Tuning the scattering length with an optically induced Feshbach resonance

We demonstrate optical tuning of the scattering length in a Bose-Einstein condensate as predicted by Fedichev et al. [Phys. Rev. Lett. 77, 2913 (1996)]. In our experiment, atoms in a 87Rb condensate are exposed to laser light which is tuned close to the transition frequency to an excited molecular state. By controlling the power and detuning of the laser beam we can change the atomic scattering length over a wide range. In view of laser-driven atomic losses, we use Bragg spectroscopy as a fast method to measure the scattering length of the atoms.     

Complex chemical potential: signature of decay in a bose-einstein condensate

We explore the zero-temperature statics of an atomic Bose-Einstein condensate in which a Feshbach resonance creates a coupling to a second condensate component of quasibound molecules. Using a variational procedure to find the equation of state, the appearance of this binding is manifest in a collapsing ground state, where only the molecular condensate is present up to some critical density. Further, an excited state is seen to reproduce the usual low-density atomic condensate behavior in this system, but the molecular component is found to produce a coherent, many-body decay, quantified by the imaginary part of the chemical potential. Most importantly, the unique decay rate dependencies on density (approximately rho (3/2)) and on scattering length (approximately (5/2)) can be measured in experimental tests of this result.     

Propagation of a dark soliton in a disordered Bose-Einstein condensate

We consider the propagation of a dark soliton in a quasi-1D Bose-Einstein condensate in presence of a random potential. This configuration involves nonlinear effects and disorder, and we argue that, contrarily to the study of stationary transmission coefficients through a nonlinear disordered slab, it is a well-defined problem. It is found that a dark soliton decays algebraically, over a characteristic length which is independent of its initial velocity, and much larger than both the healing length and the 1D scattering length of the system. We also determine the characteristic decay time.     

Cold bose gases with large scattering lengths

We calculate the energy and condensate fraction for a dense system of bosons interacting through an attractive short range interaction with positive s-wave scattering length a. At high densities n>a(-3), the energy per particle, chemical potential, and square of the sound speed are independent of the scattering length and proportional to n(2/3), as in Fermi systems. The condensate is quenched at densities na(3) approximately 1.     

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.     

Bright and dark solitons in a quasi-1D Bose-Einstein condensates modelled by 1D Gross-Pitaevskii equation with time-dependent parameters

We investigate the exact bright and dark solitary wave solutions of an effective 1D Bose-Einstein condensate (BEC) by assuming that the interaction energy is much less than the kinetic energy in the transverse direction. In particular, following the earlier works in the literature Pérez-García et al. (2004) [50], Serkin et al. (2007) [51], Gurses (2007) [52] and Kundu (2009) [53], we point out that the effective 1D equation resulting from the Gross-Pitaevskii (GP) equation can be transformed into the standard soliton (bright/dark) possessing, completely integrable 1D nonlinear Schrödinger (NLS) equation by effecting a change of variables of the coordinates and the wave function. We consider both confining and expulsive harmonic trap potentials separately and treat the atomic scattering length, gain/loss term and trap frequency as the experimental control parameters by modulating them as a function of time. In the case when the trap frequency is kept constant, we show the existence of different kinds of soliton solutions, such as the periodic oscillating solitons, collapse and revival of condensate, snake-like solitons, stable solitons, soliton growth and decay and formation of two-soliton bound state, as the atomic scattering length and gain/loss term are varied. However, when the trap frequency is also modulated, we show the phenomena of collapse and revival of two-soliton like bound state formation of the condensate for double modulated periodic potential and bright and dark solitons for step-wise modulated potentials.     

Bose-Einstein Condensates in a One-Dimensional Optical Lattice: from Superfluidity to Number-Squeezed States

We study the phase coherence property of Bose-Einstein condensates confined in a one-dimensional optical lattice formed by a standing-wave laser field. The lattice depth is determined using a method of Kapitza-Dirac scattering between a condensate and a short pulse lattice potential. Condensates are then adiabatically loaded into the optical lattice. The phase coherence property of the confined condensates is reflected by the interference patterns of the expanded atomic cloud released from the optical lattice. For weak lattice, nearly all of the atoms stay in a superfluid state. However, as the lattice depth is increased, the phase coherence of the whole condensate sample is gradually lost, which confirms that the sub-condensates in each lattice well have evolved into number-squeezed states.     

