Geometric Phase in a Two Energy Level Jaynes-Cummings Model with Imaginary Photon Process

By using the Lewis–Riesenfeld invariant theory, we have studied the dynamical and the geometric phases in a two energy level Jaynes-Cummings model with imaginary photon process. We find that the geometric phases in a cycle case have nothing to do with the frequency of the photon field, the coupling coefficient between photons and atoms, and the atom transition frequency. If we use the more accuracy device, the geometric phases in the imaginary photon process may be observed, and the geometric phases in this process have the observable physical effect.     

Imaginary Photon Field Effect in the Interaction System of Multi-atom with Single-mode Photon Field

By using the Lewis–Riesenfeld invariant theory, we have studied the dynamical and the geometric phases in the interaction system of multi-atom with single-mode photon field with imaginary photon process. We find that the geometric phases in a cycle case have nothing to do with the frequency of the photon field, the coupling coefficient between photons and atoms, and the atom transition frequency. If we use the more accuracy device, the geometric phases in the imaginary photon process may be observed, and the geometric phases in this process have the observable physical effect.     

Geometric Phase in a Λ-type <Emphasis Type="Italic">k</Emphasis>-photon Jaynes-Cummings Model with Imaginary Photon Process

By using the Lewis–Riesenfeld invariant theory, we have studied the dynamical and the geometric phases in a generalized time-dependent Λ-type k-photon Jaynes-Cummings model with imaginary photon process. We find that the geometric phases in a cycle case are independent of the frequency of the photon field, the coupling coefficient between photons and atoms, and the atom transition frequency. If we use the more accuracy device, the geometric phases in this process may be observed, and the geometric phases in this process have the observable physical effect.     

Geometric Phase in a Time-Dependent <Emphasis Type="Italic">k</Emphasis>-Photon Λ-Type Jaynes–Cummings Model

By using the Lewis–Riesenfeld invariant theory, we have studied the dynamical and the geometric phases in a generalized time-dependent k-photon Λ-type Jaynes–Cummings model. It is found that, different from the dynamical phases, the geometric phases in a cycle case are independent of the photon numbers, the frequency of the photon field, the coupling coefficient between photons and atoms, and the atom transition frequency.     

Geometric Phase in the Interaction System of Multi-atom in Micro-cavity with Single-mode Photon Field

By using the Lewis-Riesenfeld invariant theory, we have studied the dynamical and the geometric phases in the interaction system of multi-atom in micro-cavity with single-mode photon field. We find that the geometric phases in a cycle case have nothing to do with the frequency of the photon field, the coupling coefficient between photons and atoms, and the atom transition frequency.     

Geometric Phase in the Interaction System of Three-Energy Atom with Double-Mode Radiation Field

By using the Lewis–Riesenfeld invariant theory, we have studied the dynamical and the geometric phases in the interaction system of three-energy atom with double-mode radiation field, respectively. The Aharonov–Anandan phase is also obtained under the cyclical evolution.     

Quantum effect in a generalized N-atom Dicke model

We have studied the geometric phase and the sub-Poissonian photon distribution of a generalized N two-level atoms Dicke model in the thermo-dynamical limit and the off-resonant coupling case. It is found that the geometric phase in the ground state is relative to the atom number, the coupling strength between the atom and the light field, the frequency of the electromagnetic wave and the energy difference between two levels of the atom. The photons may exhibit the sub-Poissonian distribution in the ground state.     

Geometric Phase in the Interaction System of Two-Energy Atom with Double-Mode Radiation Field

By using the Lewis–Riesenfeld invariant theory, the dynamical and the geometric phases in the interaction system of two-energy atom with double-mode radiation field are given, respectively. The Aharonov-Anandan phase is also obtained under the cyclical evolution.     

Geometric Phase in a Two Energy Level <Emphasis Type="Italic">k</Emphasis>-Photon Jaynes-Cummings Model with Imaginary Photon Process

By using the Lewis-Riesenfeld invariant theory, we have studied the dynamical phase and the geometric phase in a two energy level k-photon Jaynes-Cummings model with imaginary photon process. We find that the geometric phase in a cycle case is independent of the frequency of the photon field, the coupling coefficient between photons and atoms, and the atom transition frequency. We predict the physical effect of the geometric phase in the imaginary photon process may be measured.     

