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The investigation of the fluctuations in interacting quantum systems at finite temperatures showcases the ongoing challenges in understanding complex quantum systems. Recently, atom number fluctuations in weakly interacting Bose-Einstein condensates were observed, motivating an investigation of the thermal component of partially condensed Bose gases. Here, we present a combined analysis of both components, revealing the presence of fluctuations in the thermal component. This analysis includes a comprehensive statistical evaluation of uncertainties in the preparation and parameter estimation of partially condensed Bose gases. Using Monte Carlo simulations of optical density profiles, we estimate the noise contributions to the atom number and temperature estimation of the condensed and thermal cloud, which is generally applicable in the field of ultracold atoms. Furthermore, we investigate the specific noise contributions in the analysis of atom number fluctuations and show that preparation noise in the total atom number leads to an important technical noise contribution. Subtracting all known noise contributions from the variance of the atom number in the BEC and thermal component allows us to improve the estimate of the fundamental peak fluctuations.

We present a theoretical analysis of phase separations between two repulsively interacting components in an ultracold fermionic gas, occurring at the dimensional crossover in a harmonic trap with varying aspect ratios. A tailored kinetic energy functional is derived and combined with a density-potential functional approach to develop a framework that is benchmarked with the orbital-based method. We investigate the changes in the density profile of the phase-separated gas under different interaction strengths and geometries. The analysis reveals the existence of small, partially polarized domains in certain parameter regimes, which is similar to the purely two-dimensional limit. However, the density profile is further enriched by a shell structure found in anisotropic traps. We also track the transitions that can be driven by either a change in interaction strength or trap geometry. The developed framework is noted to have applications for other systems with repulsive interactions that combine continuous and discrete degrees of freedom., Comment: 15 pages, 5 figures

The fluctuations of the atom number between a Bose-Einstein condensate and the surrounding thermal gas have been the subject of a long standing theoretical debate. This discussion is centered around the appropriate thermodynamic ensemble to be used for theoretical predictions and the effect of interactions on the observed fluctuations. Here we introduce the so-called Fock state sampling method to solve this classic problem of current experimental interest for weakly interacting gases. A suppression of the predicted peak fluctuations is observed when using a microcanonical with respect to a canonical ensemble. Moreover, interactions lead to a shift of the temperature of peak fluctuations for harmonically trapped gases. The absolute size of the fluctuations furthermore depends on the total number of atoms and the aspect ratio of the trapping potential. Due to the interplay of these effect, there is no universal suppression or enhancement of fluctuations.

We analyze the dynamics of one-dimensional quantum gases with strongly attractive contact interactions. We specify a class of initial states for which attractive forces effectively act as strongly repulsive ones during the time evolution. Our findings extend the theoretical results on the super-Tonks-Girardeau gas to a highly nonequilibrium dynamics. The novel mechanism is illustrated on the prototypical problem of the domain stability in a two-component Fermi gas. We also discuss nonlocal interactions and analyze universality of the presented results. Moreover, we use our conclusions to argue for the existence of metastable quantum droplets in the regime of strongly attractive contact and attractive dipolar interactions., Comment: 6 pages + 6 pages SM

We predict the phase separations of two-dimensional Fermi gases with repulsive contact-type interactions between two spin components. Using density-potential functional theory with systematic semiclassical approximations, we address the long-standing problem of itinerant ferromagnetism in realistic settings. We reveal a universal transition from the paramagnetic state at small repulsive interactions towards ferromagnetic density profiles at large interaction strengths, with intricate particle-number dependent phases in between. Building on quantum Monte Carlo results for uniform systems, we benchmark our simulations against Hartree-Fock calculations for a small number of trapped fermions. We thereby demonstrate that our employed corrections to the mean-field interaction energy and especially to the Thomas-Fermi kinetic energy functional are necessary for reliably predicting properties of trapped mesoscopic Fermi gases. The density patterns of the ground state survive at low finite temperatures and confirm the Stoner-type polarization behavior across a universal interaction parameter, albeit with substantial quantitative differences that originate in the trapping potential and the quantum-corrected kinetic energy. We also uncover a zoo of metastable configurations that are energetically comparable to the ground-state density profiles and are thus likely to be observed in experiments. We argue that our density-functional approach can be easily applied to interacting multi-component Fermi gases in general., Comment: 23 pages, 8 figures

