arXiv subjects

R. Graham

Publications and source records attributed to R. Graham.

At least 19 recordsLinked to original sources

arXiv2008

Ultracold bosons in lattices with binary disorder

Quantum phases of ultracold bosons with repulsive interactions in lattices in the presence of quenched disorder are investigated. The disorder is assumed to be caused by the interaction of the bosons with impurity atoms having a large effective mass. The system is described by the Bose-Hubbard Hamiltonian with random on-site energies which have a discrete binary probability distribution. The phase diagram at zero temperature is calculated using several methods like a strong-coupling expansion, an exact numerical diagonalization, and a Bose-Fermi mapping valid in the hard-core limit. It is shown that the Mott-insulator phase exists for any strength of disorder in contrast to the case of continuous probability distribution. We find that the compressibility of the Bose glass phase varies in a wide range and can be extremely low. Furthermore, we evaluate experimentally accessible quantities like the momentum distribution, the static and dynamic structure factors, and the density of excited states. The influence of finite temperature is discussed as well.

cond-mat.dis-nn↗

arXiv2007

Bose-Einstein-condensed gases in arbitrarily strong random potentials

Bose-Einstein-condensed gases in external spatially random potentials are considered in the frame of a stochastic self-consistent mean-field approach. This method permits the treatment of the system properties for the whole range of the interaction strength, from zero to infinity, as well as for arbitrarily strong disorder. Besides a condensate and superfluid density, a glassy number density due to a spatially inhomogeneous component of the condensate occurs. For very weak interactions and sufficiently strong disorder, the superfluid fraction can become smaller than the condensate fraction, while at relatively strong interactions, the superfluid fraction is larger than the condensate fraction for any strength of disorder. The condensate and superfluid fractions, and the glassy fraction always coexist, being together either nonzero or zero. In the presence of disorder, the condensate fraction becomes a nonmonotonic function of the interaction strength, displaying an antidepletion effect caused by the competition between the stabilizing role of the atomic interaction and the destabilizing role of the disorder. With increasing disorder, the condensate and superfluid fractions jump to zero at a critical value of the disorder parameter by a first-order phase transition.

cond-mat.dis-nn↗

arXiv2007

Collective Oscillations in Trapped Bose-Einstein Condensed Gases in the Presence of Weak Disorder

The influence of a weak random potential on the collective modes of a trapped interacting Bose-Einstein condensate at zero temperature is calculated in the limit when the correlation length of the disorder is smaller than the healing length of the superfluid. The problem is solved in the Thomas-Fermi limit by generalizing the superfluid hydrodynamic equations to allow for the presence of weak disorder. We find that the disorder-induced frequency-shifts of the low-energy excitations can be of the same order of magnitude as the beyond mean-field corrections in the normal interaction recently observed experimentally.

cond-mat.other↗

arXiv2007

Bose-Einstein-condensed systems in random potentials

The properties of systems with Bose-Einstein condensate in external time-independent random potentials are investigated in the frame of a self-consistent stochastic mean-field approximation. General considerations are presented, which are valid for finite temperatures, arbitrary strengths of the interaction potential, and for arbitrarily strong disorder potentials. The special case of a spatially uncorrelated random field is then treated in more detail. It is shown that the system consists of three components, condensed particles, uncondensed particles and a glassy density fraction, but that the pure Bose glass phase with only a glassy density does not appear. The theory predicts a first-order phase transition for increasing disorder parameter, where the condensate fraction and the superfluid fraction simultaneously jump to zero. The influence of disorder on the ground-state energy, the stability conditions, the compressibility, the structure factor, and the sound velocity are analyzed. The uniform ideal condensed gas is shown to be always stochastically unstable, in the sense that an infinitesimally weak disorder destroys the Bose-Einstein condensate, returning the system to the normal state. But the uniform Bose-condensed system with finite repulsive interactions becomes stochastically stable and exists in a finite interval of the disorder parameter.

cond-mat.stat-mech↗

arXiv2007

Thermodynamics of a Bose-Einstein Condensate with Weak Disorder

We consider the thermodynamics of a homogeneous superfluid dilute Bose gas in the presence of weak quenched disorder. Following the zero-temperature approach of Huang and Meng, we diagonalize the Hamiltonian of a dilute Bose gas in an external random delta-correlated potential by means of a Bogoliubov transformation. We extend this approach to finite temperature by combining the Popov and the many-body T-matrix approximations. This approach permits us to include the quasi-particle interactions within this temperature range. We derive the disorder-induced shifts of the Bose-Einstein critical temperature and of the temperature for the onset of superfluidity by approaching the transition points from below, i.e., from the superfluid phase. Our results lead to a phase diagram consistent with that of the finite-temperature theory of Lopatin and Vinokur which was based on the replica method, and in which the transition points were approached from above.

