Quantum phases and dynamics of geometric phase in a quantum spin chain under linear quench

We study the quantum phases of anisotropic XY spin chain in presence and absence of adiabatic quench. A connection between geometric phase and criticality is established from the dynamical behavior of the geometric phase for a quench induced quantum phase transition in a quantum spin chain. We predict XX criticality associated with a sequence of non-contractible geometric phases.     

GEOMETRIC PHASES AND SCHR?DINGER'S CAT STATE

A matrix method is presented for treating the dynamical phases, adiabatic phases and nonadiabatic phases of quantum superposition states. It is effective for any parameter-varying Hamiltonian system. As two examples, the evolution of mass-varying harmonic oscillator and the evolution of coherent states under parameter-varying displaced operator have been studied, Some new phenomena are obtained in the first case and the possible producing of so-called Schr?dinger's cat state by geometric phases is pointed out. The quantum state useful for the quantum optical verification of Berry's phase is introduced.     

GEOMETRIC PHASES AND SCHR?DINGER''S CAT STATE

A matrix method is presented for treating the dynamical phases, adiabatic phases and nonadiabatic phases of quantum superposition states. It is effective for any parameter-varying Hamiltonian system. As two examples, the evolution of mass-varying harmonic oscillator and the evolution of coherent states under parameter-varying displaced operator have been studied, Some new phenomena are obtained in the first case and the possible producing of so-called Schr?dinger's cat state by geometric phases is pointed out. The quantum state useful for the quantum optical verification of Berry's phase is introduced.     

Quantum tunneling via quantum geometric phase

A new geometric phase is proposed by considering both the energy and momentum conservation, where the corresponding dynamical phases have two parts differently from the conventional calculations for the phase. The results are applied to quantum tunneling process, which is helpful to distinguish the concept about the tunneling time.     

Phase Formulation and Exact Solutions for the Relativistic Klein-Gordon Field with a Time-Dependent Hamiltonian

On the basis of the phase formulation, we find the quantum and classical exact solutions and corresponding total phases for the Klein-Gordon (KG) field with a time-dependent Hamiltonian. The total phase includes both the dynamical and geometric phases (Abaronov-Anandan phase). The connection between the quantum and classical solutions is then obtained. From this connection, we discuss the condition under which the geometric phase for the KG field can be defined.     

Geometric phase induced by quantum nonlocality

By analyzing an instructive example, for testing many concepts and approaches in quantum mechanics, of a one-dimensional quantum problem with moving infinite square-well, we define geometric phase of the physical system. We find that there exist three dynamical phases from the energy, the momentum and local change in spatial boundary condition respectively, which is different from the conventional computation of geometric phase. The results show that the geometric phase can fully describe the nonlocal character of quantum behavior.     

Geometric Phase of Quantum Dots in the Time-Dependent Isotropic Magnetic Field

By using of the invariant theory, we have studied the geometric phase of quantum dots in the time-dependent isotropic magnetic field, the dynamical and geometric phases are given, respectively.     

Geometric Phase in a Generalized Jaynes-Cummings Model with Double Mode Operators and Phase Operators

By using of the invariant theory, we have studied the geometric phase of quantum dots in the time-dependent isotropic magnetic field, the dynamical and geometric phases are given, respectively.     

State-Independent Geometric Quantum Gates via Nonadiabatic and Noncyclic Evolution

Geometric phases are robust to local noises and the nonadiabatic ones can reduce the evolution time, thus nonadiabatic geometric gates have strong robustness and can approach high fidelity. However, the advantage of geometric phase has not been fully explored in previous investigations. Here,a scheme is proposed for universal quantum gates with pure nonadiabatic and noncyclic geometric phases from smooth evolution paths. In the scheme, only geometric phase can be accumulated in a fast way, and thus it not only fully utilizes the local noise resistant property of geometric phase but also reduces the difficulty in experimental realization. Numerical results show that the implemented geometric gates have stronger robustness than dynamical gates and the geometric scheme with cyclic path. Furthermore, it proposes to construct universal quantum gate on superconducting circuits, with the fidelities of single-qubit gate and nontrivial two-qubit gate can achieve 99.97% and 99.87%, respectively. Therefore, these high-fidelity quantum gates are promising for large-scale fault-tolerant quantum computation.     

Observable Berry Phase for Charge Qubit in a Dissipative Environment

A geometric phase of open system is directly obtained from Schrödinger equation with a hermitian Hamiltonian of a two-level atomic system interacting with its reservoirs. We find that the dynamical phases are proportional to the geometric phases in terms of Weisskopf-Wigner theory in the rotational frame. Thus an effective scheme to measure the Berry phase in a charge qubit dissipative system is proposed by coherently controlling the macroscopic quantum states formed in superconducting circuits. Our approach does not need any operations to cancel the dynamical phases so as to reduce the experimental errors. Furthermore, we find that the dissipative effects can be overcome by choosing adapted parameters of the superconducting circuit.     

Geometric Phase in a Generalized Time-Dependent Double-Boson Interaction Model

By using of the invariant theory and the large quantum numbers approximation, we have studied a generalized time-dependent double-Boson interaction model, the dynamical and geometric phases are given, respectively. The Aharonov-Anandan phase is also obtained under the cyclical evolution.     

