Bose-Einstein condensates in strongly disordered traps

A Bose-Einstein condensate in an external potential consisting of a superposition of a harmonic and a random potential is considered theoretically. From a semiquantitative analysis we find the size, shape, and excitation energy as a function of the disorder strength. For positive scattering length and sufficiently strong disorder the condensate decays into fragments each of the size of the Larkin length L. This state is stable over a large range of particle numbers. The frequency of the breathing mode scales as 1/L(2). For negative scattering length a condensate of size L may exist as a metastable state. These findings are generalized to anisotropic traps.     

Ground state of a Bose-Einstein condensate which scatters coherently laser radiation

We present a self-consistent method of taking into account back action of a laser radiation to a Bose-Einstein condensate of neutral atoms. The light is coherently scattered inside the degenerate atomic sample, thus its intensity and, consequently, the atomic ground level AC Stark shift are spatially varying. This leads to a small deformation of the atomic cloud and, if the external radiation is abruptly switched off, to generation of collective excitations. Received 8 May 1999 and Received in final form 11 October 1999     

New multiple histogram method for studying phase transitions

For temperature zero the effects of disorder for interacting bosons are considered. The disorder induced superfluid-insulator transition in thed-dimensional disordered Bogoliubov model is discussed. Results for a short-range and a long-range random potential are given. For short-range disorder we argue that ford<4 arbitrarily small disorder localizes the Bose condensate for vanishing interaction potential. Ford>4 a certain strength of the disorder potential is necessary in order to localize the condensate. For the three-dimensional Bogoliubov model our results are in agreement with a recent calculation. We compare our theoretical predictions with numerical experiments for a disordered boson Hubbard model.     

Quantum diffusion of matter waves in 2D speckle potentials

This paper investigates quantum diffusion of matter waves in two-dimensional random potentials, focussing on expanding Bose-Einstein condensates in spatially correlated optical speckle potentials. Special care is taken to describe the effect of dephasing, finite system size, and an initial momentum distribution. We derive general expressions for the interference-renormalized diffusion constant, the disorder-averaged probability density distribution, the variance of the expanding atomic cloud, and the localized fraction of atoms. These quantities are studied in detail for the special case of an inverted-parabola momentum distribution as obtained from an expanding condensate in the Thomas-Fermi regime. Lastly, we derive quantitative criteria for the unambiguous observation of localization effects in a possible 2D experiment.     

Expansion of a Bose-Einstein condensate in the presence of disorder

Expansion of a Bose-Einstein condensate (BEC) is studied in the presence of a random potential. The expansion is controlled by a single parameter, (microtau(eff)/variant Planck's over 2pi), where micro is the chemical potential, prior to the release of the BEC from the trap, and tau(eff) is a transport relaxation time which characterizes the strength of the disorder. Repulsive interactions (nonlinearity) facilitate transport and can lead to diffusive spreading of the condensate which, in the absence of interactions, would have remained localized in the vicinity of its initial location.     

AdS/CFT superconductors with Power Maxwell electrodynamics: Reminiscent of the Meissner effect

Based on an analytic scheme and neglecting the back reaction effect several crucial properties of holographic s-wave superconductors have been investigated in the presence of an external magnetic field in the background of a D  -dimensional Schwarzschild AdS space–time. Inspired by low energy limit of heterotic string theory, in the present Letter we replace the conventional Maxwell action by a Power Maxwell action. Immersing the holographic superconductors in an external static magnetic field the spatially dependent condensate solutions have been obtained analytically. Interestingly enough it is observed that condensation can form only below a certain critical field strength (_Bc$B_c$). Finally, and most importantly it is observed that the value of this critical field strength increases as the mass of the scalar particles gets higher, which indicates the onset of a harder condensation.     

Tunable transport with broken space–time symmetries

Transport properties of particles and waves in spatially periodic structures that are driven by external time-dependent forces manifestly depend on the space–time symmetries of the corresponding equations of motion. A systematic analysis of these symmetries uncovers the conditions necessary for obtaining directed transport. In this work we give a unified introduction into the symmetry analysis and demonstrate its action on the motion in one-dimensional periodic, both in time and space, potentials. We further generalize the analysis to quasi-periodic drives, higher space dimensions, and quantum dynamics. Recent experimental results on the transport of cold and ultracold atomic ensembles in ac-driven optical potentials are reviewed as illustrations of theoretical considerations.     

