arXiv subjects

A. N. Salgueiro

Publications and source records attributed to A. N. Salgueiro.

12 recordsLinked to original sources

arXiv2010

Doorway states and the Bose-Hubbard model

We introduce an efficient method to solve the Mott-Hubbard model. The Schrödinger equation is solved by the successive construction of doorway states. The ground state wavefunction derived by this method contains all relevant many-body correlations introduced by the hamiltonian, but the dimensionality of the Hilbert space is greatly reduced. We apply the doorway method to obtain the chemical potential, the on-site fluctuations and the visibility of the interference pattern arising from atoms in a one-dimensional periodic lattice. Excellent agreement with exact numerical calculations as well as recent experimental observations is found.

cond-mat.other↗

arXiv2006

Quantum dynamics of bosons in a double-well potential: Josephson oscillations, self-trapping and ultralong tunneling times

The dynamics of the population imbalance of bosons in a double-well potential is investigated from the point of view of many-body quantum mechanics in the framework of the two-mode model. For small initial population imbalances, coherent superpositions of almost equally spaced energy eigenstates lead to Josephson oscillations. The suppression of tunneling at population imbalance beyond a critical value is related to a high concentration of initial state population in the region of the energy spectrum with quasi-degenerate doublets resulting in imbalance oscillations with a very small amplitude. For unaccessible long times, however, the system recovers the regime of Josephson oscillations.

quant-ph↗

arXiv2004

Entanglement of a Multiparticle Schroedinger Cat State

We characterize the degree of entanglement of a subsystem of $k$ particles in a $N$-two level system ($k\leq N/2$) initially prepared in a mesoscopic superposition $|ψ>=\int dθf(θ) (|ϕ_{1}(θ)>^{\otimes N}+|ϕ_{2}(θ)>^{\otimes N})$, where $f(θ)$ is a gaussian or a delta function, subject to the time evolution described by a dephasing channel. Negativity is used as a measure of entanglement for such system. For an arbitrary number of particles $N$, numerical results are given for the full time evolution up to ten particles. Analytical results are obtained for short times and asymptotic time regimes. We show that negativity is initially proportional to the square root of the product of the number of particles in each partition, the overlap ${|<ϕ_1(θ)|ϕ_2(θ)>|}^2$ and the coupling to the environment. Asymptotically, negativity tends to zero, a necessary condition for separability.

quant-ph↗

arXiv2002

Number-conserving rate equation for sympathetic cooling of a boson gas

We derive a particle number-conserving rate equation for the ground state and for the elementary excitations of a bosonic system which is in contact with a gas of a different species (sympathetic cooling). We use the Giradeau-Arnowitt method and the model derived by Lewenstein et. al. with an additional assumption: the high-excited levels thermalize much faster with the cooling agent than the other levels. Evaporation of particles, know to be important in the initial stages of the cooling process, is explicitly included.

cond-mat.stat-mech↗

arXiv2002

Sympathetic cooling and growth of a Bose-Einstein condensate

We study two sets of rate equations for sympathetic cooling of harmonically trapped Bose gases. Calculations for mixtures of Na-Rb and Li-Cs show that both sets yield similar results for the cooling times. The equilibration rates are in fair agreement with each other and differ considerably from classical rates. The onset of Bose-Einstein condensation is rather sudden and non-exponential in time, and the growth of the condensate differs for the two different mixtures we studied.

cond-mat.soft↗

arXiv2001

Density Matrix of a Bose--Einstein Condensate: Steady--State versus Mean--Field Approach

We compare the equilibrium solution for the condensate obtained in the mean--field approximation to the master equation for sympathetic cooling with the one obtained by Scully for a system in contact with a heat bath with the help of an analogy with the laser. While the mean--field approach yields analytical formulas for the approach towards equilibrium and for the equilibrium solution, it neglects the correlations between occupation numbers of different single--particle states which are approximately kept in Scully's approach. Such neglect is admissible as long as the fraction of Bosons in the condensate does not exceed a few percent or so.

