Using semiclassical approximation method, Bose-Einstein condensation (BEC) of a relativistic ideal boson gas (RIBG) with and without antibosons in three-dimensional (3-D) harmonic traps is investigated. The BEC transition temperature T_{c} and the Helmholtz free energy at T_{c} are calculated. The effect of the rest mass of the boson on the properties of the system is also studied. We find that T_{c} of RIBG is higher than that of the nonrelativistic approximation. The RIBG with antibosons is also investigated and it is found that the Helmholtz free energy of the system with antibosons at T_{c} is lower than that of the system without antibosons. It implies that the system with antibosons is more stable.
A Bose gas in an external potential is studied by means of the local density approximation. Analytical results are derived for the thermodynamic properties of an ideal Bose gas in a generic power-law trapping potential, and their dependence on the mutual interaction of atoms in the case of a non-ideal Bose gas.
We study the Bose-Einstein condensation for a 3-d system of ideal Bose gas which is harmonically trapped along two perpendicular directions and is confined in between two slabs along the other perpendicular direction. We calculate the Casimir force between the two slabs for this system of trapped Bose gas. At finite temperatures this force for thermalized photons in between two plates has a classical expression which is independent of $\hbar$. At finite temperatures the Casimir force for our system depends on $\hbar$. For the calculation of Casimir force we consider only the Dirichlet boundary…
A Bose gas in an external potential is studied by means of the semi-classical approximation. Analytical results are derived for the energy of an interacting Bose gas in a generic power-law trapping potential. An expression for the chemical potential below the critical temperature is also obtained. The theoretical results are in qualitative agreement with a recent energy measurement.
We investigate the collective oscillations of a Bose condensate in an anisotropic harmonic trap. We analytically calculate the values of the trap deformation for which the normal modes are in resonance. In presence of low-order resonances, the amplitude dependence of frequencies is strongly enhanced. We also study the transition to chaos of the collective modes as a function of the trap anisotropy.
In this paper we study the properties of Bose-Einstein condensates in shallow traps. We discuss the case of a Gaussian potential, but many of our results apply also to the traps having a small quadratic anharmonicity. We show the errors introduced when a Gaussian potential is approximated with a parabolic potential, these errors can be quite large for realistic optical trap parameter values. We study the behavior of the condensate fraction as a function of trap depth and temperature and calculate the chemical potential of the condensate in a Gaussian trap. Finally we calculate the frequencies …
Bose-Einstein condensation has been achieved in a magnetic surface micro trap with 4x10^5 87Rb atoms. The strongly anisotropic trapping potential is generated by a microstructure which consists of microfabricated linear copper conductors at a width ranging from 3 to 30 micrometer. After loading a high number of atoms from a pulsed thermal source directly into a magneto-optical trap (MOT) the magnetically stored atoms are transferred into the micro trap by adiabatic transformation of the trapping potential. The complete in vacuo trap design is compatible with ultrahigh vacuum below 2x10^(-11) m…
The theory of Bose-Einstein condensation in a two-dimensional(2D) harmonic trap is developed from 2D Gross-Pitaevskii equation. The 2D interaction strength is obtained from a 2D collision theory. We show the realization of 2D condensation of trapped Bose atoms directly by obtaining the stable solutions for the condensate wave function from the 2D Gross-Pitaevskii equation. We calculate the ground-state energy of the 2D system, and also the wave function of the 2D vortex state. In particular, the 2D energy state becomes less stable than the 3D case with the number of trapped atoms. The results …
We investigate the possibilities of distinguishing the mean-field and fluctuation effects on the critical temperature of a trapped Bose gas with repulsive interatomic interactions. Since in a direct measurement of the critical temperature as a function of the number of trapped atoms these effects are small compared to the ideal gas results, we propose to observe Bose-Einstein condensation by adiabatically ramping down the trapping frequency. Moreover, analyzing this adiabatic cooling scheme, we show that fluctuation effects can lead to the formation of a Bose condensate at frequencies which ar…
For spin one atoms localized in a quadrapole magnetic field gradient, the atoms may be impeded from spin flipping their way out from the center of the trap by the application of a rotating uniform magnetic field. From a quantum mechanical viewpoint, such a trap for a Bose condensate is equivalent to having a superfluid in a rotating bucket. Vorticity is then expected to be induced in the condensate fluid flow without the application of any further external perturbations.
The macroscopic quantum states of a condensed neutral Bose gas in one-dimensional power-law traps are obtained by solving the Gross-Pitaevskii equation numerically. A suitable candidate for a trial wave function for the variational calculation of ground state energy is suggested, and shown that the suggested function produces a lower ground state energy than the conventional Gaussian trial wave function.
Based on an analytic solution of the Gross-Pitaevskii equation in the large-condensate (Thomas-Fermi) limit we determine the structure of a stationary vortex in a Bose-Einstein condensate in a nonaxisymmetric rotating trap. The condensate velocity field has cylindrical symmetry only near the vortex core and becomes intrinsically anisotropic near the condensate boundaries. Rotating the anisotropic trap induces an additional irrotational velocity field even for a vortex-free condensate.
We present an analytical approximation for nonlinear dynamics of trapped Bose-co ndensed gases. The new approximation is a substantial improvement over the Thomas-Fermi approximation and is shown to be applicable for systems with a rather small number of atoms $N$. The calculated aspect ratios after ballistic expansion are found to be in good agreement with those observed in recent experiments.
We present a theoretical model to describe the dynamics of Bose-Einstein condensates in anharmonic trapping potentials. To first approximation the center-of-mass motion is separated from the internal condensate dynamics and the problem is reduced to the well known scaling solutions for the Thomas-Fermi radii. We discuss the validity of this approach and analyze the model for an anharmonic waveguide geometry which was recently realized in an experiment \cite{Ott2002c}.
