization dynamics of the central spin for a bath prepared in the spin coherent state. Under the resonant condition and at the isotropic point of the bath, the polarization dynamics for S > 1/2 exhibit collapse-revival behaviors with fine structures. However, the collapse-revival phenomena are found to be fragile with respect to the anisotropy of the intrabath coupling.     

Quantum dynamics of Gaudin magnets

Quantum dynamics of many-body systems is a fascinating and significant subject for both theory and experiment. The question of how an isolated many-body system evolves to its steady state after a sudden perturbation or quench still remains challenging. In this paper, using the Bethe ansatz wave function, we study the quantum dynamics of an inhomogeneous Gaudin magnet. We derive explicit analytical expressions for various local dynamic quantities with an arbitrary number of flipped bath spins, such as: the spin distribution function, the spin–spin correlation function, and the Loschmidt echo. We also numerically study the relaxation behavior of these dynamic properties, gaining considerable insight into coherence and entanglement between the central spin and the bath. In particular, we find that the spin–spin correlations relax to their steady value via a nearly logarithmic scaling, whereas the Loschmidt echo shows an exponential relaxation to its steady value. Our results advance the understanding of relaxation dynamics and quantum correlations of long-range interacting models of the Gaudin type.     

Quantum spin dynamics of mode-squeezed Luttinger liquids in two-component atomic gases

We report on the observation of many-body spin dynamics of interacting, one-dimensional (1D) ultracold bosonic gases with two spin states. By controlling the nonlinear atomic interactions close to a Feshbach resonance we are able to induce a phase diffusive many-body spin dynamics of the relative phase between the two components. We monitor this dynamical evolution by Ramsey interferometry, supplemented by a novel, many-body echo technique, which unveils the role of quantum fluctuations in 1D. We find that the time evolution of the system is well described by a Luttinger liquid initially prepared in a multimode squeezed state. Our approach allows us to probe the nonequilibrium evolution of one-dimensional many-body quantum systems.     

Quantum Speed Limit for Dynamics of Central Spin Model with Initial System-Bath Correlations

We investigate the quantum speed limit (QSL) time of an electronic spin coupled to a bath of nuclear spins. We consider three types of initial states with different correlations between the system and bath, i.e., quantum correlation, classical correlation, and no any correlation. Interestingly, we show that the QSL times of the central spin for these three types of initial correlations are identical when the couplings are homogeneous. However, it is remarkable different for inhomogenous couplings. The QSL time of the central spin is sensitive to the initial states, the average coupling strength, the distribution of the couplings between the system and bath and the number of the nuclear spins in the bath. Furthermore, we find that the coherence in the initial state has significant influences on the QSL time of the system, and can lead to the increase of QSL time for homogeneous couplings.     

转动双星同步和轨道圆化的物理过程研究

潮汐效应是影响恒星结构和演化非常重要的物理因素.本文研究了影响潮汐同步和轨道圆化的物理因素,如恒星质量、初始转速、轨道周期、金属丰度、对流超射等,并根据转动恒星的角动量转移和元素扩散方程,给出了这些因素对转动双星演化和元素混合的影响.结果表明：具有大质量子星、初始转速慢、对流超射小、轨道周期短的双星系统,能更早地达到平衡速度和轨道圆化;初始转速快的恒星,由于潮汐同步过程减速,双星系统中氮元素增丰没有单星的氮元素增丰显著;大质量星、高金属丰度、超射大和短周期的双星系统,氮增丰相对显著;质量小、金属丰度低、转速慢、超射大的恒星具有较小的恒星半径,而低金属丰度恒星表面却具有较高的有效温度,快速转动单星向低温和低光度端演化.     

Dynamics and protection of tripartite quantum correlations in a thermal bath

We study the dynamics and protection of tripartite quantum correlations in terms of genuinely tripartite concurrence, lower bound of concurrence and tripartite geometric quantum discord in a three-qubit system interacting with independent thermal bath. By comparing the dynamics of entanglement with that of quantum discord for initial GHZ state and W state, we find that W state is more robust than GHZ state, and quantum discord performs better than entanglement against the decoherence induced by the thermal bath. When the bath temperature is low, for the initial GHZ state, combining weak measurement and measurement reversal is necessary for a successful protection of quantum correlations. But for the initial W state, the protection depends solely upon the measurement reversal. In addition, the protection cannot usually be realized irrespective of the initial states as the bath temperature increases.     

