arXiv subjects
Publications and source records attributed to K. M. Fonseca Romero.
The archetypal one-qubit noisy channels ---depolarizing, phase-damping and amplitude-damping channels--- describe both Markovian and non-Markovian evolution. Simple microscopic models for the depolarizing channel, both classical and quantum, are considered. Microscopic models which describe phase damping and amplitude damping channels are briefly reviewed.
We analytically exploit the two-mode Gaussian states nonunitary dynamics. We show that in the zero temperature limit, entanglement sudden death (ESD) will always occur for symmetric states (where initial single mode compression is $z_0$) provided the two mode squeezing $r_0$ satisfies $0 < r_0 < 1/2 \log (\cosh (2 z_0)).$ We also give the analytical expressions for the time of ESD. Finally, we show the relation between the single modes initial impurities and the initial entanglement, where we exhibit that the later is suppressed by the former.
We study and compare the information loss of a large class of Gaussian bipartite systems. It includes the usual Caldeira-Leggett type model as well as Anosov models (parametric oscillators, the inverted oscillator environment, etc), which exhibit instability, one of the most important characteristics of chaotic systems. We establish a rigorous connection between the quantum Lyapunov exponents and coherence loss, and show that in the case of unstable environments coherence loss is completely determined by the upper quantum Lyapunov exponent, a behavior which is more universal than that of the Caldeira-Leggett type model.
Decoherence free subspaces (DFS) is a theoretical tool towards experimental implementation of quantum information storage and processing. However, they represent an experimental challenge, since conditions for their existence are very stringent. This work explores the situation in which a system of $N$ oscillators coupled to a bath of harmonic oscillators is close to satisfy the conditions for the existence of DFS. We show, in the Born-Markov limit and for small deviations from separability and degeneracy conditions, that there are {\emph{weak decoherence subspaces}} which resemble the original notion of DFS.
We consider the spin 1/2 model coupled to a slowly varying magnetic field in the presence of a weak damping represented by a Lindblad-form operators. We show that Berry's geometrical phase remains unaltered by the two dissipation mechanism considered. Dissipation effects are twofold: a shrinking in the modulus of the Bloch's vector, which characterizes coherence loss and a time dependent (dissipation related) precession angle. We show that the line broadening of the Fourier transformation of the components of magnetization is only due to the presence of dissipation.
We study the adiabatic limit in the density matrix approach for a quantum system coupled to a weakly dissipative medium. The energy spectrum of the quantum model is supposed to be non-degenerate. In the absence of dissipation, the geometric phases for periodic Hamiltonians obtained previously by M.V. Berry are recovered in the present approach. We determine the necessary condition satisfied by the coefficients of the linear expansion of the non-unitary part of the Liouvillian in order to the imaginary phases acquired by the elements of the density matrix, due to dissipative effects, be geometric. The results derived are model-independent. We apply them to spin 1/2 model coupled to reservoir at thermodynamic equilibrium.
We consider N identical oscillators coupled to a single environment and show that the conditions for the existence of decoherence free subspaces are degeneracy of the oscillator frequencies and separability of the coupling with the environment. A formal exact equation for the evolution in the case of two oscillators is found and the decoherence free subspace is explicitly determined. A full analytical solution for any initial condition and general parameters (frequencies and dissipation constants) is given in the markovian approximation and zero temperature. We find that slight relaxation of degeneracy and separability conditions leads to the appearence of two components in the dynamical evolution with very different decoherence times. The ratio between the characteristic time of the weak and strong decoherent components is given by $τ_{WD}/τ_{SD}\approx k/δk$, where $δk$ is a measure of the nonseparability of the coupling to the environment and $k$ is the mean decay constant of the oscillators.
The exact reduced dynamics for the independent oscillator model in the RWA approximation at zero and finite temperatures is derived. It is shown that the information about the interaction and the environment is encapsulated into three time dependent coefficients of the master equation, one of which vanishes in the zero temperature case. In currently used optical cavities all the information about the field dynamics is contained into {\it two} (or three) experimentally accesible and physically meaningful real functions of time. From the phenomenological point of view it suffices then to carefully measure two ({\it three}) adequate observables in order to map the evolution of any initial condition, as shown with several examples: (generalized) coherent states, Fock states, Schrödinger cat states, and squeezed states.