Bose gas of small density in a random field

Bose gas in a random external field is considered. The effective action both for weak and strong random fields, compared with the interaction between particles, is derived in the framework of the path integral Keldysh-Schwinger technique. Using this effective action the properties of the system in strongly fluctuating random field are analyzed. Used approximation shows a gap in the chemical potential, when it flows from negative to positive values.     

Condensate fraction and critical temperature of interacting Bose gas in anharmonic trap

The spectral flow of three-body (trimer) states consisting of two heavy (impurity) particles sitting in a condensate of light bosons is considered. Assuming that the condensate is weakly interacting and that an impurity and a boson have a resonant zero-range two-body interaction, we use the Born-Oppenheimer approximation to determine the effective three-body potential. We solve the resulting Schrödinger equation numerically and determine the trimer binding energies as a function of the coherence length of the light bosonic condensate particles. The binding energy is found to be suppressed by the presence of the condensate when the energy scale corresponding to the coherence length becomes of order the trimer binding energy in the absence of the condensate. We find that the Efimov scaling property is reflected in the critical values of the condensate coherence length at which the trimers are pushed into the continuum.     

Upper bound on the condensate in the hard-core Bose lattice gas

Using methods developed by G. Roepstorf, we prove an upper bound for the amount of condensate in ahard-core Bose lattice gas.On leave from the Mathematical Institute of the Hungarian Academy of Sciences, Budapest, H-1053, Hungary.     

A remark on the condensation in the hard-core lattice Bose gas

We point out that Bose-Einstein condensation occurs at sufficiently low temperature in a hard-core ^d-lattice Bose gas for d3 and particle density 1/2, by exploiting its equivalence to a spin-1/2XY model.     

Strongly inhibited transport of a degenerate 1D Bose gas in a lattice

We report the observation of strongly damped dipole oscillations of a quantum degenerate 1D atomic Bose gas in a combined harmonic and optical lattice potential. Damping is significant for very shallow axial lattices (0.25 photon recoil energies), and increases dramatically with increasing lattice depth, such that the gas becomes nearly immobile for times an order of magnitude longer than the single-particle tunneling time. Surprisingly, we see no broadening of the atomic quasimomentum distribution after damped motion. Recent theoretical work suggests that quantum fluctuations can strongly damp dipole oscillations of a 1D atomic Bose gas, providing a possible explanation for our observations.     

Long-wavelength excitations in a Bose gas at zero temperature

The long-wavelength excitations in a simple model of a dilute Bose gas at zero temperature are investigated from a purely microscopic viewpoint. The role of the interaction and the effects of the condensate are emphasized in a dielectric formulation, in which the response functions are expressed in terms of regular functions that do not involve an isolated single-interaction line nor an isolated single-particle line. Local number conservation is incorporated into the formulation by the generalized Ward identities, which are used to express the regular functions involving the density in terms of regular functions involving the longitudinal current. A perturbation expansion is then developed for the regular functions, producing to a given order in the perturbation expansion an elementary excitation spectrum without a gap and simultaneously response functions that obey local number conservation and related sum rules.Explicit results to the first order beyond the Bogoliubov approximation in a simple one-parameter model are obtained for the elementary excitation spectrum ω_k, the dynamic structure function $\text{S}$(k, ω), the associated structure function $\text{S}$_m(k), and the one-particle spectral function $\text{A}$(k, ω), as functions of the wavevector k and frequency ω. These results display the sharing of the gapless spectrum ω_k by the various response functions and are used to confirm that the sum rules of interest are satisfied. It is shown that ω_k and some of the $\text{S}$_m(k) are not analytic functions of k in the long wavelength limit. The dynamic structure function $\text{S}$(k, ω) can be conveniently separated into three parts: a one-phonon term which exhausts the f sum rule, a backflow term, and a background term. The backflow contribution to the static structure function $\text{S}$₀(k) leads to the breakdown of the one-phonon Feynman relation at order k³. Both $\text{S}$(k, ω) and $\text{A}$(k, ω) display broad backgrounds because of two-phonon excitations. Simple arguments are given to indicate that some of the qualitative features found for various physical quantities in the first-order model calculation might also be found in superfluid helium.     

Critical temperature of a trapped, weakly interacting Bose gas

We report on measurements of the critical temperature of a harmonically trapped, weakly interacting Bose gas as a function of atom number. Our results exclude ideal-gas behavior by more than two standard deviations, and agree quantitatively with mean-field theory. At our level of sensitivity, we find no additional shift due to critical fluctuations. In the course of this measurement, the onset of hydrodynamic expansion in the thermal component has been observed. Our thermometry method takes this feature into account.     

BEC transition temperature of a dilute homogeneous imperfect Bose gas

The leading-order effect of interactions on a homogeneous Bose gas is theoretically predicted to shift the critical temperature by an amount DeltaT(c) approximately equal to ca(sc)n(1/3)T(0) from the ideal gas result T(0), where a(sc) is the scattering length, n is the density, and c is a pure number. There have been several different theoretical estimates for c. We claim to settle the issue by measuring the numerical coefficient in a lattice simulation of O(2) straight phi(4) field theory in three dimensions-an effective theory which, as observed previously in the literature, can be systematically matched to the dilute Bose gas problem to reproduce nonuniversal quantities such as the critical temperature. We find c = 1.32+/-0.02.     

Nontrivial critical behaviour in a lattice model of random surfaces

A model of “planar random surfaces without spikes” on hypercubical lattices was introduced some years ago as a discretization of quantum string theory. We review some general properties of this model and present results from a Monte Carlo study of its critical behaviour in d = 4, 8 and 10 dimensions. In d = 4 dimensions we find a Hausdorff dimension d_H ≈ 4 and an anomalous dimensions η ≈ 1. These critical exponents imply a deviation from mean field theory in contrast to other lattice random surface models. Furthermore, we find evidence for mean field behaviour in 8 and 10 dimensions, indicating an upper critical dimension d_c^u ⩽ 8.     

