Decoherence-free generation of many-particle entanglement by adiabatic ground-state transitions

We discuss a decoherence insensitive method to create many-particle entanglement in a spin system with controllable collective interactions and propose an implementation in an ion trap. An adiabatic change of parameters allows a transfer from separable to a large variety of entangled eigenstates. We show that the Hamiltonian can have a supersymmetry permitting an explicit construction of the ground state at all times. Of particular interest is a transition in a nondegenerate ground state with a finite energy gap since here the influence of collective as well as individual decoherence mechanisms is substantially reduced. A lower bound for the energy gap is given.     

具有三自旋相互作用XX模型纠缠特性研究

利用Concurrence判据,研究了具有三自旋相互作用的XX模型的纠缠特性;分别在铁磁和反铁磁模型中研究了三自旋相互作用J_2和温度T对两自旋纠缠度的影响.结果表明,三自旋相互作用J_2提高系统的两体纠缠度,但是提高程度会因最近邻自旋间发生铁磁、反铁磁相互作用而有所差异;并且J_2影响两自旋系统纠缠消失的临界温度T_C,T_C会随J_2的增大而减小.系统温度T影响两体纠缠度,随着温度的降低,纠缠度会得到提高.此外,分别在系统本征态和基态中研究了两自旋的纠缠度,求出了系统发生量子相变的量子临界点.     

Hard chaos and adiabatic quantization: The wedge billiard

We present a study of a series of eigenstates occurring in the wedge billiard which may be quantized about tori by sejiclassical adiabatic quantization, even though the underlying classical system exhibits hard chaos and strictly possesses no tori. We also show that adiabatic eigenstates should be common in many chaotic systems, especially among the lower eigenstates, and present a heuristic argument as to why this should be so.     

Entanglement in the supermolecular dimer [Mn4]2

This paper investigates the entanglement in the supermolecular dimer [Mn4]2 consisting of a pair of single molecular magnets with antiferromagnetic exchange-coupllng J. The conventional yon Neumann entropy as a function of the exchange-coupling is calculated explicitly for all eigenstates with the quantum number range from M = M1 ＋ M2 = -9 to 0. It is shown that the yon Neumann entropy is not a monotonic function of the coupling strength. However, it is significant that the entropy of entanglement has the maximum values and the minimum values for most eigenstates, which is extremely useful in the quantum computing. It also presents the time-evolution of entanglement from various initial states. The results are useful in the design of devices based on the entanglement of two molecular magnets.     

Simulating a topological transition in a superconducting phase qubit by fast adiabatic trajectories

The significance of topological phases has been widely recognized in the community of condensed matter physics. The well controllable quantum systems provide an artificial platform to probe and engineer various topological phases. The adiabatic trajectory of a quantum state describes the change of the bulk Bloch eigenstates with the momentum, and this adiabatic simulation method is however practically limited due to quantum dissipation. Here we apply the “shortcut to adiabaticity” (STA) protocol to realize fast adiabatic evolutions in the system of a superconducting phase qubit. The resulting fast adiabatic trajectories illustrate the change of the bulk Bloch eigenstates in the Su-Schrieffer-Heeger (SSH) model. A sharp transition is experimentally determined for the topological invariant of a winding number. Our experiment helps identify the topological Chern number of a two-dimensional toy model, suggesting the applicability of the fast adiabatic simulation method for topological systems.     

基于绝热捷径快速实现远距离的四维纠缠态的制备

作为量子信息处理的载体,量子纠缠态一直以来都是量子信息领域的研究热点.相比于低维纠缠态,高维纠缠态使得量子通信具有更快的传输速度、更强的安全性、更高的噪声容忍阈值等特点.另外,绝热技术因其对实验参数起伏不敏感而被广泛应用于纠缠态的制备,然而绝热过程需要相当长的演化时间,因此绝热捷径应运而生.本文提出了一种采用无跃迁量子驱动构建绝热捷径实现快速制备两个原子的四维纠缠态的理论方案,该系统中的两个原子分别被囚禁在两个由光纤连接的双模腔中.为了获得一个技术上可操作的物理系统,本方案采用能级失谐设计出一个可精确驱动系统沿着某一个系统的瞬时本征态演化的哈密顿.该方案所采用的无跃迁量子驱动构建绝热捷径不仅大大缩短了演化时间,而且在实验上也比较容易实现.本文还数值模拟了消相干因素对四维纠缠态保真度的影响,结果表明,只要脉冲参数选取在一定范围内,光纤耗散、腔场耗散和原子自发辐射等不利因素都会被大大抑制.     

