Dynamics of the geometric phase in the adiabatic limit of a quench induced quantum phase transition

The geometric phase associated with a many body ground state exhibits a signature of quantum phase transition. In this context, we have studied the behavior of the geometric phase during a linear quench caused by a gradual turning off of the magnetic field interacting with a spin chain.     

The quantum geometric phase as a transformation invariant

The kinematic approach to the theory of the geometric phase is outlined. This phase is shown to be the simplest invariant under natural groups of transformations on curves in Hilbert space. The connection to the Bargmann invariant is brought out, and the case of group representations described.     

量子逻辑网络的核磁共振实现

利用相位相反技术,设计出了实现精确的CN门的脉冲序列;构造了三量子位的双重控制相位旋转门（CCS门）,它是将核磁共振(NMR)实现Grover量子算法从二量子位推广到三量子位的关键逻辑门,而且,依此方法,可以用NMR实现N量子位的Grover量子算法;还给出了量子Toffoli门以及量子态的各种对称操作的逻辑部件。所有这些逻辑操作都是构建量子态工程的工具。文中大部分脉冲序列己经在实验中得到验证,这些结果对于量子计算的理论研究和实验实现都具有现实意义。     

Characterizing quantum phase transition by teleportation

In this paper we provide a novel way to explore the relation between quantum teleportation and quantum phase transition. We construct a quantum channel with a mixed state which is made from one dimensional quantum Ising chain with infinite length, and then consider the teleportation with the use of entangled Werner states as input qubits. The fidelity as a figure of merit to measure how well the quantum state is transferred is studied numerically. Remarkably we find the first-order derivative of the fidelity with respect to the parameter in quantum Ising chain exhibits a logarithmic divergence at the quantum critical point. The implications of this phenomenon and possible applications are also briefly discussed.     

Quantum renormalization group approach to geometric phases in spin chains

A relation between geometric phases and criticality of spin chains are studied using the quantum renormalization-group approach. I have shown how the geometric phase evolve as the size of the system becomes large, i.e., the finite size scaling is obtained. The renormalization scheme demonstrates how the first derivative of the geometric phase with respect to the field strength diverges at the critical point and maximum value of the first derivative, and its position, scales with the exponent of the system size.     

基于腔QED系统的几何量子失谐及其传送

研究了基于腔量子电动力学（腔QED）系统的几何量子失谐及其传送。该系统包括两个独立的子系统,每个子系统由两个二能级原子与单模腔共振相互作用。结果表明,所有初始存储在原子A1A2中的几何量子失谐最终被转移到原子B1B2和腔C1C2。同时,原子A1A2 ,B1B2和腔C1C2的几何量子失谐在该量子系统中可以发生猝死（DSD）以及纠缠突然死亡（ESD）。但是,在该量子系统中几何量子失谐不能完全由于原子的自发辐射和腔衰减而复活。此外,原子A1A2 ,B1B2和腔C1C2几何量子失谐的量,取决于其纯度p,并与其成比例,p的值越小,几何失谐越小。它也表明,在原子自发辐射和腔衰减的情况下,原子A1A2 ,B1B2和腔C1C2的几何量子失谐将经历振荡衰减并最终衰减到零。不过,在没有原子自发辐射和腔衰减的情况下,原子A1A2 ,B1B2和腔C1C2的几何量子失谐却没有衰减。     

基于腔QED系统的几何量子失谐及其传送

研究了基于腔量子电动力学（腔QED）系统的几何量子失谐及其传送。该系统包括两个独立的子系统,每个子系统由两个二能级原子与单模腔共振相互作用。结果表明,所有初始存储在原子A1A2中的几何量子失谐最终被转移到原子B1B2和腔C1C2。同时,原子A1A2 ,B1B2和腔C1C2的几何量子失谐在该量子系统中可以发生猝死（DSD）以及纠缠突然死亡（ESD）。但是,在该量子系统中几何量子失谐不能完全由于原子的自发辐射和腔衰减而复活。此外,原子A1A2 ,B1B2和腔C1C2几何量子失谐的量,取决于其纯度p,并与其成比例,p的值越小,几何失谐越小。它也表明,在原子自发辐射和腔衰减的情况下,原子A1A2 ,B1B2和腔C1C2的几何量子失谐将经历振荡衰减并最终衰减到零。不过,在没有原子自发辐射和腔衰减的情况下,原子A1A2 ,B1B2和腔C1C2的几何量子失谐却没有衰减。     

Implementation of controlled phase shift gates and Collins version of Deutsch-Jozsa algorithm on a quadrupolar spin-7/2 nucleus using non-adiabatic geometric phases

In this work controlled phase shift gates are implemented on a qaudrupolar system, by using non-adiabatic geometric phases. A general procedure is given, for implementing controlled phase shift gates in an ‘N’ level system. The utility of such controlled phase shift gates, is demonstrated here by implementing 3-qubit Deutsch–Jozsa algorithm on a spin-7/2 quadrupolar nucleus oriented in a liquid crystal matrix.     

Sudden change of geometric quantum discord in finite temperature reservoirs

We investigate sudden change (SC) behaviors of the distance-based measures of geometric quantum discords (GQDs) for two non-interacting qubits subject to the two-sided and the one-sided thermal reservoirs. We found that the GQDs defined by different distances exhibit different SCs, and thus the SCs are the combined result of the chosen discord measure and the property of a state. We also found that the thermal reservoir may generate states having different orderings related to different GQDs. These inherent differences of the GQDs reveal that they are incompatible in characterizing quantum correlations both quantitatively and qualitatively.     