We analyze how the presence of the bound state on top of strong intercomponent contact repulsion affects the dynamics of a two-component ultracold Fermi gas confined in a one-dimensional harmonic trap. By performing full many-body numerical calculations, we retrieve dynamics of an initially phase separated state that has been utilized to excite the spin-dipole mode in experimental settings. We observe an appearance of pairing correlations at the domain wall, heralding the onset of a molecular faction at the interlayer between the components. We find that such a mechanism can be responsible for the stabilization of the phase separation., Comment: 6 pages + 10 pages SM

Strongly interacting many-body system of bosons exhibiting the quantum carpet pattern is investigated exactly by using Gaudin solutions. We show that this highly coherent design usually present in noninteracting, single-body scenarios gets destroyed by weak-to-moderate interatomic interactions in an ultracold bosonic gas trapped in a box potential. However, it becomes revived in a very strongly interacting regime, when the system undergoes fermionization. We track the whole single- to many-body crossover, providing an analysis of de- and rephasing present in the system., Comment: 12 pages, 5 figures

By analyzing breathing mode of a Bose-Einstein condensate repulsively interacting with a polarized fermionic cloud, we further the understanding of a Bose-Fermi mixture recently realized by Lous et al. [\textit{Phys. Rev. Lett.} \textbf{120}, 243403]. We show that a hydrodynamic description of a domain wall between bosonic and fermionic atoms reproduces experimental data of Huang et al. [\textit{Phys. Rev. A} \textbf{99}, 041602(R)]. Two different types of interaction renormalization are explored, based on lowest order constrained variational and perturbation techniques. In order to replicate nonmonotonic behavior of the oscillation frequency observed in the experiment, temperature effects have to be included. We find that the frequency down-shift is caused by the fermion-induced compression and rethermalization of the bosonic species as the system is quenched into the strongly interacting regime., Comment: 7 pages + Supplemental Materials

We directly compare the mean-field and the many-body approach in a one-dimensional Bose system in a harmonic trap. Both contact and dipolar interactions are considered. We propose a multi-atom version of the phase imprinting method to generate dark solitons in the system. We begin with a general analysis of system dynamics and observe the emergence of a dark soliton and a shock wave. Center of mass and soliton motion become decoupled because the shock wave oscillates with the trap frequency and soliton does not. A detailed investigation of frequencies reveals significant differences between results obtained in the mean-field and the many-body pictures., Comment: 6 pages, 3 figures, any comments welcome

A study of an interacting system of bosons in a ring trap at a finite temperature is presented. We consider a gas with contact and long-range dipolar interactions within a framework of the classical fields approximation. For a repulsive gas we have obtained coherence length, population of the ground state and its fluctuations as a function of temperature. In the case of an attractive gas we study local density fluctuations. Additionally, we exactly calculate the partition function for the ideal gas in the canonical ensemble and derive several other macroscopic state functions., Comment: 11 pages, 6 figures

We calculate frequencies of collective oscillations of two-component Fermi gas that is kept on the repulsive branch of its energy spectrum. Not only is a paramagnetic phase explored, but also a ferromagnetically separated one. Both in-, and out-of-phase perturbations are investigated, showing contributions from various gas excitations. Additionally, we compare results coming from both time-dependent Hartree-Fock and density-functional approaches., Comment: 16 pages, 4 figures, Resubmission to SciPost

We exploit a few- to many-body approach to study strongly interacting dipolar bosons in the quasi-one-dimensional system. The dipoles attract each other while the short range interactions are repulsive. Solving numerically the multi-atom Schr\"{o}dinger equation, we discover that such systems can exhibit not only the well known bright soliton solutions but also novel quantum droplets for a strongly coupled case. For larger systems, basing on microscopic properties of the found few-body solution, we propose a new equation for a density amplitude of atoms. It accounts for fermionization for strongly repelling bosons by incorporating the Lieb-Liniger energy in a local density approximation and approaches the standard Gross-Pitaevskii equation (GPE) in the weakly interacting limit. Not only does such a framework provide an alternative mechanism of the droplet stability, but it also introduces means to further analyze this previously unexplored quantum phase. In the limiting strong repulsion case, yet another simple multi-atom model is proposed. We stress that the celebrated Lee-Huang-Yang term in the GPE is not applicable in this case., Comment: 6+6 pages, 4+2 figures, comments welcome, version accepted in Physical Review Letters