cond-mat.other↗

arXiv2006

Mean-field phase diagram of disordered bosons in a lattice at non-zero temperature

Bosons in a periodic lattice with on-site disorder at low but non-zero temperature are considered within a mean-field theory. The criteria used for the definition of the superfluid, Mott insulator and Bose glass are analysed. Since the compressibility does never vanish at non-zero temperature, it can not be used as a general criterium. We show that the phases are unambiguously distinguished by the superfluid density and the density of states of the low-energy exitations. The phase diagram of the system is calculated. It is shown that even a tiny temperature leads to a significant shift of the boundary between the Bose glass and superfluid.

cond-mat.other↗

arXiv2005

First- and second-order superfluid--Mott-insulator phase transitions of spin-1 bosons with coupled ground states in optical lattices

We investigate the superfluid--Mott-insulator quantum phase transition of spin-1 bosons in an optical lattice created by pairs of counterpropagating linearly polarized laser beams, driving an $F_g=1$ to $F_e=1$ internal atomic transition. The whole parameter space of the resulting two-component Bose-Hubbard model is studied. We find that the phase transition is not always second order as in the case of spinless bosons, but can be first order in certain regions of the parameter space. The calculations are done in the mean-field approximation by means of exact numerical diagonalization as well as within the framework of perturbaton theory.

cond-mat.other↗

arXiv2004

Spin-1 bosons with coupled ground states in optical lattices

The superfluid--Mott-insulator phase transition of ultracold spin-1 bosons with ferromagnetic and antiferromagnetic interactions in an optical lattice is theoretically investigated. Two counterpropagating linearly polarized laser beams with the angle $θ$ between the polarization vectors (lin-$θ$-lin configuration), driving an $F_g=1$ to $F_e=1$ internal atomic transition, create the optical lattice and at the same time couple atomic ground states with magnetic quantum numbers $m=\pm 1$. Due to the coupling the system can be described as a two-component one. At $θ=0$ the system has a continuous isospin symmetry, which can be spontaneously broken, thereby fixing the number of particles in the atomic components. The phase diagram of the system and the spectrum of collective excitations, which are density waves and isospin waves, are worked out. In the case of ferromagnetic interactions, the superfluid--Mott-insulator phase transition is always second order, but in the case of antiferromagnetic interactions for some values of system parameters it is first order and the superfluid and Mott phases can coexist. Varying the angle $θ$ one can control the populations of atomic components and continuously turn on and tune their asymmetry.

cond-mat.other↗

arXiv2004

Bose-Einstein condensate of kicked rotators with time-dependent interaction

A modification of the quantum kicked rotator is suggested with a time-dependent delta-kicked interaction parameter which can be realized by a pulsed turn-on of a Feshbach resonance. The mean kinetic energy increases exponentially with time in contrast to a merely diffusive or linear growth for the first few kicks for the quantum kicked rotator with a constant interaction parameter. A recursive relation is derived in a self-consistent random phase approximation which describes this superdiffusive growth of the kinetic energy and is compared with numerical simulations. Unlike in the case of the quantum rotator with constant interaction, a Lax pair is not found. In general the delta-kicked interaction is found to lead to strong chaotic behaviour.

cond-mat.stat-mech↗

arXiv2004

Exact results for one-dimensional disordered bosons with strong repulsion

We study one-dimensional incommensurate bosons with strong repulsive interactions and weak disorder. In analogy to the clean Tonks-Girardeau gas, a Bose-Fermi mapping expresses this problem in terms of disordered free fermions. Thereby many known results apply, in particular for the density-density correlations, the distribution function of the local density of states, and the complete spectral statistics. We also analyze the bosonic momentum distribution, and comment on the experimental observability of these predictions in ultracold atomic gases.

cond-mat.stat-mech↗

arXiv2004

Bose-Einstein condensate of kicked rotators

A concrete proposal for the realization of a Bose-Einstein condensate of kicked rotators is presented. Studying their dynamics via the one-dimensional Gross-Pitaevskii equation on a ring we point out the existence of a Lax-pair and an infinite countable set of conserved quantities. Under equal conditions we make numerical comparisons of the dynamics and their effective irreversibility in time, of ensembles of chaotic classical-, and BECs of interaction-free quantum-, and interacting quantum kicked rotators.

cond-mat.stat-mech↗

arXiv2003

Interference of atomic levels and superfluid -- Mott insulator phase transition in a two-component Bose-Einstein condensate