Dynamics control of geometric quantum discord for two coupling qubits in a squeezed vacuum reservoir

We investigate the dynamics of geometric quantum discord of coupled qubits in a squeezed vacuum reservoir. The results show that there is distinct difference between the dynamics of geometric quantum discord and that of quantum entanglement near (or away from) the decoherence free subspace. We also find that the squeezed vacuum reservoir with high squeezed amplitude is more suitable for geometric quantum discord to survive. The robustness of geometric quantum discord is stronger than that of quantum entanglement.     

具有三体相互作用海森堡自旋链模型的纠缠与几何失协

近年来有研究发现量子失协可以度量非纠缠的量子关联,而且非纠缠的量子关联在量子通信和量子计算中起到很重要的作用.研究了磁场,两种三体相互作用,各向异性参数,耦合常数,温度等参数对同时具有两种三体相互作用海森堡XXZ自旋链系统的量子纠缠,几何失协的影响以及与量子相变的关系.研究表明:量子纠缠和几何失协都可以清晰的表征本模型系统的量子相变现象; 随着XZX+YZY型三体相互作用的增加量子纠缠和几何失协即使在高温时也可达到最大值;几何失协比量子纠缠更全面地描述了量子关联; XZY-YZX型三体相互作用的增加对量子纠缠有抑制作用;XZY-YZX型三体相互作用在一定区域内的增加对几何失协有抑制作用,在另一区域的增加可使几何失协增大到一个稳定的非零值。增大磁场和自旋耦合常数,减小各向异性参数会使纠缠的临界温度变大; 调节自旋耦合常数可更有效的使量子纠缠和几何失协在高温时仍有一个较大的值.同时发现,在磁场 和各向异性参数 的区域两种量子关联都可以维持在最大值.     

具有三体相互作用海森堡自旋链模型的纠缠与几何失协

近年来有研究发现量子失协可以度量非纠缠的量子关联,而且非纠缠的量子关联在量子通信和量子计算中起到很重要的作用.本文研究了磁场,两种三体相互作用,各向异性参数,耦合常数,温度等参数对同时具有两种三体相互作用海森堡XXZ自旋链系统的量子纠缠,几何失协的影响以及与量子相变的关系.研究表明:量子纠缠和几何失协都可以清晰的表征本模型系统的量子相变现象;随着XZX+YZY型三体相互作用的增加量子纠缠和几何失协即使在高温时也可达到最大值;几何失协比量子纠缠更全面地描述了量子关联;XZY-YZX型三体相互作用的增加对量子纠缠有抑制作用;XZY-YZX型三体相互作用在一定区域内的增加对几何失协有抑制作用,在另一区域的增加可使几何失协增大到一个稳定的非零值.增大磁场和自旋耦合常数,减小各向异性参数会使纠缠的临界温度变大;调节自旋耦合常数可更有效的使量子纠缠和几何失协在高温时仍有一个较大的值.同时发现,在磁场0B5和各向异性参数-1J_Z10的区域两种量子关联都可以维持在最大值.     

Pancharatnam geometric phase originating from successive partial projections

The spin of a polarized neutron beam subjected to a partial projection in another direction, traces a geodesic arc in the 2-sphere ray space. We delineate the geometric phase resulting from two successive partial projections on a general quantal state and derive the direction and strength of the third partial projection that would close the geodesic triangle. The constraint for the three successive partial projections to be identically equivalent to a net spin rotation regardless of the initial state, is derived.      

Observation of a non-adiabatic geometric phase for elastic waves

We report the experimental observation of a geometric phase for elastic waves in a waveguide with helical shape. The setup reproduces the experiment by Tomita and Chiao [A. Tomita, R.Y. Chiao, Phys. Rev. Lett. 57 (1986) 937–940, 2471] that showed first evidence of a Berry phase, a geometric phase for adiabatic time evolution, in optics. Experimental evidence of a non-adiabatic geometric phase has been reported in quantum mechanics. We have performed an experiment to observe the polarization transport of classical elastic waves. In a waveguide, these waves are polarized and dispersive. Whereas the wavelength is of the same order of magnitude as the helix’s radius, no frequency dependent correction is necessary to account for the theoretical prediction. This shows that in this regime, the geometric phase results directly from geometry and not from a correction to an adiabatic phase.     

关于Lewis-Riesenfeld相位和量子几何相位

评注了《大学物理》21 23一文关于量子几何相位与Lewis相位论述与《物理学报》48 2018一文的结论有极大不同.指出前者对Lewis导出的相位与量子几何相位关系的错误陈述，而后者的结论是正确的. 关键词： 量子几何相位 不变量方法 Lewis-Riesenfeld相位     

Geometric phase within the complex quantum Hamilton-Jacobi formalism

We derive a geometric phase using the quantum kinematic approach within the complex quantum Hamilton-Jacobi formalism. The single valuedness of the wave function implies that the geometric phase along an arbitrary path in the complex plane must be equal to an integer multiple of 2π. The nonzero geometric phase indicates that we travel along the path through the branch cut of the phase function from one Riemann sheet to another.