cond-mat↗

arXiv2001

Mean-Field Approximation to the Master Equation for Sympathetic Cooling of Trapped Bosons

We use the mean-field approximation to simplify the master equation for sympathetic cooling of Bosons. For the mean single-particle occupation numbers, this approach yields the same equations as the factorization assumption introduced in an erlier paper. The stationary or equilibrium solution of the resulting master equation for the one-body density matrix shows that the mean-field approximation breaks down whenever the fraction of condensate Bosons exceeds ten percent or so of the total. Using group-theoretical methods, we also solve the time-dependent master equation for the one-body density matrix. Given the time dependence of the mean single-particle occupation numbers, this solution is obtained by quadratures. It tends asymptotically towards the equilibrium solution.

cond-mat↗

arXiv2001

Rate Equations for Sympathetic Cooling of Trapped Bosons or Fermions

We derive two different sets of rate equations for sympathetic cooling of harmonically trapped Bosons or Fermions. The rate equations are obtained from a master equation derived earlier by Lewenstein et al. [Phys. Rev. A 51 (1995) 4617] by means of decoherence and ergodicity arguments. We show analytically that the thermal equilibrium state is a stationary solution of our rate equation. We present analytical results for the rate coefficients which are needed to solve the rate equations, and we give approximate formulae that permit their computation in practice. We solve the two sets of rate equations numerically and compare the results. The cooling times obtained in both approaches agree very well. The equilibration rates show fair agreement.

cond-mat.soft↗

arXiv2001

Modelling the Recoherence of Mesoscopic Superpositions in Dissipative Environments

A model is presented to describe the recently proposed experiment (J. Raimond, M. Brune and S. Haroche Phys. Rev. Lett {\bf 79}, 1964 (1997)) where a mesoscopic superposition of radiation states is prepared in a high-Q cavity which is coupled to a similar resonator. The dynamical coherence loss of such state in the absence of dissipation is reversible and can in principle be observed. We show how this picture is modified due to the presence of the environmental couplings. Analytical expressions for the experimental conditional probabilities and the linear entropy are given. We conclude that the phenomenon can still be observed provided the ratio between the damping constant and the inter-cavities coupling does not exceed about a few percent. This observation is favored for superpositions of states with large overlap.

quant-ph↗

arXiv2001

Time Evolution of tunneling and decoherence: soluble model

Decoherence effects associated to the damping of a tunneling two-level system are shown to dominate the tunneling probability at short times in strong coupling regimes in the context of a soluble model. A general decomposition of tunneling rates in dissipative and unitary parts is implemented. Master equation treatments fail to describe the model system correctly when more than a single relaxation time is involved.

quant-ph↗

arXiv1998

Quasi-classical dynamics of interacting Bose condensates

The dynamics of the composition of uniform Bose condensates involving two species capable of reciprocal interconversion is treated in terms of a collective quasi-spin model. This collective model quickly reduces to classical form towards the thermodynamic limit. Quantum solutions are easily obtained numerically short of this limit which give insight into the dynamically relevant correlation processes.

quant-ph↗

arXiv1998

Decoherence of mesoscopic states of cavity fields

We show that two-atom correlation measurements of the type involved in a recent experimental study of the evolution of a mesoscopic superposition state prepared in a definite mode of a high-Q cavity can be used to determine the eigenvalues of the reduced density matrix of the field, provided the assumed dynamical conditions are actually fulfilled to experimental accuracy. These conditions involve i) a purely dispersive coupling of the field to the Rydberg atoms used to manipulate and to monitor the cavity field, and ii) the effective absence of correlations in the ground state of the system consisting of the cavity coupled to the ``reservoir'' which accounts for the decoherence and damping processes. A microscopic calculation at zero temperature is performed and compared to master equation results.

quant-ph↗