We report a formation of sharp, solitonlike structures in an experimentally accessible ultracold Fermi gas, as a quantum carpet solution is analyzed in a many body system. The effect is perfectly coherent in a noninteracting gas, but in the presence of repulsive interaction in a two-component system, the structures vanish at a finite time. As they disappear, the system enters a dynamical equilibrium, in which kinetic energies of atoms tend to the same average value. The coherence is revived in a strong interaction regime, with the onset of phase separation, and with a double quantum carpet appearing., Comment: 12 pages, 8 figures

We study the lowest energy states for fixed total momentum, i.e. yrast states, of $N$ bosons moving on a ring. As in the paper of A. Syrwid and K. Sacha \cite{syrwid2015} , we compare mean field solitons with the yrast states, being the many-body Lieb-Liniger eigenstates. We show that even in the limit of vanishing interaction the yrast states possess features typical for solitons, like the phase jumps and the density notches. These properties are simply effects of the bosonic symmetrization and are encoded in the Dicke states hidden in the yrast states., Comment: 9 pages, 8 Figures, accepted to PRA

We solve numerically exactly the many-body 1D model of bosons interacting via short-range and dipolar forces and moving in the box with periodic boundary conditions. We show that the lowest energy states with fixed total momentum can be smoothly transformed from the typical states of collective character to states resembling single particle excitations. In particular, we identify the celebrated roton state. The smooth transition is realized by simultaneous tuning short-range interactions and adjusting a trap geometry. With our methods we study the weakly interacting regime as well as the regime beyond the range of validity of the Bogoliubov approximation., Comment: 7 pages, 4 figures

An absorption of a weak pulse by two identical atoms moving in a trap is investigated. Based on atom-light interactions we present a microscopic model of a two-body wave function diagnosis. We study the influence of pulse properties on the results. We show that a pulse duration impact a resulting one-photon and two-photons absorption probabilities significantly., Comment: 6 pages, 4 figure

We study a binary spin-mixture of a zero-temperature repulsively interacting $^6$Li atoms using both the atomic-orbital and the density functional approaches. The gas is initially prepared in a configuration of two magnetic domains and we determine the frequency of the spin-dipole oscillations which are emerging after the repulsive barrier, initially separating the domains, is removed. We find, in agreement with recent experiment (G. Valtolina et al., arXiv:1605.07850 (2016)), the occurrence of a ferromagnetic instability in an atomic gas while the interaction strength between different spin states is increased, after which the system becomes ferromagnetic. The ferromagnetic instability is preceded by the softening of the spin-dipole mode., Comment: 5 pages, 2 figures

We study energy levels of two heteronuclear molecules moving in a spherically symmetric harmonic trap. A role of electric dipole interactions is compared and contrasted with our earlier results (https://arxiv.org/abs/1512.00631) for two magnetic dipolar atoms. We stress importance of a rotational energy with its value which is very high compared to the energy of dipolar interaction. We show that dipolar forces do not play a significant role in the ground state of the system under typical experimental conditions. However, there exist excited states that exhibit anticrossings similar to the ones observed for magnetic dipoles., Comment: 6 pages, 3 figures

We numerically analyze the impact of a single Rydberg electron onto a Bose-Einstein condensate. Both $S-$ and $D-$ Rydberg states are studied. The radial size of $S-$ and $D-$states are comparable, hence the only difference is due to the angular dependence of the wavefunctions. We find the atom losses in the condensate after the excitation of a sequence of Rydberg atoms. Additionally, we investigate the mechanical effect in which the Rydberg atoms force the condensate to oscillate. Our numerical analysis is based on the classical fields approximation. Finally, we compare numerical results to experimental data., Comment: 6 pages, 4 figures, 4 tables

