Related papers: Operational geometric phase for mixed quantum stat…
Various phenomena related to geometric phases in quantum mechanics are reviewed and explained by analyzing some examples.The concepts of 'parallelism' ,'connections' and 'curvatures' are applied to Aharonov-Bohm (AB) effect, to U(1)phase…
We study the geometric phase of the ground state in the extended quantum compass model in presence of a transverse field. The exact solution is obtained by using the Jordan-Wigner transformation which maps the Hamiltonian on a fermionic…
The relationship between quantum phase transition and complex geometric phase for open quantum system governed by the non-Hermitian effective Hamiltonian with the accidental crossing of the eigenvalues is established. In particular, the…
We develop the widest possible generalisation of the well-known connection between quantum mechanical Bargmann invariants and geometric phases. The key notion is that of null phase curves in quantum mechanical ray and Hilbert spaces.…
Geometric phase plays an important role in evolution of pure or mixed quantum states. However, when a system undergoes decoherence the development of geometric phase may be inhibited. Here, we show that when a quantum system interacts with…
In this article, we provide theoretical support for the use of geometric measures of nonclassicality as a general tool to identify quantum phase transitions. We argue that divergences in the susceptibility of any geometric measure of…
Magnetometry is a powerful technique for the non-invasive study of biological and physical systems. A key challenge lies in the simultaneous optimization of magnetic field sensitivity and maximum field range. In interferometry-based…
We construct a generalized class of quantum gravity condensate states, that allows the description of continuum homogeneous quantum geometries within the full theory. They are based on similar ideas already applied to extract effective…
We demonstrate that a geometric phase, generated via a sequence of four optomechanical interactions, can be used to increase, or generate nonlinearities in the unitary evolution of a mechanical resonator. Interactions of this form lead to…
Through the quantum trajectory approach, we calculate the geometric phase acquired by a bipartite system subjected to decoherence. The subsystems that compose the bipartite system interact with each other, and then are entangled in the…
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 describe the geometric (Berry) phases arising when some quantum systems are driven by control classical parameters but also by outer classical stochastic processes (as for example classical noises). The total geometric phase is then…
We deduce the appearance of a polymeric phase in 4-dimensional simplicial quantum gravity by varying the values of the coupling constants and discuss the geometric structure of the phase in terms of ergodic moves. A similar result is true…
Holonomic quantum computation is the idea to use non-Abelian geometric phases to implement universal quantum gates that are robust to fluctuations in control parameters. Here, we propose a compact design for a holonomic quantum computer…
Quantum coherence is an important quantum resource and it is intimately related to various research fields. The geometric coherence is a coherence measure both operationally and geometrically. We study the trade-off relation of geometric…
The theory of geometric phase is generalized to a cyclic evolution of the eigenspace of an invariant operator with $N$-fold degeneracy. The corresponding geometric phase is interpreted as a holonomy inherited from the universal connection…
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 non-equilibrium dynamics revealed by the…
The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement, already present in a number of settings [A. Shimony, Ann. NY.…
We give an explicit expression for the geometric measure of entanglement for three qubit states that are linear combinations of four orthogonal product states. It turns out that the geometric measure for these states has three different…
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…