Adiabatic evolution under quantum control

One difficulty with adiabatic quantum computation is the limit on the computation time. Here we propose two schemes to speed-up the adiabatic evolution. To apply this controlled adiabatic evolution to adiabatic quantum computation, we design one of the schemes without any explicit knowledge of the instantaneous eigenstates of the final Hamiltonian. Whereas in another scheme, we assume that the ground state of the Hamiltonian is known, and this information can be used to design the control. By these techniques, a linear speed-up proportional to the nonlinearity can be predicted. As an illustration, we study a two-level system driven by a time-dependent magnetic field under the control. The problem of finding an item in an unsorted database by adiabatic evolution is also examined. The physics behind the control scheme is interpreted.     

Adiabatic condition for nonlinear systems

The adiabatic approximation is an important concept in quantum mechanics. In linear systems, the adiabatic condition is derived with the help of the instantaneous eigenvalues and eigenstates of the Hamiltonian, a procedure that breaks down in the presence of nonlinearity. Using an explicit example relevant to photoassociation of atoms into diatomic molecules, we demonstrate that the proper way to derive the adiabatic condition for nonlinear mean-field (or classical) systems is through a linearization procedure, using which an analytic adiabatic condition is obtained for the nonlinear model under study.     

Macroscopic inequivalent entanglement witness in Heisenberg spin chain

Motivated by the wise idea of entanglement witness (EW), we present an inequivalent entanglement witness (IEEW) that can analogously classify certain eigenstates entangled in inequivalent ways under stochastic local operations and classical communication (SLOCC) in the Heisenberg spin chain. Since the IEEW is the absolute value of magnetization | M| that is a macroscopically measurable quantity, our conclusions provide a macroscopic method to detect inequivalent entanglement between microscopic spins, on the one hand, and clearly show that inequivalent entanglement can yield different macroscopic effects, on the other hand.     

Quantum decoherence from adiabatic entanglement with external one or a few degrees of freedom

Based on the Born-Oppenhemer approximation, the concept of adiabatic quantum entanglement is introduced to account for quantum decoherence of a quantum system due to its interaction with a large system of one or a few degrees of freedom. In the adiabatic limit, it is shown that the wave function of the total system formed by the quantum system plus the large system can be factorized as an entangled state with correlation between adiabatic quantum states and quasi-classical motion configurations of the large system. In association with a novel viewpoint about quantum measurement, which has been directly verified by most recent experiments [e.g., S. Durr et al., Nature 33, 359 (1998)], it is shown that the adiabatic entanglement is indeed responsible for the quantum decoherence and thus can be regarded as a “clean” quantum measurement when the large system behaves as a classical object. By taking the large system respectively to be a macroscopically distinguishable spatial variable, a high spin system and a harmonic oscillator with a coherent initial state, three illustrations are presented with their explicit solutions in this paper. Received 26 February 2000 and Received in final form 14 July 2000     

Entanglement for Two Dissipative Qubits

Entanglement dynamics of two qubits from environmental perturbations with different initial conditions is investigated. The results show that the qubit-qubit interaction leads to a periodic disentanglement and entanglement. It is surprised that the sudden death of entanglement (ESD) does not happen for non-interacting qubits, but for both the cases of a pure dephasing environment and a normal environment, ESD emerges. The results may provide a useful clue to implement an entanglement quantum information.     

绝热演化中一般量子态的几何相位

在绝热演化中的几何相位（即Berry相位）被推广到包括非本征态的一般量子态.这个新的几何相位同时适用于线性量子系统和非线性量子系统.它对于后者尤其重要因为非线性量子系统的绝热演化不能通过本征态的线性叠加来描述.在线性量子系统中,新定义的几何相位是各个本征态Berry相位的权重平均.     

Berry phase of primordial scalar and tensor perturbations in single-field inflationary models

In the framework of the single-field slow-roll inflation, we derive the Hamiltonian of the linear primordial scalar and tensor perturbations in the form of time-dependent harmonic oscillator Hamiltonians. We find the invariant operators of the resulting Hamiltonians and use their eigenstates to calculate the adiabatic Berry phase for sub-horizon modes in terms of the Lewis–Riesenfeld phase. We conclude by discussing the discrepancy in the results of Pal et al. (2013) [21] for these Berry phases, which is resolved to yield agreement with our results.     

