Experiments with Bose-Einstein condensates of dilute atomic gases require temperatures as low as hundreds of nanokelvins but obviously cannot be performed at zero absolute temperature. So the approximate theory of such a gas at nonzero temperatures is needed. In this topical review we describe a classical field approximation which satisfies this need. As modes of light, also modes of atomic field may be treated as classical waves, provided they contain sufficiently many quanta. We present a detailed description of the classical field approximation stressing the significant role of the observation process as the necessary interface between our calculations and measurements. We also discuss in detail the determination of temperature in our approach and stress its limitations. We also review several applications of the classical field approximation to dynamical processes involving atomic condensates. M This article features online multimedia enhancements

We theoretically consider the formation of bright solitons in a mixture of Bose and Fermi degenerate gases. While we assume the forces between atoms in a pure Bose component to be effectively repulsive, their character can be changed from repulsive to attractive in the presence of fermions provided the Bose and Fermi gases attract each other strongly enough. In such a regime the Bose component becomes a gas of effectively attractive atoms. Hence, generating bright solitons in the bosonic gas is possible. Indeed, after a sudden increase of the strength of attraction between bosons and fermions (realized by using a Feshbach resonance technique or by firm radial squeezing of both samples) soliton trains appear in the Bose-Fermi mixture.Solitonic solutions are a very general feature of nonlinear wave equations. Solitons have been studied in many different physical systems ranging from particle physics to optics. They differ from ordinary wave packets as they retain their shape while propagating instead of spreading due to dispersion. This intriguing feature is based on the existence of a nonlinear interaction which compensates for dispersion and produces a self-focusing effect on the propagating wave packet.Dilute atomic quantum gases offer a unique environment to study fundamental solitonic excitations in a pure quantum system with intrinsic nonlinearity. Since the interparticle interaction causing this nonlinearity can be both attractive and repulsive, the Gross-Pitaevskii equation describing the evolution of the condensate wave function exhibits both dark and bright solitonic solutions [1]. Dark solitons as a fundamental excitation in stable BoseEinstein condensates with repulsive interparticle interaction have been studied in different geometries [2,3,4].Bright solitons have been observed in Bose-Einstein condensates of 7 Li in quasi-one-dimensional geometry [5,6]. However, in three-dimensional geometry usually used to prepare the sample the necessary large and negative scattering length leads to density-limited particle numbers (dynamical instability -collapse). The observation of bright solitons was therefore only possible due to magnetic tuning of the interactions from repulsive (used to form a stable Bose-Einstein condensate) to attractive during the experiments.Another experimental approach to bright matter wave solitons was realized in the recently reported observation of gap solitons [7] in a condensate with repulsive interactions by engineering of the matter wave dispersion relation via sophisticated manipulation in a periodic potential (concept of negative effective mass [8]).In this Letter we propose a novel scheme to realize bright solitons in one-dimensional atomic quantum gases. In particular we study the formation of bright solitons in a Bose-Einstein condensate embedded in a quantum degenerate Fermi gas. One important feature is that this mixture allows tuning of the one-dimensional interactions not only by Feshbach resonances but also by simply changing the trap geometry.We consider the bare inte...

We theoretically consider a spin polarized, optically trapped condensate of 87Rb atoms in F=1. We observe a transfer of atoms to other Zeeman states due to the dipolar interaction which couples the spin and the orbital degrees of freedom. Therefore the transferred atoms acquire an orbital angular momentum. This is a realization of the Einstein-de Haas effect in systems of cold gases. We find resonances which make this phenomenon observable even in very weak dipolar systems, when the Zeeman energy difference on transfer is fully converted to rotational kinetic energy.

Eigenstates of Bose particles with repulsive contact interactions in one-dimensional space with periodic boundary conditions can be found with the help of the Bethe ansatz. The type~II excitation spectrum identified by E. H. Lieb, reproduces the dispersion relation of dark solitons in the mean-field approach. The corresponding eigenstates possess translational symmetry which can be broken in measurements of positions of particles. We analyze emergence of single and double solitons in the course of the measurements and investigate dynamics of the system. In the weak interaction limit, the system follows the mean-field prediction for a short period of time. Long time evolution reveals many-body effects that are related to an increasing uncertainty of soliton positions. In the strong interaction regime particles behave like impenetrable bosons. Then, the probability densities in the configuration space become identical to the probabilities of non-interacting fermions but the wave-functions themselves remember the original Bose statistics. Especially, the phase flips that are key signatures of the solitons in the weak interaction limit, can be observed in the time evolution of the strongly interacting bosons.Comment: 11 pages, 9 figure

A classical fields approximation to the finite temperature microcanonical thermodynamics of weakly interacting Bose gas is applied to the idealized case of atoms confined in a box with periodic boundary conditions. We analyze in some detail the microcanonical temperature in the model. We also analyze the spectral properties of classical amplitudes of the plane waves -the eigenmodes of the time averaged one-particle density matrix. Looking at the zero momentum component -the order parameter of the condensate, we obtain the nonperturbative results for the chemical potential. Analogous analysis of the other modes yields nonperturbative temperature dependent Bogoliubov frequencies and their damping rates. Damping rates are linear functions of momenta in the phonon range and show more complex behavior for the particle sector. Where available, we make comparison with the analytic estimates of these quantities.