We study, within a framework of the classical fields approximation, the static structure factor of a weakly interacting Bose gas at thermal equilibrium. As in a recent experiment (R. Schley et al., Phys. Rev. Lett. 111, 055301 (2013)), we find that the thermal distribution of phonons in a three-dimensional Bose gas follows the Planck distribution. On the other hand we find a disagreement between the Planck and phonon (calculated just like for the bulk gas) distributions in the case of elongated quasi-one-dimensional systems. We attribute this discrepancy to the existence of spontaneous dark solitons (i.e., thermal solitons as reported in T. Karpiuk et al., Phys. Rev. Lett. 109, 205302 (2012)) in an elongated Bose gas at thermal equilibrium., Comment: 5 pages, 4 figures

We present a numerical study of the behaviour of two magnetic dipolar atoms trapped in a harmonic potential and exhibiting the standard Einstein-de Haas effect while subject to a time dependent homogeneous magnetic field. Using a simplified description of the short range interaction and the full expression for the dipole-dipole forces we show, that under experimentally realisable conditions two dysprosium atoms may be pumped to a high ($l>20$) value of the relative orbital angular momentum., Comment: 6 pages, 4 figures

Dynamical properties of a few ultra-cold fermions confined in a double-well potential is studied. We show that the dynamics, which is governed by single-particle tunnelings for vanishing interactions, is completely different for strong interactions. Depending on the details of the configuration, for sufficiently strong interactions (repulsions or attractions) the particle flow through the barrier can be accelerated or slowed down. This effect cannot be explained with the single-particle picture. It is clarified with direct inspection to the spectrum of the few-body Hamiltonian., Comment: Authors' version accepted in EPL

Two identical dipolar atoms moving in a harmonic trap without an external magnetic field are investigated. Using the algebra of angular momentum a semi - analytical solutions are found. We show that the internal spin - spin interactions between the atoms couple to the orbital angular momentum causing an analogue of Einstein - de Haas effect. We show a possibility of adiabatically pumping our system from the s-wave to the d-wave relative motion. The effective spin-orbit coupling occurs at anti-crossings of the energy levels., Comment: 8 pages, 2 figures, submitted to Physical Review A

We numerically generate, and then study the basic properties of dark soliton-like excitations in a dipolar gas confined in a quasi one dimensional trap. These excitations, although very similar to dark solitons in a gas with contact interaction, interact with each other and can form bound states. During collisions these dipolar solitons emit phonons, loosing energy, but accelerating. Even after thousands of subsequent collisions they survive as gray solitons and finally reach dynamical equilibrium with background quasiparticles. Finally, in the frame of classical field approximation, we verified, that these solitons appear spontaneously in thermal samples, analogously to the type II excitations in a gas of atoms with contact interaction., Comment: 9 pages, 12 figures

In this work we present a very simple and efficient numerical scheme which can be applied to study the dynamics of bosonic systems like, for instance, spinor Bose-Einstein condensates with nonlocal interactions but equally well works for Fermi gases. The method we use is a modification of well known Split Operator Method (SOM). We carefully examine this algorithm in the case of $F=1$ spinor Bose-Einstein condensate without and with dipolar interactions and for strongly interacting two-component Fermi gas. Our extension of the SOM method has many advantages: it is fast, stable, and keeps constant all the physical constraints (constants of motion) at high level., Comment: 21 pages, 7 figures

We study a strongly attractive system of a few spin-1/2 fermions confined in a one-dimensional harmonic trap, interacting via two-body contact potential. Performing exact diagonalization of the Hamiltonian we analyze the ground state and the thermal state of the system in terms of one-- and two--particle reduced density matrices. We show how for strong attraction the correlated pairs emerge in the system. We find that the fraction of correlated pairs depends on temperature and we show that this dependence has universal properties analogous to the gap function known from the theory of superconductivity. In contrast to the standard approach based on the variational ansatz and/or perturbation theory, our predictions are exact and are valid also in a strong attraction limit. Our findings contribute to the understanding of strongly correlated few-body systems and can be verified in current experiments on ultra-cold atoms., Comment: 6 figures

