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.     

Decoherence-driven cooling of a degenerate spinor Bose gas

We investigate the relationship between the coherence of a partially Bose-condensed spinor gas and its temperature. We observe cooling of the normal component driven by decoherence as well as the effect of temperature on decoherence rates.     

Bose-einstein condensation in a Bose gas under cooling conditions

The mechanism of condensation of a weakly nonideal Bose gas into a superfluid state (described in [1]) is analyzed by taking into account strong density fluctuations. The probability of occurrence of an optimal fluctuation leading to the formation of a superfluid phase is calculated. The relationship between the results of this study and the analysis presented in [1] is discussed.     

Condensate fraction in a 2D Bose gas measured across the Mott-insulator transition

We realize a single-band 2D Bose-Hubbard system with Rb atoms in an optical lattice and measure the condensate fraction as a function of lattice depth, crossing from the superfluid to the Mott-insulating phase. We quantitatively identify the location of the superfluid to normal transition by observing when the condensed fraction vanishes. Our measurement agrees with recent quantum Monte Carlo calculations for a finite-sized 2D system to within experimental uncertainty.     

Excitations in a Dipolar Bose–Einstein Condensate

We study excitations in a dipolar Bose–Einstein condensate with Green’s function. In Bogoliubov approximation, we obtain the dispersion relation. The excitation energy is dependent on the angle between the momentum and the magnetic moment. In the long-wave limit, the dispersion relation reduces to an anisotropic phonon-like dispersion relation.     

Stable and Unstable Vortex Knots in a Trapped Bose Condensate

The dynamics of a quantum vortex toric knot T_P,Q and other analogous knots in an atomic Bose condensate at zero temperature in the Thomas–Fermi regime is considered in the hydrodynamic approximation. The condensate has a spatially inhomogeneous equilibrium density profile ρ(z, r) due to the action of an external axisymmetric potential. It is assumed that z_*= 0, r_*= 1 is the point of maximum of function rρ(z, r), so that δ(rρ) ≈ –(α–)z²/2–(α + )(δr)²/2 for small z and δr. The geometrical configuration of a knot in the cylindrical coordinates is determined by a complex 2πP-periodic function A(?, t) = Z(?, t) + i[R(?, t))–1]. When |A| ? 1, the system can be described by relatively simple approximate equations for P rescaled functions \({W_n}(\varphi ) \propto A(2\pi n + \varphi ):i{W_{n,t}} = - ({W_{n,\varphi \varphi }} + \alpha {W_n} - \in W_n^*)/2 - \sum\nolimits_{j \ne n} {1/(W_n^* - W_j^*)} \). For = 0, examples of stable solutions of type W _n = θ _n (?–γt)exp(–iωt) with a nontrivial topology are found numerically for P = 3. In addition, the dynamics of various unsteady knots with P = 3 is modeled, and the tendency to the formation of a singularity over a finite time interval is observed in some cases. For P = 2 and small ≠ 0, configurations of type W₀–W₁ ≈ B₀exp(iζ) + C(B₀, α)exp(–iζ) + D(B₀, α)exp(3iζ), where B₀ > 0 is an arbitrary constant, ζ = k₀?–Ω₀t + ζ0, k₀ = Q/2, and Ω₀ = (–α)/2–2/B₀², which rotate about the z axis, are investigated. Wide stability regions for such solutions are detected in the space of parameters (α, B₀). In unstable zones, a vortex knot may return to a weakly excited state.     

The stability of a quantized vortex in a dilute Bose gas confined to a toroidal trap

We investigate the stability of a quantized vortex in a weakly interacting Bose gas, trapped in a toroidal container with hard walls. Calculating the excitation spectrum numerically and determining the stability condition by the Landau criterion, we examine the effect of reducing the confinement region of the condensate on the vortex stability. We find that tight confinement of the condensate increases the stabilization of the quantized vortex because an increase in the zero sound velocity due to tight confinement prevents the emergence of the elementary excitation which breaks superfluidity of the Bose system. We also discuss the experimental setup to observe such an effect.     

Condensate statistics in one-dimensional interacting Bose gases: exact results

Recently, a quantum Monte Carlo method alternative to the path integral Monte Carlo method was developed for solving the N-boson problem; it is based on the stochastic evolution of classical fields. Here we apply it to obtain exact results for the occupation statistics of the condensate mode in a weakly interacting trapped one-dimensional Bose gas. The temperature is varied across the critical region down to temperatures lower than the trap level spacing. We also derive the condensate statistics in the Bogoliubov theory: this reproduces the exact results at low temperature and explains the suppression of odd numbers of noncondensed particles at T approximately 0.     