Ground state of graphene in the presence of random charged impurities

We calculate the carrier-density-dependent ground-state properties of graphene in the presence of random charged impurities in the substrate taking into account disorder and interaction effects nonperturbatively on an equal footing in a self-consistent theoretical formalism. We provide detailed quantitative results on the dependence of the disorder-induced spatially inhomogeneous two-dimensional carrier density distribution on the external gate bias, the impurity density, and the impurity location. We find that the interplay between disorder and interaction is strong, particularly at lower impurity densities. We show that, for the currently available typical graphene samples, inhomogeneity dominates graphene physics at low (< or approximately 10(12) cm(-2)) carrier density with the density fluctuations becoming larger than the average density.     

球形粒子复合介质非线性有效电导交流响应

利用摄动方法，研究了在外加交流电场作用下，含球形杂质的非线性复合介质有效电导的交流响应问题。在一类形如E1sinωt +E3sin3ωt的正弦电场作用下，分别导出了非线性复合介质中杂质粒子及基质所在区域的局部电势。在杂质浓度较低时，进一步得到了复合介质非线性有效电导在基频和三阶谐波下的响应，并讨论了二者之间的关系。     

Phase dynamics of a Josephson junction ladder driven by modulated currents

Phase dynamics of disordered Josephson junction ladders (JJLs) driven by external currents which are spatially and temporally modulated is studied using a numerical simulation based on a random field XY model. This model is considered theoretically as an effective model of JJLs with structural disorder in a magnetic field. The spatiotemporal modulation of external currents causes peculiar dynamical effects of phases in the system under certain conditions, such as the directed motion of phases and the mode-locking in the absence of dc currents. We clarify the details of effects of the spatiotemporal modulation on the phase dynamics.     

Bose–Einstein condensates in 1D- and 2D optical lattices

Bose–Einstein condensates of rubidium atoms are transferred into one- and two-dimensional optical lattice potentials. The phase coherence of the condensate wavefunction in the lattice potential is studied by suddenly releasing the atoms from the trapping potential and observing the multiple matter-wave interference pattern of several thousand expanding quantum gases. We show how arbitrary phase gradients can be mapped onto the periodic wavefunction through the application of a potential gradient. Furthermore, the experimentally measured strength of the momentum components is compared to a theoretical model of the condensate wavefunction in the lattice. Received: 3 July 2001 / Revised version: 26 September 2001 / Published online: 23 November 2001     

Localized Waves in Nonlinear Systems with Spatially Inhomogeneous Nonlinearity

A type of （2＋1）-dimensional nonlinear Schrǒdinger equation with spatially inhomogeneous nonlinearity and an external potential is studied. It is found that special external potentials and spatially nonlinearities can support nonlinear localized waves.     

Mott-insulator transition in a two-dimensional atomic Bose gas

Cold atoms in periodic potentials are versatile quantum systems for implementing simple models prevalent in condensed matter theory. Here we realize the 2D Bose-Hubbard model by loading a Bose-Einstein condensate into an optical lattice, and study the resulting Mott insulator. The measured momentum distributions agree quantitatively with theory (no adjustable parameters). In these systems, the Mott insulator forms in a spatially discrete shell structure which we probe by focusing on correlations in atom shot noise. These correlations show a marked dependence on the lattice depth, consistent with the changing size of the insulating shell expected from simple arguments.     

Density,phase and coherence properties of a low dimensional Bose-Einstein systems moving in a disordered potential

We present a detailed numerical study of the dynamics of a disordered one-dimensional Bose-Einstein condensates in position and momentum space. We particularly focus on the region where non-linearity and disorder simultaneously effect the time propagation of the condensate as well as the possible interference between various parts of the matter wave. We report oscillation between spatially extended and localized behavior for the propagating condensate which dies down with increasing non-linearity. We also report intriguing behavior of the phase fluctuation and the coherence properties of the matter wave. We also briefly compare these behavior with that of a two-dimensional condensate. We mention the relevance of our results to the related experiments on Anderson localization and indicate the possibility of future experiments     