The quantum mechanical states of electrons in atoms and molecules are distinct orbitals, which are fundamental for our understanding of atoms, molecules and solids. Electronic orbitals determine a wide range of basic atomic properties, allowing also for the explanation of many chemical processes. Here, we propose a novel technique to optically image the shape of electron orbitals of neutral atoms using electron-phonon coupling in a Bose-Einstein condensate. To validate our model we carefully analyze the impact of a single Rydberg electron onto a condensate and compare the results to experimental data. Our scheme requires only well-established experimental techniques that are readily available and allows for the direct capture of textbook-like spatial images of single electronic orbitals in a single shot experiment., Comment: New J. Phys., accepted

We analyze a process of splitting of the Bose-Einstein condensate and the mutual coherence of two separated atomic clouds. Within the classical fields approximation we show that coherence between clouds is degraded if atoms interact and if we account for the sufficiently long observation time. We also show, that upon recombination, the coherence across the sample is restored. The coherence is not fully degraded if the splitting potential remains sufficiently penetrable. We calculate the variance of atom number difference for this time-averaging measurement and show that for low temperatures it can be well below Poissonian limit like it was observed in the experiments.

Interacting two component Fermi gases are at the heart of our understanding of macroscopic quantum phenomena like superconductivity. Changing nature of the interaction is expected to head to novel quantum phases. Here we study the ground state of a two component fermionic gas in a harmonic potential with dipolar and contact interactions. Using a variational Wigner function we present the phase diagram of the system with equal but opposite values of the magnetic moment. We identify the second order phase transition from paramagnetic to ferronematic phase. Moreover, we show the impact of the experimentally relevant magnetic field on the stability and the magnetization of the system. We also investigate a two component Fermi gas with large but almost equal values of the magnetic moment to study how the interplay between contact and dipolar interactions affects the stability properties of the mixture. To be specific we discuss experimentally relevant parameters for ultracold $^{161}$Dy.

We study a quasi two dimensional dipolar gas at finite, but ultralow temperatures using the classical field approximation. The method, already used for a contact interacting gas, is extended here to samples with a weakly interacting long-range inter-atomic potential. We present statistical properties of the system for the current experiment with Chromium [Phys. Rev. A 84 053601 (2011)] and compare them with statistics for atoms with larger magnetic dipole moments. Significant enhancement of the third order correlation function, relevant for the particle losses, is found.

We study in detail the effect of quasicondensation. We show that this effect is strictly related to dimensionality of the system. It is present in one dimensional systems independently of interactions - exists in repulsive, attractive or in non-interacting Bose gas in some range of temperatures below characteristic temperature of the quantum degeneracy. Based on this observation we analyze the quasicondensation in terms of a ratio of the two largest eigenvalues of the single particle density matrix for the ideal gas. We show that in the thermodynamic limit in higher dimensions the second largest eigenvalue vanishes (as compared to the first one) with total number of particles as $\simeq N^{-\gamma}$ whereas goes to zero only logarithmically in one dimension. We also study the effect of quasicondensation for various geometries of the system: from quasi-1D elongated one, through spherically symmetric 3D case to quasi-2D pancake-like geometry.

We investigate the ground state properties of a polarized dipolar Bose-Einstein condensate trapped in a triple-well potential. By solving the dipolar Gross-Pitaevskii equation numerically for different geometries we identify states which reveal the non-local character of the interaction. Depending on the strength of the contact and dipolar interaction we depict the stable and unstable regions in parameter space., Comment: 13 pages, 5 figures

Using classical field approximation we present the first study of statistical properties of one dimensional Bose gas with attractive interaction. The canonical probability distribution is generated with the help of a Monte Carlo method. This way we obtain not only the depletion of the condensate with growing temperature but also its fluctuations. The most important is our discovery of a reduced coherence length, the phenomenon observed earlier only for the repulsive gas, known as quasicondensation., Comment: 4 pages, 4 figures

We study the dynamics of ultracold attractive atoms in a weakly linked two potential wells. We consider an unbalanced initial state and monitor dynamics of the population difference between the two wells. The average imbalance between wells undergoes damped oscillations, like in a classical counterpart, but then it revives almost to the initial value. We explain in details the whole behavior using three different models of the system. Furthermore we investigate the sensitivity of the revivals on the decoherence caused by one- and three-body losses. We include the dissipative processes using appropriate master equations and solve them using the stochastic wave approximation method.