The superfluid -- Mott insulator phase transition in a Bose-Einstein condensate of neutral atoms with doubly degenerate internal ground states in an optical lattice is theoretically investigated. The optical lattice is created by two counterpropagating linearly polarized laser beams with the angle $θ$ between the polarization vectors (lin-angle-lin configuration). The phase diagram of the system and the critical values of the parameters are worked out. It is shown that the sign of the detuning plays an important role and that there is a strong suppression of the Mott transition in the case of blue detuning. Varying the laser intensity and/or the angle $θ$ one can manipulate the Mott-insulator to superfluid quantum phase transition as well as prepare the condensate in physically distinguishable "ferromagnetic" and "antiferromagnetic" superfluid states.

cond-mat↗

arXiv1999

Shifts and widths of collective excitations in trapped Bose gases by the dielectric formalism

We present predictions for the temperature dependent shifts and damping rates. They are obtained by applying the dielectric formalism to a simple model of a trapped Bose gas. Within the framework of the model we use lowest order perturbation theory to determine the first order correction to the results of Hartree-Fock-Bogoliubov-Popov theory for the complex collective excitation frequencies, and present numerical results for the temperature dependence of the damping rates and the frequency shifts. Good agreement with the experimental values measured at JILA are found for the m=2 mode, while we find disagreements in the shifts for m=0. The latter point to the necessity of a non-perturbative treatment for an explanation of the temperature-dependence of the m=0 shifts.

cond-mat↗

arXiv1998

Finite temperature excitations of Bose gases in anisotropic traps

The mode frequencies of a weakly interacting Bose gas in a magnetic trap are studied as a function of the anisotropy of the trap. As in earlier works the generalized Hartree-Fock-Bogoliubov equations within the Popov approximation (HFB-Popov) are used for our calculations. The new feature of our work is the combined use of a mode expansion in a finite basis and a semiclassical approximation of the highly excited states. The results are applied to check the accuracy of the recently suggested equivalent zero-temperature condensate (EZC) approximation which involves a much simpler model.

cond-mat↗

arXiv1998

Dynamical quantum noise in Bose-Einstein condensates

We introduce the study of dynamical quantum noise in Bose-Einstein condensates through numerical simulation of stochastic partial differential equations obtained using phase space representations. We derive evolution equations for a single trapped condensate in both the positive-$P$ and Wigner representations, and perform simulations to compare the predictions of the two methods. The positive-$P$ approach is found to be highly susceptible to the stability problems that have been observed in other strongly nonlinear, weakly damped systems. Using the Wigner representation, we examine the evolution of several quantities of interest using from a variety of choices of initial state for the condensate, and compare results to those for single-mode models.

cond-mat.soft↗

arXiv1997

Transition from Poissonian to GOE level statistics in a modified Artin's billiard

One wall of Artin's billiard on the Poincaré half plane is replaced by a one-parameter ($c_p$) family of nongeodetic walls. A brief description of the classical phase space of this system is given. In the quantum domain, the continuousand gradual transition from the Poisson like to GOE level statistics due to the small perturbations breaking the symmetry responsible for the 'arithmetic chaos' at $c_p=1$ is studied. Another GOE $\rightrrow$ Poisson transition due to the mixed phase space for large perturbations is also investigated. A satisfactory description of the intermediate level statistics by the Brody distribution was found in boh cases. The study supports the existence of a scaling region around $c_p=1$. A finite size scaling relation for the Brody-parameter as a function of $1-c_p$ and the number of levels considered can be established.

chao-dyn↗

arXiv1997

Collapses and Revivals of Collective Excitations in Trapped Bose Condensates

We present a quantum theory of low-lying excitations in a trapped Bose condensate with finite particle numbers. We find that even at zero temperature condensate number fluctuations and/or fluctuations of the excitation frequency due to quantum uncertainties of the mode occupation lead to a collapse of the collective modes due to dephasing. Coherent revivals of the collective excitations are predicted on a much longer timescale. Depletion of collective modes due to second-harmonic generation is discussed.

cond-mat↗

arXiv1997

Phase preparation by atom counting of Bose-Einstein condensates in mixed states

We study the build up of quantum coherence between two Bose-Einstein condensates which are initially in mixed states. We consider in detail the two cases where each condensate is initially in a thermal or a Poisson distribution of atom number. Although initially there is no relative phase between the condensates, a sequence of spatial atom detections produces an interference pattern with arbitrary but fixed relative phase. The visibility of this interference pattern is close to one for the Poisson distribution of two condensates with equal counting rates but it becomes a stochastic variable in the thermal case, where the visibility will vary from run to run around an average visibility of $π/4.$ In both cases, the variance of the phase distribution is inversely proportional to the number of atom detections in the regime where this number is large compared to one but small compared with the total number of atoms in the condensates.

quant-ph↗