Enhancing capacity of coherent optical information storage and transfer in a Bose-Einstein condensate

The coherent optical information storage capacity of an atomic Bose-Einstein condensate is examined. The theory of slow light propagation in atomic clouds is generalized to the short-pulse regime by taking into account group velocity dispersion. It is shown that the number of stored pulses in the condensate can be optimized for a particular coupling laser power, temperature, and interatomic interaction strength. Analytical results are derived for a semi-ideal model of the condensate using the effective uniform density zone approximation. Detailed numerical simulations are also performed. It is found that the axial density profile of the condensate protects the pulse against group velocity dispersion. Furthermore, taking into account the finite radial size of the condensate, multimode light propagation in an atomic Bose-Einstein condensate is investigated. The number of modes that can be supported by a condensate is found. The single-mode condition is determined as a function of experimentally accessible parameters including trap size, temperature, condensate number density, and scattering length. Quantum coherent atom-light interaction schemes are proposed for enhancing multimode light propagation effects.     

Nature of the condensate in mass transport models

We study the phenomenon of real space condensation in the steady state of a class of one-dimensional mass transport models. We derive the criterion for the occurrence of a condensation transition and analyze the precise nature of the shape and the size of the condensate in the condensed phase. We find two distinct condensate regimes: one where the condensate is Gaussian distributed and the particle number fluctuations scale normally as L(1/2) where L is the system size, and the second regime where the particle number fluctuations become anomalously large and the condensate peak is non-Gaussian. We interpret these results within the framework of sums of random variables.     

Polymer Quantization in the Bogoliubov’s Regime for a Homogeneous One-Dimensional Bose-Einstein Condensate

In the present report we analyze the modifications caused by the polymer quantization upon the ground state of a homogeneous one–dimensional Bose–Einstein condensate. We obtain the ground state energy of the corresponding N–body system and consequently, the corresponding speed of sound, allowing us to explore the sensitivity of the system to corrections caused by the polymer length scale. Such corrections can be enhanced for dense systems together with small values of the corresponding one–dimensional scattering length. However, these corrections remain constrained due to finite size effects of the system. The contributions of the polymer length scale to the properties of the ground state energy of the system allow us to explore, as a first approximation and when the Bogoliubov’s formalism is valid, the sensitivity of this many–body system to traces caused by the discreteness of space suggested by the polymer quantization.     

Macroscopic quantum tunneling of a bose condensate

We study, by means of a variational method, the stability of a condensate in a magnetically trapped atomic Bose gas with a negative scattering length and find that the condensate is unstable in general. However, for temperatures sufficiently close to the critical temperature the condensate turns out to be metastable. For that case we determine in the usual WKB approximation the decay rate of the condensate due to macroscopic quantum fluctuations. When appropriate, we also calculate the decay rate due to thermal fluctuations. An important feature of our approach is that (nonsingular) phase fluctuations of the condensate are taken into account exactly.     

Variational theory for the ground state and collective excitations of an elongated dipolar condensate

We develop a variational theory for a dipolar condensate in an elongated(cigar shaped)confinement potential. Our formulation provides an effective one-dimensional extended meanfield theory for the ground state and its collective excitations. We apply our theory to investigate the properties of rotons in the system comparing the variational treatment to a full numerical solution. We consider the effect of quantum fluctuations on the scattering length at which the roton excitation softens to zero energy.     

The contact in the BCS–BEC crossover for finite range interacting ultracold Fermi gases

Using mean-field theory for the Bardeen–Cooper–Schriefer (BCS) to the Bose–Einstein condensate (BEC) crossover we investigate the ground state thermodynamic properties of an interacting homogeneous Fermi gas. The interatomic interactions modelled through a finite range potential allows us to calculate the thermodynamic behaviour as a function of the potential parameters in the whole crossover region. We concentrate in studying the Contact variable, the thermodynamic conjugate of the inverse of the s-wave scattering length. Our analysis leads to predict a quantum phase transition – like in the case of large potential range. This finding is a direct consequence of the k-dependent energy gap.     