Monte Carlo method within, so called, classical fields approximation is applied to one dimensional weakly interacting repulsive Bose gas trapped in a harmonic potential. Equilibrium statistical properties of the condensate are calculated within a canonical ensemble. We also calculate experimentally relevant low order correlation functions of the whole gas.

We study dynamics of two interacting ultra cold Bose atoms in a harmonic oscillator potential in one spatial dimension. Making use of the exact solution of the eigenvalue problem of a particle in the delta-like potential we study time evolution of initially separable state of two particles. The corresponding time dependent single particle density matrix is obtained and diagonalized and single particle orbitals are found. This allows to study decoherence as well as creation of entanglement during the dynamics. The evolution of the orbital corresponding to the largest eigenvalue is then compared to the evolution according to the Gross-Pitaevskii equation. We show that if initially the center of mass and relative degrees of freedom are entangled then the Gross-Pitaevskii equation fails to reproduce the exact dynamics and entanglement is produced dynamically. We stress that predictions of our study can be verified experimentally in an optical lattice in the low-tunneling limit., Comment: 9 figures, 5 movies available on-line

We optimize the classical field approximation of the version described in J. Phys. B 40, R1 (2007) for the oscillations of a Bose gas trapped in a harmonic potential at nonzero temperatures, as experimentally investigated by Jin et al. [Phys. Rev. Lett. 78, 764 (1997)]. Similarly to experiment, the system response to external perturbations strongly depends on the initial temperature and on the symmetry of perturbation. While for lower temperatures the thermal cloud follows the condensed part, for higher temperatures the thermal atoms oscillate rather with their natural frequency, whereas the condensate exhibits a frequency shift toward the thermal cloud frequency (m=0 mode), or in the opposite direction (m=2 mode). In the latter case, for temperatures approaching critical, we find that the condensate begins to oscillate with the frequency of the thermal atoms, as in the m=0 mode. A broad range of frequencies of the perturbing potential is considered., Comment: 10 pages, 9 figures, added references, changed content, improved English

All experiments with ultracold atoms are performed in the presence of background residual gas. With the help of a suitable master equation we investigate a role of these fast atoms on the loss of coherence in optical lattices. We present an exact solution of the master equation and give the analytic formulas for all correlation functions in the presence of one body losses. Additionally we discuss existing of a Schr\"odinger cat state predicted in this system in [1]., Comment: 5 figures

Classical fields counterpart of the ideal Bose gas statistics in a trap is investigated by performing calculations in the canonical ensemble. There exists the optimal cut-off which allows to match the full probability distribution of the condensate population by its classical counterpart. Universal scaling of that cut-off with temperature and dimensionality is derived., Comment: 4 pages, 5 figures

We consider a spinor condensate of $^{87}$Rb atoms in F=1 hyperfine state confined in an optical dipole trap. Putting initially all atoms in $m_F=0$ component we find that the system evolves towards a state of thermal equilibrium with kinetic energy equally distributed among all magnetic components. We show that this process is dominated by the dipolar interaction of magnetic spins rather than spin mixing contact potential. Our results show that because of a dynamical separation of magnetic components the spin mixing dynamics in $^{87}$Rb condensate is governed by dipolar interaction which plays no role in a single component rubidium system in a magnetic trap.

We study the instability of multiply charged vortices in the presence of thermal atoms and find various scenarios of splitting of such vortices. The onset of the decay of a vortex is always preceded by the increase of a number of thermal (uncondensed) atoms in the system and manifests itself by the sudden rise of the amplitude of the oscillations of the quadrupole moment. Our calculations show that the decay time gets shorter when the multiplicity of a vortex becomes higher., Comment: 4 pages, 6 figures

We consider a spinor condensate of 87Rb atoms in its F=1 hyperfine state at finite temperatures. Putting initially all atoms in m_F=0 component we find that the system evolves into the state of thermal equilibrium. This state is approached in a step-like process and when established it manifests itself in distinguishable ways. The atoms in states m_F=+1 and m_F=-1 start to rotate in opposite directions breaking the chiral symmetry and showing highly regular spin textures. Also the coherence properties of the system changes dramatically. Depending on the strength of spin-changing collisions the system first enters the stage where the m_F=+1 and m_F=-1 spinor condensate components periodically loose and recover their mutual coherence whereas their thermal counterparts get completely dephased. For stronger spin changing collisions the system enters the regime where also the strong coherence between other components is built up., Comment: 5 pages, 4 figures

