Related papers: Open system geometric phase based on system-reserv…
We study the geometric phase of an open two-level quantum system under the influence of a squeezed, thermal environment for both non-dissipative as well as dissipative system-environment interactions. In the non-dissipative case, squeezing…
Time-dependent $\mathcal{PT}$-symmetric quantum mechanics is featured by a varying inner-product metric and has stimulated a number of interesting studies beyond conventional quantum mechanics. In this paper, we explore geometric aspects of…
We illustrate the geometric phase associated with the cyclic dynamics of a classical system of coupled oscillators. We use an analogy between a classical coupled oscillator and a two-state quantum mechanical system to represent the…
The geometric phase of a bi-particle model is discussed. For different initial states, especially when the initial state is pure or mixed, the geometric phase will show different properties. The relationship between the geometric phase and…
We consider the STIRAP process in a three-level atom. Viewed as a closed system, no geometric phase is acquired. But in the presence of spontaneous emission and/or collisional relaxation we show numerically that a non-vanishing, purely…
Steering a quantum harmonic oscillator state along cyclic trajectories leads to a path-dependent geometric phase. Here we describe an experiment observing this geometric phase in an electronic harmonic oscillator. We use a superconducting…
The geometric and open path phases of a four-state system subject to time varying cyclic potentials are computed from the Schr\"{o}dinger equation. Fast oscillations are found in the non-adiabatic case. For parameter values such that the…
We investigate the qubit geometric phase and its properties in dependence on the mechanism for decoherence of a qubit weakly coupled to its environment. We consider two sources of decoherence: dephasing coupling (without exchange of energy…
We analyze the geometric aspects of unitary evolution of general states for a multilevel quantum system by exploiting the structure of coadjoint orbits in the unitary group Lie algebra. Using the same method in the case of SU(3) we study…
In this thesis we provide a uniform treatment of two non-adiabatic geometric phases for dynamical systems of mixed quantum states, namely those of Uhlmann and of Sj\"{o}qvist et al. We develop a holonomy theory for the latter which we also…
The geometric phases of cyclic evolutions for mixed states are discussed in the framework of unitary evolution. A canonical one-form is defined whose line integral gives the geometric phase which is gauge invariant. It reduces to the…
The geometric phase for a pure quantal state undergoing an arbitrary evolution is a ``memory'' of the geometry of the path in the projective Hilbert space of the system. We find that Uhlmann's geometric phase for a mixed quantal state…
The connection between the geometric phase and quantum phase transition has been discussed extensively in the two-band model. By introducing the twist operator, the geometric phase can be defined by calculating its ground-state expectation…
We introduce an operational framework to analyze non-adiabatic Abelian and non-Abelian, cyclic and non-cyclic, geometric phases in open quantum systems. In order to remove the adiabaticity condition, we generalize the theory of dynamical…
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…
We propose a new way to generate an observable geometric phase by means of a completely incoherent phenomenon. We show how to imprint a geometric phase to a system by "adiabatically" manipulating the environment with which it interacts. As…
In this paper, we investigate the geometric phase (GP) acquired by two-mode mixed squeezed-coherent states (SCSs) during unitary cyclic evolution, focusing on the influence of squeezing parameters and classical weight. We analyze the GP for…
We develop a new interpretation of the geometric phase in evolution with a non-Hermitian real value Hamiltonian by relating it to the angle developed during the parallel transport along a closed curve by a unit vector triad in the…
The concept of relative state is used to introduce geometric phases that originate from correlations in states of composite quantum systems. In particular, we identify an entanglement-induced geometric phase in terms of a weighted average…
We calculate the geometric phase of a bipartite two-level system coupled to an external environment. We analyze the reduced density matrix for an arbitrary initial state of the composite system and compute the correction to the unitary…