Bose gas in gravitational field

The Bose gas in an arbitrary curved space-time is considered. A method of construction of the thermodynamic potential of a quantum gas by means of a finite-temperature Green's function is proposed. On this basis the Bose and Boltzmann distributions are derived. The behavior of the chemical potential is investigated. The phenomenon of Bose-Einstein condensation is discussed.     

Scaling behaviour in the Bose gas

The scaling behaviour of fluctuations of the Bose field (f) in the ergodic infinite volume equilibrium states of ad-dimensional Bose gas at temperatureT and density , can be classified in terms of the testfunctionsf. In the low density regime, the space of testfunctions splits up in two subspaces, leading to two different types of non-commuting macroscopic field fluctuation observables. Testfunctionsf with Fourier transform yield normal fluctuation observables. The local fluctuations of the field operators (f) must be scaled subnormally (i.e. with a negative scaling index) if the testfunctionf has . The macroscopic fluctuations of these fields can then again be described by a Bose field. The situation changes when the density of the gas exceeds the critical density. The field operators which have normal fluctuations in the low density regime need to be scaled abnormally in the high density regime, yielding classical macroscopic fluctuation observables. Another difference with the low density regime is that the space of testfunctions with splits up in two subspaces when the critical density is reached: for a first subspace the algebraic character of the macroscopic field fluctuation observables in also classical because it is necessary to scale the fluctuations of the field operators normally, while for the remaining subclass, the same negative scaling index is required as in the low density regime and hence also the algebraic character of these macroscopic fluctuations is again CCR.     

Scaling in the ideal Bose gas

We have made a detailed study of scaling in the ideal Bose gas in order to resolve the apparent inconsistencies that occur in the scaling laws when the dimensionality of the system is greater than four. We have found that there are not one, but two critical exponents associated with the specific heat singularity that appear in the scaling laws. We have proposed a modification of the scaling laws which is correct in any dimension.     

Equilibrium superradiance in a Bose gas

A model of free₄He atoms interacting with radiation exhibits an equilibrium phase transition in which the atomic ground-state Bose condensation is coupled to condensations of virtual photons and virtually excited atoms of the same macroscopic wavelength. The condensed phase has a twofold polarization degeneracy. It is suggested that this might furnish a mechanism for a discrete symmetry-related phase degeneracy of superfluid liquid⁴He required to explain the transition according to Tisza's generalized Gibbsian thermodynamics. A more realistic model would require inclusion of repulsive interactions.Supported in part by the National Science Foundation, Grant DMR76-17467.     

Tunneling of a Dipolar Bose–Einstein Condensate in an Optical Lattice

We have studied the tunneling and fluctuations of a dipolar Bose–Einstein condensate in an optical lattice, it is found that there exist the tunneling and fluctuations between lattices l and l+1, l and l−1, respectively. In particular, when the optical lattice is infinitely long and the spin excitations are in the long-wavelength limit, tunneling effects disappear between lattices l and l+1, and that l and l−1, in this case the fluctuations are a constant, and the magnetic soliton appears.     

On the instability of a homogeneous state of a weakly interacting Bose gas under external cooling

The behavior of a weakly interacting Bose gas with a finite particle lifetime has been studied in the framework of hydrodynamic equations under the conditions of a constant mass and energy inflow in the presence of external cooling. A spatially homogeneous state of such a gas is shown to be unstable with respect to the formation of an inhomogeneous density structure. A possible connection of the present results with experiments [3, 4] is discussed. Original Russian Text ? R.B. Saptsov, 2007, published in Pis’ma v Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2007, Vol. 86, No. 10, pp. 779–784.     

On the instability of a homogeneous state of a weakly interacting Bose gas under external cooling

The behavior of a weakly interacting Bose gas with a finite particle lifetime has been studied in the framework of hydrodynamic equations under the conditions of a constant mass and energy inflow in the presence of external cooling. A spatially homogeneous state of such a gas is shown to be unstable with respect to the formation of an inhomogeneous density structure. A possible connection of the present results with experiments [3, 4] is discussed.     

Anisotropic superfluidity in a dipolar Bose gas

We study the superfluid character of a dipolar Bose-Einstein condensate (DBEC) in a quasi-two dimensional geometry. We consider the dipole polarization to have some nonzero projection into the plane of the condensate so that the effective interaction is anisotropic in this plane, yielding an anisotropic dispersion relation. By performing direct numerical simulations of a probe moving through the DBEC, we observe the sudden onset of drag or creation of vortex-antivortex pairs at critical velocities that depend strongly on the direction of the probe's motion. This anisotropy emerges because of the anisotropic manifestation of a rotonlike mode in the system.