27 research outputs found
Control of the geometric phase and pseudo-spin dynamics on coupled Bose-Einstein condensates
We describe the behavior of two coupled Bose-Einstein condensates in
time-dependent (TD) trap potentials and TD Rabi (or tunneling) frequency, using
the two-mode approach. Starting from Bloch states, we succeed to get analytical
solutions for the TD Schroedinger equation and present a detailed analysis of
the relative and geometric phases acquired by the wave function of the
condensates, as well as their population imbalance. We also establish a
connection between the geometric phases and constants of motion which
characterize the dynamic of the system. Besides analyzing the affects of
temporality on condensates that differs by hyperfine degrees of freedom
(internal Josephson effect), we also do present a brief discussion of a one
specie condensate in a double-well potential
(external Josephson effect).Comment: 1 tex file and 11 figures in pdf forma
A general treatment of geometric phases and dynamical invariants
Based only on the parallel transport condition, we present a general method
to compute Abelian or non-Abelian geometric phases acquired by the basis states
of pure or mixed density operators, which also holds for nonadiabatic and
noncyclic evolution. Two interesting features of the non-Abelian geometric
phase obtained by our method stand out: i) it is a generalization of Wilczek
and Zee's non-Abelian holonomy, in that it describes nonadiabatic evolution
where the basis states are parallelly transported between distinct degenerate
subspaces, and ii) the non-Abelian character of our geometric phase relies on
the transitional evolution of the basis states, even in the nondegenerate case.
We apply our formalism to a two-level system evolving nonadiabatically under
spontaneous decay to emphasize the non-Abelian nature of the geometric phase
induced by the reservoir. We also show, through the generalized invariant
theory, that our general approach encompasses previous results in the
literature
Dynamical invariants and nonadiabatic geometric phases in open quantum systems
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 invariants to the context of open systems evolving under arbitrary
convolutionless master equations. Geometric phases are then defined through the
Jordan canonical form of the dynamical invariant associated with the
super-operator that governs the master equation. As a by-product, we provide a
sufficient condition for the robustness of the phase against a given decohering
process. We illustrate our results by considering a two-level system in a
Markovian interaction with the environment, where we show that the
non-adiabatic geometric phase acquired by the system can be constructed in such
a way that it is robust against both dephasing and spontaneous emission.Comment: 9 pages, 3 figures. v2: minor corrections and subsection IV.D added.
Published versio
Nonadiabatic coherent evolution of two-level systems under spontaneous decay
In this paper we extend current perspectives in engineering reservoirs by
producing a time-dependent master equation leading to a nonstationary
superposition equilibrium state that can be nonadiabatically controlled by the
system-reservoir parameters. Working with an ion trapped inside a nonindeal
cavity we first engineer effective Hamiltonians that couple the electronic
states of the ion with the cavity mode. Subsequently, two classes of
decoherence-free evolution of the superposition of the ground and decaying
excited levels are achieved: those with time-dependent azimuthal or polar
angle. As an application, we generalise the purpose of an earlier study [Phys.
Rev. Lett. 96, 150403 (2006)], showing how to observe the geometric phases
acquired by the protected nonstationary states even under a nonadiabatic
evolution.Comment: 5 pages, no figure
Using quantum state protection via dissipation in a quantum-dot molecule to solve the Deutsch problem
The wide set of control parameters and reduced size scale make semiconductor
quantum dots attractive candidates to implement solid-state quantum
computation. Considering an asymmetric double quantum dot coupled by tunneling,
we combine the action of a laser field and the spontaneous emission of the
excitonic state to protect an arbitrary superposition state of the indirect
exciton and ground state. As a by-product we show how to use the protected
state to solve the Deutsch problem.Comment: 8 pages, 1 figure, 2 table