Coherent transport in a homojunction between an excitonic insulator and semimetal

From the solution of a two-band model, we predict that the thermal and electrical transport across the junction of a semimetal and an excitonic insulator will exhibit high resistance behavior and low entropy production at low temperatures, distinct from a junction of a semimetal and a normal semiconductor. This phenomenon, ascribed to the dissipationless exciton flow which dominates over the charge transport, is based on the much longer length scale of the change of the effective interface potential for electron scattering due to the coherence of the condensate than in the normal state.     

Dynamics of a single vortex line in a Bose-Einstein condensate

We study experimentally the line of a single quantized vortex in a rotating prolate Bose-Einstein condensate confined by a harmonic potential. In agreement with predictions, we find that the vortex line is in most cases curved at the ends. We monitor the vortex line leaving the condensate. Its length is measured as a function of time and temperature. For a low temperature, the survival time can be as large as 10 sec. The length of the line and its deviation from the center of the trap are related to the angular momentum per particle along the condensate axis.     

Ratchet-induced matter-wave transport and soliton collisions in Bose-Einstein condensates

We study the dynamics of bright matter-wave solitons in a Bose-Einstein condensate with negative scattering length under the influence of a time-periodic ratchet potential. The potential is formed by a one-dimensional bichromatic optical lattice which flashes on and off so that the time average of its amplitude vanishes. Due to the broken space and time-reversal symmetries of the potential, the soliton is transported with a nonzero average velocity. By employing the non-dissipative mean-field model for the matter waves, we study the dependence of the transport velocity on the initial state of the soliton and show how the properties of the individual localized states affect the outcome of their collisions. A useful insight into the transport properties is provided by Hamiltonian theory for the mean field, which treats the extended matter-wave excitation as an effective classical particle.     

用F-G-H方法研究玻色-爱因斯坦凝聚体基态性质

用F-G-H方法数值求解描述BEC凝聚体的非线性薛定谔方程-Gross-Pitaevskii方程.研究总粒子数、粒子间相互作用、谐振频率和一般幂指数外势对玻色凝聚体粒子数密度分布、基态能量的影响.结果表明,增大幂指数外势、谐振频率,降低粒子间的排斥作用会增加凝聚体中心的粒子数密度、缩小凝聚体半径;增大总粒子数、谐振频率、粒子间的排斥作用和幂指数外势的指数会增大体系的基态能量;随着总粒子数增大,数值结果与托马斯-费米近似结果渐趋一致,托马斯-费米近似在大粒子数条件下是一种较好的近似方法,在粒子数有限时,结果与真实情形偏差较大,应采用数值解法.     

New type of instability of a Bose-Einstein condensate in a trap due to the onlocal interaction of atoms

It is shown analytically that, in a trap filled by a Bose-Einstein condensate of atoms with a negative S-scattering length, there exists an instability caused by the nonlocal interaction of atoms. For this effect to be efficiently discovered experimentally, it is necessary to considerably decrease the absolute value of the scattering length using the Feshbach effect.     

Exploring the phase space of the quantum delta-kicked accelerator

We experimentally explore the underlying pseudoclassical phase space structure of the quantum delta-kicked accelerator. This was achieved by exposing a Bose-Einstein condensate to the spatially corrugated potential created by pulses of an off-resonant standing light wave. For the first time quantum accelerator modes were realized in such a system. By utilizing the narrow momentum distribution of the condensate we were able to observe the discrete momentum state structure of a quantum accelerator mode and also to directly measure the size of the structures in the phase space.     

Bose systems in spatially random or time-varying potentials

Bose systems, subject to the action of external random potentials, are considered. For describing the system properties, under the action of spatially random potentials of arbitrary strength, the stochastic mean-field approximation is employed. When the strength of disorder increases, the extended Bose-Einstein condensate fragments into spatially disconnected regions, forming a granular condensate. Increasing the strength of disorder even more transforms the granular condensate into the normal glass. The influence of time-dependent external potentials is also discussed. Fastly varying temporal potentials, to some extent, imitate the action of spatially random potentials. In particular, strong time-alternating potential can induce the appearance of a nonequilibrium granular condensate.