Long time evolution of a spin interacting with a spin bath in arbitrary magnetic field

We introduce a completely different method to calculate the evolution of a spin interacting with a sufficient large spin bath,especially suitable for treating the central spin model in a quantum dot(QD).With only an approximation on the envelope of central spin,the symmetry can be exploited to reduce a huge Hilbert space which cannot be calculated with computers to many small ones which can be solved exactly.This method can be used to calculate spin-bath evolution for a spin bath containing many(say,1000)spins,without a perturbative limit such as strong magnetic field condition,and works for long-time regime with sufficient accuracy.As the spin-bath evolution can be calculated for a wide range of time and magnetic field,an optimal dynamic of spin flip-flop can be found,and more sophisticated approaches to achieve extremely high polarization of nuclear spins in a QD could be developed.     

Thermal tripartite quantum correlations: quantum discord and entanglement perspectives

We investigate thermal tripartite quantum correlations for a spin star network and for a new extended version of it. In a spin star network, three peripheral spins interact with the central spin identically while in extended spin star network, three peripheral spins interact with two central spatially separated spins in the same way. We exploit the method of [C.C. Rulli, M.S. Sarandy, Phys. Rev. A 84, 042109 (2011)] to evaluate the tripartite quantum discord (TQD) and the method of [M. Li, S. Fei, Z. Wang, Rep. Math. Phys 65, 289 (2010)] called as lower bound of tripartite concurrence (LBTC) to evaluate the tripartite entanglement (TE) of the the peripheral parties in both systems. It is found that thermal TQD is much more robust than thermal TE as a function of temperature T. Also, the peripheral parties of the extended spin star network, in comparison with those of the spin star one, can exhibit higher values of TQD at T > 0. This, indeed, motivates us to realise improved quantum information and quantum computation tasks at finite temperatures.     

Intrinsic spin fluctuations reveal the dynamical response function of holes coupled to nuclear spin baths in (In,Ga)As quantum dots

The problem of how single central spins interact with a nuclear spin bath is essential for understanding decoherence and relaxation in many quantum systems, yet is highly nontrivial owing to the many-body couplings involved. Different models yield widely varying time scales and dynamical responses (exponential, power-law, gaussian, etc.). Here we detect the small random fluctuations of central spins in thermal equilibrium [holes in singly charged (In,Ga)As quantum dots] to reveal the time scales and functional form of bath-induced spin relaxation. This spin noise indicates long (400 ns) spin correlation times at a zero magnetic field that increase to ～5 μs as dominant hole-nuclear relaxation channels are suppressed with small (100 G) applied fields. Concomitantly, the noise line shape evolves from Lorentzian to power law, indicating a crossover from exponential to slow [～1/log(t)] dynamics.     

Brownian motion of spins; generalized spin Langevin equation

We derive the Langevin equations for a spin interacting with a heat bath, starting from a fully dynamical treatment. The obtained equations are non-Markovian with multiplicative fluctuations and concommitant dissipative terms obeying the fluctuation-dissipation theorem. In the Markovian limit our equations reduce to the phenomenological equations proposed by Kubo and Hashitsume. The perturbative treatment on our equations lead to Landau-Lifshitz equations and to other known results in the literature.     

Decoherence-and Dimerization-assisted Energy Transport in Protomer of Light-Harvesting Complexes

We have investigated the dynamics of a protomer coupled to two different decoherent environments,each in a configuration called the spin star configuration.Using the quantum mechanics method,in different situations,we obtain the analytical expressions for the transition probability in the protomer system.In thermal equilibrium,there exist well-defined ranges of parameters for which decoherent interaction between the protomer and the environment assists energy transfer in the protomer system,while in pure quantum mechanics states,the decoherent interaction assists energy transfer for an eigenstate but against energy transfer for quantum mechanics averages.In particular,we also find that the dimerization of two bacteriochlorophylls in protomer can always assist energy transfer in certain parameter range,and in the appropriate spin bath energy,the efficiency of energy transport is sensitively depended on the temperature of environments.