Slow quench dynamics of a one-dimensional Bose gas confined to an optical lattice

We analyze the effect of a linear time variation of the interaction strength on a trapped one-dimensional Bose gas confined to an optical lattice. The evolution of different observables such as the experimentally accessible on site particle distribution are studied as a function of the ramp time by using time-dependent numerical techniques. We find that the dynamics of a trapped system typically displays two regimes: For long ramp times, the dynamics is governed by density redistribution, while at short ramp times, local dynamics dominates as the evolution is identical to that of an homogeneous system. In the homogeneous limit, we also discuss the nontrivial scaling of the energy absorbed with the ramp time.     

磁阱中超冷玻色气体临界行为的观测

超冷玻色气体为研究量子临界现象提供了一个非常干净的实验系统. 弱相互作用下的三维玻色气体的临界行为与⁴He发生超流相变时的临界行为类似, 都属于三维XY型普适类. 从正常流体到超流的量子相变过程中, 系统会经历一个从无序相到长程有序相的转变; 而在相变点附近, 系统参量会表现出一些奇点的特征. 本文从实验上观测到了静磁阱中超冷⁸⁷Rb玻色气体在凝聚体相变温度T_c附近的临界行为. 原子气体从静磁阱中释放, 经过30 ms的自由飞行后, 通过吸收成像得到原子气体的动量分布; 然后从中扣除热原子气体的动量分布, 提取出空间上处于临界区域内的原子气体动量分布, 并对不同温度下的动量分布半高宽进行统计. 统计结果显示: 在非常接近相变温度T_c时, 动量分布的半高宽突然减小, 表现出十分明显的奇点行为.     

On the critical point of an interacting two-dimensional trapped Bose gas

We consider a quantized vortex excitation in a two-dimensional, harmonically trapped Bose gas and derive an equation for the Berezinskii-Kosterlitz-Thouless transition temperature based on a simple free-energy argument. We relate the critical phase-space density at the transition to the ratio between the entropy gain and the corresponding cost in energy of creating a free vortex excitation in the system.     

Long-distance asymptotics of temperature correlators of the impenetrable Bose gas

The inverse scattering method is applied to the integrable nonlinear system describing temperature correlators of the impenetrable bosons in one space dimension. The corresponding matrix Riemann problems are constructed for two-point as well as for multi-point correlators. Long-distance asymptotics of two-point correlators is calculated.     

Critical temperature shift in weakly interacting Bose gas

With a high-performance Monte Carlo algorithm we study the interaction-induced shift of the critical point in weakly interacting three-dimensional /psi/(4) theory (which includes quantum Bose gas). In terms of critical density, n(c), mass, m, interaction, U, and temperature, T, this shift is universal: Deltan(c)(T) = -Cm(3)T(2)U, the constant C found to be equal to 0.0140+/-0.0005. For quantum Bose gas with the scattering length a this implies DeltaT(c)/T(c) = C(0)an(1/3), with C(0) = 1.29+/-0.05.     

Quantum phases of Bose gases on a lattice with pair-tunneling

We investigate the strongly interacting lattice Bose gases on a lattice with two-body interaction of nearest neighbors characterized by pair tunneling.The excitation spectrum and the depletion of the condensate of lattice Bose gases are investigated using the Bogoliubov transformation method and the results show that there is a pair condensate as well as a single particle condensate.The various possible quantum phases,such as the Mott-insulator phase(MI),the superfluid phase(SF) of an individual atom,the charge density wave phase(CDW),the supersolid phase(SS),the pair-superfluid(PSF) phase,and the pair-supersolid phase(PSS) are discussed in different parametric regions within our extended Bose-Hubbard model using perturbation theory.     

Condensed fraction of an atomic Bose gas induced by critical correlations

We study the condensed fraction of a harmonically trapped atomic Bose gas at the critical point predicted by mean-field theory. The nonzero condensed fraction f(0) is induced by critical correlations which increase the transition temperature T(c) above T(c) (MF). Unlike the T(c) shift in a trapped gas, f(0) is sensitive only to the critical behavior in the quasiuniform part of the cloud near the trap center. To leading order in the interaction parameter a/λ(0), where a is the s-wave scattering length and λ(0) the thermal wavelength, we expect a universal scaling f(0) proportionally (a/λ(0))(4). We experimentally verify this scaling using a Feshbach resonance to tune a/λ(0). Further, using the local density approximation, we compare our measurements with the universal result obtained from Monte Carlo simulations for a uniform system, and find excellent quantitative agreement.     

Critical temperature of a trapped Bose gas: comparison of theory and experiment

We apply the projected Gross-Pitaevskii equation (PGPE) formalism to the experimental problem of the shift in critical temperature Tc of a harmonically confined Bose gas as reported in Gerbier et al., Phys. Rev. Lett. 92, 030405 (2004). The PGPE method includes critical fluctuations and we find the results differ from various mean-field theories, and are in best agreement with experimental data. To unequivocally observe beyond mean-field effects, however, the experimental precision must either improve by an order of magnitude, or consider more strongly interacting systems. This is the first application of a classical field method to make quantitative comparison with experiment.     

Gauge theory on a random lattice

A general formulation of gauge theory on a random lattice is developed and the strong coupling limit of the Wilson string tension worked out. The confining force found in this strong coupling limit is identical to that predicted by the relativistic string model. In particular, the force between two color-triplet charges is a constant for large separation and the tube of electric flux joining the charges fluctuates, giving it a net thickness proportional to the logarithm of its length.