We consider the formation of bright solitons in a mixture of Bose and Fermi degenerate gases confined in a three-dimensional elongated harmonic trap. The Bose and Fermi atoms are assumed to effectively attract each other whereas bosonic atoms repel each other. Strong enough attraction between bosonic and fermionic components can change the character of the interaction within the bosonic cloud from repulsive to attractive making thus possible the generation of bright solitons in the mixture. On the other hand, such structures might be in danger due to the collapse phenomenon existing in attractive gases. We show, however, that under some conditions (defined by the strength of the Bose-Fermi components attraction) the structures which neither spread nor collapse can be generated. For elongated enough traps the formation of solitons is possible even at the ``natural'' value of the mutual Bose-Fermi ($^{87}$Rb -$^{40}$K in our case) scattering length., Comment: 6 pages, 6 figures, 1 table

We use the classical fields approximation to study a translational flow of the condensate with respect to the thermal cloud in a weakly interacting Bose gas. We study both, subcritical and supercritical relative velocity cases and analyze in detail a state of stationary flow which is reached in the dynamics. This state corresponds to the thermal equilibrium, which is characterized by the relative velocity of the condensate and the thermal cloud. The superfluidity manifests itself in the existence of many thermal equilibria varying in (the value of this velocity) the relative velocity between the condensate and the thermal cloud. We pay a particular attention to excitation spectra in a phonon as well as in a particle regime. Finally, we introduce a measure of the amount of the superfluid fraction in a weakly interacting Bose gas, allowing for the precise distinction between the superfluid and the condensed fractions in a single and consistent framework., Comment: 8 pages, 5 figures

We investigate the experiment of collapses and revivals of matter wave field in more detail. To this end we calculate the lowest-order correlation functions of the Bose field. We compare predictions of the total Fock state with the commonly used coherent state approximation. We also show how to observe an interference pattern for the celebrated Mott state.

Classical fields approximation to cold weakly interacting bosons allows for a unified treatment of condensed and uncondensed parts of the system. Until now, however, the quantitative predictions were limited by a dependence of the results on a grid chosen for numerical implementation of the method. In this paper we propose replacing this unphysical ambiguity by an additional postulate: the temperature of the gas at thermal equilibrium should be the same as that of an ideal Bose gas with the same fraction of condensed atoms. As it turns-out, with this additional assumption, nearly all atoms are within the classical fields, thus the method applies to the whole system.

While investigating quantum correlations in atomic systems, we note that single measurements contain information about these correlations. Using a simple model of measurement -- analogous to the one used in quantum optics -- we show how to extract higher order correlation functions from individual "phtotographs" of the atomic sample. As a possible application we apply the method to detect a subtle phase coherence in mesoscopic superpostitions., Comment: 4 pages, 2 figures, provisionally accepted to Physical Review Letters

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., Comment: 9 pages, 12 figures

We analyze the ground state of the two--component gas of trapped ultracold fermionic atoms. We neglect the forces between atoms in the same hyperfine state (the same component). For the case when the forces between distinguishable atoms (i.e., atoms in different hyperfine states) are repulsive (positive mutual scattering length), we find the existence of critical interaction strength above which one atomic fraction expels the other from the center of the trap. When atoms from different components attract each other (negative mutual scattering length) the ground state of the system dramatically changes its structure for strong enough attraction -- the Cooper pairs built of atoms in different hyperfine states appear., Comment: 10 pages, 14 figures

We show that the phase imprinting method is capable of generating vortices in a one-component gas of neutral fermionic atoms at zero and finite temperatures. We find qualitative differences in dynamics of vortices in comparision with the case of Bose-Einstein condensate. The results of the imprinting strongly depend on the geometry of the trap, e.g., in asymmetric traps no single vortex state exists. The observations could be considered as a signature of Cooper-pair based superfluidity in a Fermi gas., Comment: 4 pages, 4 figures