Effect of Anisotropic Spin-Orbit Coupling on the Ground State of Bose-Einstein Condensate in an External Potential

Spin-orbit coupled Bosonic atoms confined in external potentials open up new avenues for quantumstate manipulation and will contribute to the design and exploration of novel quantum devices.Here we consider a quasi-two-dimensional spin-orbit coupled Bose-Einstein condensate confined in an external harmonic potential,with emphasis on the effects of anisotropic spin-orbit coupling on the equilibrium ground-state structure of such a system.For the cases with spin-orbit coupling solely in x- or y-axis direction,the ground-state structure can develop to the well-known standing wave phase,in which the two components always form an alternative density arrangement.For a two-dimensional anisotropic spin-orbit coupling,the separated lumps first become bend,then form two rows of stripe structure along y direction with further increasing the strength of spin-orbit coupling in x-direction.Furthermore,the distance between these two rows of stripe structure is also investigated in detail.     

Free cooling phase-diagram of hard-spheres with short- and long-range interactions

We study the stability, the clustering and the phase-diagram of free cooling granular gases. The systems consist of mono-disperse particles with additional non-contact (long-range) interactions, and are simulated here by the event-driven molecular dynamics algorithm with discrete (short-range shoulders or wells) potentials (in both 2D and 3D). Astonishingly good agreement is found with a mean field theory, where only the energy dissipation term is modified to account for both repulsive or attractive non-contact interactions. Attractive potentials enhance cooling and structure formation (clustering), whereas repulsive potentials reduce it, as intuition suggests. The system evolution is controlled by a single parameter: the non-contact potential strength scaled by the fluctuation kinetic energy (granular temperature). When this is small, as expected, the classical homogeneous cooling state is found. However, if the effective dissipation is strong enough, structure formation proceeds, before (in the repulsive case) non-contact forces get strong enough to undo the clustering (due to the ongoing dissipation of granular temperature). For both repulsive and attractive potentials, in the homogeneous regime, the cooling shows a universal behaviour when the (inverse) control parameter is used as evolution variable instead of time. The transition to a non-homogeneous regime, as predicted by stability analysis, is affected by both dissipation and potential strength. This can be cast into a phase diagram where the system changes with time, which leaves open many challenges for future research.     

On the Nature of Bose-Einstein Condensation in Disordered Systems

We study the perfect Bose gas in random external potentials and show that there is generalized Bose-Einstein condensation in the random eigenstates if and only if the same occurs in the one-particle kinetic-energy eigenstates, which corresponds to the generalized condensation of the free Bose gas. Moreover, we prove that the amounts of both condensate densities are equal. Our method is based on the derivation of an explicit formula for the occupation measure in the one-body kinetic-energy eigenstates which describes the repartition of particles among these non-random states. This technique can be adapted to re-examine the properties of the perfect Bose gas in the presence of weak (scaled) non-random potentials, for which we establish similar results. In addition some of our results can be applied to models with diagonal interactions, that is, models which conserve the occupation density in each single particle eigenstate.     

Mean-field phase diagram for Bose-Hubbard Hamiltonians with random hopping

The zero temperature phase diagram for ultracold bosons in a random 1D potential is obtained through a site decoupling mean-field scheme performed over a Bose-Hubbard (BH) Hamiltonian, whose hopping term is considered as a random variable. As for the model with random on-site potential, the presence of disorder leads to the appearance of a Bose glass phase. The different phases—i.e., Mott insulator, superfluid, and Bose glass—are characterized in terms of condensate fraction and superfluid fraction. Furthermore, the boundary of the Mott lobes is related to an off-diagonal Anderson model featuring the same disorder distribution as the original BH Hamiltonian.     

Fidelity decay in trapped bose-einstein condensates

The quantum coherence of a Bose-Einstein condensate is studied using the concept of quantum fidelity (Loschmidt echo). The condensate is confined in an elongated anharmonic trap and subjected to a small random potential such as that created by a laser speckle. Numerical experiments show that the quantum fidelity stays constant until a critical time, after which it drops abruptly over a single trap oscillation period. The critical time depends logarithmically on the number of condensed atoms and on the perturbation amplitude. This behavior may be observable by measuring the interference fringes of two condensates evolving in slightly different potentials.