非马尔可夫环境下原子的几何相位演化

从微观哈密顿量出发,研究了原子在非马尔可夫环境影响下的几何相位演化. 结果表明,在强耦合条件下原子的几何相位比弱耦合时获得的几何相位大, 而且这一差别随环境损耗的增加而增大. 在环境损耗较小时,原子的几何相位随时间变化出现连续和不连续两种演化行为,且不连续的范围随环境的损耗增加而增大. 总之,在非马尔可夫环境下,原子的几何相位演化将出现丰富而复杂的演化特征. 关键词： 几何相位 原子 腔场 非幺正     

Inversion of low-energy electron diffraction data with no pre-knowledge factor beyond optical holography

In this review, I describe how low-energy (typically below 500eV) electron diffraction spectra can be inverted to produce three-dimensional coordinates of atoms neighbouring a reference atom with no prior knowledge of what type or types of atom are present. The reference atom may be one of many equivalent near-surface atoms from which a core-level photoelectron is excited or, in the case of diffuse low-energy electron diffraction, one of many equivalent adsorbate atoms (lacking in long-range order) on the surface of a crystalline substrate. Other variants apply to low-energy electron diffraction, Kikuchi electron diffraction and time-reversed versions in which the wavenumber (energy) and direction of the incident beam are varied. I show that, for such low-energy electron diffraction spectra, the relative phases between the reference wave and scattered waves have a known geometric form if the spectra are taken from within a small angular cone in the near-back-scattering directions. By using the back-scattering small cone at each direction of interest, a simple algorithm is developed to invert the spectra and extract object atomic positions with no input of calculated dynamical factors. The article also reviews key ideas and works which led to the current understanding of this field.     

Geometric Phase and Entanglement of a Three-Level Atom With and Without Rotating Wave Approximation

In this paper, we study the dynamics of entanglement between three-level atom and optical field, initially prepared in the squeezed coherent state. We discuss the dynamical behavior of the geometric phase and entanglement, measured by the von Neumann entropy, with and without rotating wave approximation during the time of evolution. The effect of the squeezing and detuning parameters on the evolution of entanglement and geometric phase will be examined. We find that the squeezing and detuning parameters play a central role on the evolution of the geometric phase and nonlocal correlation between the field and the three-level atom. Moreover, we show that the dynamics of the system in the presence of rotating wave approximation has a richer structure compared with the absence of rotating wave approximation.     

Quantum-vacuum geometric phases in the noncoplanarly curved fiber system

The connection between the quantum-vacuum geometric phases (which originates from the vacuum zero-point electromagnetic fluctuation) and the non-normal order for operator product is considered in the present paper. In order to investigate this physically interesting geometric phases at quantum-vacuum level, we suggest an experimentally feasible scheme to test it by means of a noncoplanarly curved fiber made of gyrotropic media. A remarkable feature of the present experimental realization is that one can easily extract the nonvanishing and nontrivial quantum-vacuum geometric phases of left- and/or right-handed circularly polarized light from the vanishing and trivial total quantum-vacuum geometric phases. Since the normal-order procedure may remove globally the vacuum energy of time-dependent quantum systems, the potential physical vacuum effects (e.g., quantum-vacuum geometric phases) may also be removed by this procedure. Thus the detection of the geometric phases at quantum-vacuum level may answer whether the normal-order technique is valid or not in the time-dependent quantum field theory.Received: 4 February 2004, Published online: 29 June 2004PACS: 03.65.Vf Phases: geometric; dynamic or topological - 03.70. + k Theory of quantized fields - 42.70.-a Optical materials - 42.50.Xa Optical tests of quantum theory     

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.     

Geometric Phase in the Interaction of a Time-Dependent Light Field with <Emphasis Type="Italic">ℑ</Emphasis><Superscript>(3)</Superscript> System

By using of the invariant theory, we have studied the geometric phase in the interaction of a time-dependent light field with ℑ ⁽³⁾ system, the dynamical and geometric phases are given, respectively. The disappearing condition of the geometric phase is given.     

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。     

Exploring energy-time entanglement using geometric phase

Using the signal and idler photons produced by parametric down-conversion, we report an experimental observation of a violation of the Bell inequality for energy and time based purely on the geometric phases of the signal and idler photons. We thus show that energy-time entanglement between the signal and idler photons can be explored by means of their geometric phases. These results may have important practical implications for quantum information science by providing an additional means by which entanglement can be manipulated.     

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 Population Inversion in Rabi Oscillation

The relations between geometric phases and population inversion in Rabi oscillation are investigated for all possible cases. The results show that the population inverse is an elliptically symmetric distribution as a function of the difference of geometric phases so as resiliently to rebut certain types of computational and experiment errors in geometric quantum computation.