Related papers: Geometric Phases for Coherent States
Quantum versions of cylindric phase space, like for the motion of a particle on the circle, are obtained through different families of coherent states. The latter are built from various probability distributions of the action variable. The…
Coherent state theory is shown to reproduce three categories of representations of the spectrum generating algebra for an algebraic model: (i) classical realizations which are the starting point for geometric quantization; (ii) induced…
The geometric phases of the cyclic states of a generalized harmonic oscillator with nonadiabatic time-periodic parameters are discussed in the framework of squeezed state. A class of cyclic states are expressed as a superposition of an…
Geometric positions of square roots of coherent states of CCR algebras are investigated along with an explicit formula for transition amplitudes among them, which is a natural extension of our previous results on quasifree states and will…
We investigate the entanglement properties of thermal states of the harmonic lattice in one, two and three dimensions. We establish the value of the critical temperature for entanglement between neighbouring sites and give physical reasons.…
Geometrical phases have been applied in virtually every major branch of physics and they play an important role in topology and knot theory in mathematics and quantum computation. However, most of the early works focus on pure quantum…
The geometric phase (GP) for bipartite systems in transverse external magnetic fields is investigated in this paper. Two different situations have been studied. We first consider two non-interacting particles. The results show that because…
Coherent structures emerge from the dynamics of many kinds of dissipative, externally driven, nonlinear systems, and continue to provoke new questions that challenge our physical and mathematical understanding. In one specific sub-class of…
We investigate the construction of coherent states for quantum theories of connections based on graphs embedded in a spatial manifold, as in loop quantum gravity. We discuss the many subtleties of the construction, mainly related to the…
An explicit parameterization is given for the density matrices for $n$-state systems. The geometry of the space of pure and mixed states and the entropy of the $n$-state system is discussed. Geometric phases can arise in only specific…
Quantum mechanical methods for getting geometric phases for mixed states are analyzed. Parallel transport equations for pure states are generalized to mixed states by which dynamical phases are eliminated. The geometric phases of mixed…
Within the framework of thermofield dynamics, we construct a thermalized coherent thermal state, which is a general type of the coherent state with the thermal effects and can be presumably produced experimentally. The wavefunction and the…
We consider a geometrization, i.e., we identify geometrical structures, for the space of density states of a quantum system. We also provide few comments on a possible application of this geometrization for composite systems.
Garrison and Wright showed that upon undergoing cyclic quantum evolution a meta-stable state acquires both a geometric phase and a geometric decay probability. This is described by a complex geometric ``phase'' associated with the cyclic…
We review entangled coherent state research since its first implicit use in 1967 to the present. Entangled coherent states are important to quantum superselection principles, quantum information processing, quantum optics, and mathematical…
A simple technique is used to obtain a general formula for the Berry phase (and the corresponding Hannay angle) for an arbitrary Hamiltonian with an equally-spaced spectrum and appropriate ladder operators connecting the eigenstates. The…
We make a geometric study of the phases acquired by a general pure bipartite two level system after a cyclic unitary evolution. The geometric representation of the two particle Hilbert space makes use of Hopf fibrations. It allows for a…
Practical implementations of quantum computing are always done in the presence of decoherence. Geometric phase is useful in the context of quantum computing as a tool to achieve fault tolerance. Recent experimental progresses on coherent…
We present an analytical approach to evaluate the geometric measure of multiparticle entanglement for mixed quantum states. Our method allows the computation of this measure for a family of multiparticle states with a certain symmetry and…
This paper is concerned with the construction of phase operators, phase states, vector phase states, and coherent states for a generalized Weyl-Heisenberg algebra. This polynomial algebra (that depends on real parameters) is briefly…