Quantum entanglement in exactly soluble atomic models: the Moshinsky model with three electrons,and with two electrons in a uniform magnetic field

We investigate the entanglement-related features of the eigenstates of two exactly soluble atomic models: a one-dimensional three-electron Moshinsky model, and a three-dimensional two-electron Moshinsky system in an external uniform magnetic field. We analytically compute the amount of entanglement exhibited by the wavefunctions corresponding to the ground, first and second excited states of the three-electron model. We found that the amount of entanglement of the system tends to increase with energy, and in the case of excited states we found a finite amount of entanglement in the limit of vanishing interaction. We also analyze the entanglement properties of the ground and first few excited states of the two-electron Moshinsky model in the presence of a magnetic field. The dependence of the eigenstates’ entanglement on the energy, as well as its behaviour in the regime of vanishing interaction, are similar to those observed in the three-electron system. On the other hand, the entanglement exhibits a monotonically decreasing behavior with the strength of the external magnetic field. For strong magnetic fields the entanglement approaches a finite asymptotic value that depends on the interaction strength. For both systems studied here we consider a perturbative approach in order to shed some light on the entanglement’s dependence on energy and also to clarify the finite entanglement exhibited by excited states in the limit of weak interactions. As far as we know, this is the first work that provides analytical and exact results for the entanglement properties of a three-electron model.     

Entanglement dynamics in two-component Bose--Einstein condensates

Based on the exact solution of the time-dependent Schr\"{o}dinger equation for two-species Bose--Einstein condensates (BECs) consisting of two hyperfine states of the atoms coupled by a tuned adiabatic and time-varying Raman coupling, we obtain analytically the entanglement dynamics of the system with various initial states, particularly the SU(2) coherent state, for both of cases with and without the nonlinear interactions. It is shown that the effect of nonlinear interaction on the entanglement appears only in a longer time period depending on the BEC parameters.     

周期驱动的Harper模型的量子计算鲁棒性与量子混沌

以周期驱动的量子Harper(quantum kicked Harper, QKH)模型为例，研究复杂量子动力系统的量子计算在各种干扰下的稳定性.通过对Floquet算子本征态的统计遍历性及其Husimi函数的分析，比较随机噪声干扰和静态干扰对量子计算不同程度的影响.进一步的保真度摄动分析表明，在随机噪声干扰下保真度随系统演化呈指数衰减，而静态干扰下的保真度为高斯衰减，并通过数值计算得到了干扰下的可信计算时间尺度.与经典混沌仿真中误差使状态产生指数分离不同，量子计算对状态干扰的稳定性和仿真模型的动力学特性无关. 关键词： 量子Harper模型 量子计算 量子混沌 保真度     

Quantum entanglement in a soluble two-electron model atom

We investigate the entanglement properties of bound states in an exactly soluble two-electron model, the Moshinsky atom. We present exact entanglement calculations for the ground, first and second excited states of the system. We find that these states become more entangled when the relative inter-particle interaction becomes stronger. As a general trend, we also observe that the entanglement of the eigenstates tends to increase with the states’ energy. There are, however, “entanglement level-crossings” where the entanglement of a state becomes larger than the entanglement of other states with higher energy. In the limit of weak interaction, we also compute (exactly) the entanglement of higher excited states. Excited states with anti-parallel spins are found to involve a considerable amount of entanglement even for an arbitrarily weak (but non zero) interaction. This minimum amount of entanglement increases monotonically with the state’s energy. Finally, the connection between entanglement and the Hartree-Fock approximation in the Moshinsky model is addressed. The quality of the ground-state Hartree-Fock approximation is shown to deteriorate, and the corresponding correlation energy to grow, as the entanglement of the (exact) ground state increases. The present work goes beyond previous related studies because we fully take into account the identical character of the two constituting particles in the entanglement calculations, and provide analytical, exact results both for the ground and the first few excited states.     

Nonadiabatic Berry Phase of a Two-State System and Nonstationarity of Quantum States

The nonadiabatic Berry phases in the magnetic resonance under .various initial conditions are investigated and compared with ,the adiabatic Berry phase. The generaJ formalism for calculating the nonadiabatic Berry phase of a two-state system in terpls of the expansion of instantaneous energy eigenstates is presented. Some numerical calculations and discussions are made. The Berry phase of a two-statesystem under an impulsive interaction is addressed.     

远距离三原子量子纠缠特性与其应用

三原子分别被束缚在用光纤环形连接单侧泄漏微光学腔场中,在微腔中输入激光驱动场和施加局域激光场,利用输入-输出技术及绝热近似理论,推导出一维Ising链模型的有效哈密顿量,该哈密顿量表明该系统会诱导出三原子中的任意两原子纠缠及三原子纠缠,用伴随数(concurrence)度量两原子纠缠,用内禀纠缠度量三原子纠缠,通过数值计算,给出两原子和三原子纠缠随时间演化曲线,通过适当调控激光驱动场和局域激光场,在远距离三原子中任意两原子实现未知量子态的隐形传送。     

Quantum phase control of entanglement

A method of phase control of entanglement in two-qubit systems is proposed. We show that by changing a relative phase of the pulses that drive the transitions in a two-qubit system with closed-loop couplings, one can control entanglement at will. The method relies on adiabatic dynamics via time-delayed pulse sequences and can be implemented with both resonant and nonresonant transitions.