Quantization,coherent states and geometric phases of a generalized nonstationary mesoscopic RLC circuit

We present an alternative quantum treatment for a generalized mesoscopic RLC circuit with time-dependent resistance, inductance and capacitance. Taking advantage of the Lewis and Riesenfeld quantum invariant method and using quadratic invariants we obtain exact nonstationary Schrödinger states for this electromagnetic oscillation system. Afterwards, we construct coherent and squeezed states for the quantized RLC circuit and employ them to investigate some of the system’s quantum properties, such as quantum fluctuations of the charge and the magnetic flux and the corresponding uncertainty product. In addition, we derive the geometric, dynamical and Berry phases for this nonstationary mesoscopic circuit. Finally we evaluate the dynamical and Berry phases for three special circuits. Surprisingly, we find identical expressions for the dynamical phase and the same formulae for the Berry’s phase.     

量子相变与几何相位

量子相变是凝聚态物理中的重要研究课题，而几何相位的发现是近几十年来量子力学中的重要进展，它们毫无关联地各自发展。但最近的研究表明，它们之间有密切联系：多体体系基态的几何相位在量子相变点附近具有标度性；不可收缩的几何相位可用来作为量子相变的标志等，文章将介绍最近在量子相变和几何相位的关系方面的研究进展，并用XY自旋链模型来详细说明．这些结果应会吸引凝聚态和几何相位领域工作的研究人员的关注和兴趣。     

利用暗本征态的绝热演化实现非几何条件相位移动:一种实现量子计算的新方法

利用绝热演化，文章提出一种新的方法以实现量子相位门，这种相位移动既非源于动力学过程，也非源于几何操纵，它来源于暗态本身的演化，基于绝热演化的优点，这种量子逻辑门对实验参量的起伏不敏感，与几何相位门相比，这种相位门更简单，并且保真度可得到进一步提高。文章对这种相位门做一简述。     

Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum

We present direct measurements of a new geometric phase acquired by optical beams carrying orbital angular momentum. This phase arises when the transverse mode of a beam is transformed following a closed path in the space of modes. The measurements were done via the interference of two copropagating optical beams that pass through the same interferometer parts but acquire different geometric phases. The method is insensitive to dynamical phases. The magnitude and sign of the measured phases are in excellent agreement with theoretical predictions.     

Geometry of time-dependent PT-symmetric quantum mechanics

A new type of quantum theory known as time-dependent PT-symmetric quantum mechanics has received much attention recently. It has a conceptually intriguing feature of equipping the Hilbert space of a PT-symmetric system with a time-varying inner product. In this work, we explore the geometry of time-dependent PT-symmetric quantum mechanics. We find that a geometric phase can emerge naturally from the cyclic evolution of a PT-symmetric system,and further formulate a series of related differential-geometry concepts, including connection, curvature, parallel transport,metric tensor, and quantum geometric tensor. These findings constitute a useful, perhaps indispensible, tool to investigate geometric properties of PT-symmetric systems with time-varying system's parameters. To exemplify the application of our findings, we show that the unconventional geometric phase [Phys. Rev. Lett. 91 187902(2003)], which is the sum of a geometric phase and a dynamical phase proportional to the geometric phase, can be expressed as a single geometric phase unveiled in this work.     

Geometric phase for adiabatic evolutions of general quantum states

The concept of a geometric phase (Berry's phase) is generalized to the case of noneigenstates, which is applicable to both linear and nonlinear quantum systems. This is particularly important to nonlinear quantum systems, where, due to the lack of the superposition principle, the adiabatic evolution of a general state cannot be described in terms of eigenstates. For linear quantum systems, our new geometric phase reduces to a statistical average of Berry's phases. Our results are demonstrated with a nonlinear two-level model.     

Nongeometric conditional phase shift via adiabatic evolution of dark eigenstates: a new approach to quantum computation

We propose a new approach to quantum phase gates via the adiabatic evolution. The conditional phase shift is neither of dynamical nor geometric origin. It arises from the adiabatic evolution of the dark state itself. Taking advantage of the adiabatic passage, this kind of quantum logic gates is robust against moderate fluctuations of experimental parameters. In comparison with the geometric phase gates, it is unnecessary to drive the system to undergo a desired cyclic evolution to obtain a desired solid angle. Thus, the procedure is simplified, and the fidelity may be further improved since the errors in obtaining the required solid angle are avoided. We illustrate such a kind of quantum logic gates in the ion trap system. The idea can also be realized in other systems, opening a new perspective for quantum information processing.     

Geometric phase contribution to quantum nonequilibrium many-body dynamics

We study the influence of geometry of quantum systems underlying space of states on its quantum many-body dynamics. We observe an interplay between dynamical and topological ingredients of quantum nonequilibrium dynamics revealed by the geometrical structure of the quantum space of states. As a primary example we use the anisotropic XY ring in a transverse magnetic field with an additional time-dependent flux. In particular, if the flux insertion is slow, nonadiabatic transitions in the dynamics are dominated by the dynamical phase. In the opposite limit geometric phase strongly affects transition probabilities. This interplay can lead to a nonequilibrium phase transition between these two regimes. We also analyze the effect of geometric phase on defect generation during crossing a quantum-critical point.     

Observation of nonadditive mixed-state phases with polarized neutrons

In a neutron polarimetry experiment the mixed-state relative phases between spin eigenstates are determined from the maxima and minima of measured intensity oscillations. We consider evolutions leading to purely geometric, purely dynamical, and combined phases. It is experimentally demonstrated that the sum of the individually determined geometric and dynamical phases is not equal to the associated total phase which is obtained from a single measurement, unless the system is in a pure state.