The Bogoliubov approximation and the Gross-Pitaevskii equation characterize the effect of repulsive interactions on a dilute ideal Bose-Einstein gas in a spherical harmonic trap. For large $N$, the interactions expand the condensate relative to an ideal Bose gas; both the speed of sound and critical angular velocity $Ω_{c1}$ for creation of a quantized vortex depend crucially on the interparticle repulsion through the coherence length $ξ$.
In this letter, atom optic techniques are proposed to control the excitation of a Bose-Einstein condensate in an atomic trap. We show that by employing the dipole potential induced by four highly detuned travelling-wave laser beams with appropriate phases and frequencies, one can coherently excite a trapped Bose-Einstein condensate composed of ultracold alkali atoms into a state rotating around the trap center. The connection to vortex states is discussed.
We study the Bose-Einstein condensate in the MIT double-well trap. We calculate the ground state density profile of $^{23}$Na atoms and the Bogoliubov spectrum of the elementary excitations as function of the strength of the double-well barrier. In particular, we analyze the behavior of quantum-mechanical collective excitations. Finally, we discuss the observability criteria for macroscopic quantum tunneling and macroscopic quantum self-trapping.
We present a Hartree-Fock-Bogoliubov (HFB) theoretical treatment of the two-dimensional trapped Bose gas and indicate how semiclassical approximations to this and other formalisms have lead to confusion. We numerically obtain results for the fully quantum mechanical HFB theory within the Popov approximation and show that the presence of the trap stabilizes the condensate against long wavelength fluctuations. These results are used to show where phase fluctuations lead to the formation of a quasicondensate.
We question the validity of the grand canonical ensemble for the description of Bose-Einstein condensation of small ideal Bose gas samples in isolated harmonic traps. While the ground state fraction and the specific heat capacity can be well approximated with the help of the conventional grand canonical arguments, the calculation of the fluctuation of the number of particles contained in the condensate requires a microcanonical approach. Resorting to the theory of restricted partitions of integer numbers, we present analytical and numerical results for such fluctuations in one- and three-dimen…
We present a semiclassical two-fluid model for an interacting Bose gas confined in an anisotropic harmonic trap and solve it in the experimentally relevant region for a spin-polarized gas of Rb-87 atoms, obtaining the temperature dependence of the internal energy and of the condensate fraction. Our results are in agreement with recent experimental observations by Ensher et al.
We show that the dynamics of phonons in a set of trapped ions interacting with lasers is described by a Bose-Hubbard model whose parameters can be externally adjusted. We investigate the possibility of observing several quantum many-body phenomena, including (quasi) Bose-Einstein condensation as well as a superfluid-Mott insulator quantum phase transition.
Dilute Bose gas with attractive interactions is considered at zero temperature, when practically all atoms are in Bose-Einstein condensate. The problem is addressed aiming at answering the question: What is the optimal trap shape allowing for the condensation of the maximal number of atoms with negative scattering lengths? Simple and accurate analytical formulas are derived allowing for an easy analysis of the optimal trap shapes. These analytical formulas are the main result of the paper.
We describe the construction and operation of a time-orbiting potential trap (TOP trap) that has different oscillation frequencies along its three principal axes. These axes can be rotated and we have observed Bose-Einstein condensates of 87^Rb with a rotating ellipsoidal shape. Under these conditions it has been predicted that quantized vortices form and are stable.
Multistep Bose-Einstein condensation of an ideal Bose gas in anisotropic harmonic atom traps is studied. In the presence of strong anisotropy realized by the different trap frequency in each direction, finite size effect dictates a series of dimensional crossovers into lower-dimensional excitations. Two-step condensation and the dynamical reduction of the effective dimension can appear in three separate steps. When the multistep behavior occurs, the occupation number of atoms excited in each dimension is shown to behave similarly as a function of the temperature.
We report on the realisation of a stiff magnetic trap with independently adjustable trap frequencies, $ω_z$ and $ω_r$, in the axial and radial directions respectively. This has been achieved by applying an axial modulation to a Time-averaged Orbiting Potential (TOP) trap. The frequency ratio of the trap, $ω_z / ω_r$, can be decreased continuously from the original TOP trap value of 2.83 down to 1.6. We have transferred a Bose-Einstein condensate (BEC) into this trap and obtained very good agreement between its observed anisotropic expansion and the hydrodynamic predictions. Our method can be e…
We investigate some aspects of the Bose-Einstein condensation (BEC) of quantum gases in the presence of inhomogeneous conditions. We consider three-dimensional (3D) quantum gases trapped by an external potential when the temperature is sufficiently low to show a BEC phase region around the center of the trap. If the trap is sufficiently large, different phases may coexist in different space regions, when moving from the center of the trap. We show that the quantum gas develops a peculiar critical behavior at the boundary of the BEC region, whose scaling behavior is controlled by the universali…
We discuss the transition from a fully decoherent to a (quasi-)condensate regime in a harmonically trapped weakly interacting 1D Bose gas. By using analytic approaches and verifying them against exact numerical solutions, we find a characteristic crossover temperature and crossover atom number that depend on the interaction strength and the trap frequency. We then identify the conditions for observing either an interaction-induced crossover scenario or else a finite-size Bose-Einstein condensation phenomenon characteristic of an \textit{ideal} trapped 1D gas.
We study the Bose-Einstein condensation of an interacting gas with attractive interaction confined in a harmonic trap using a semiclassical two-fluid mean-field model. The condensed state is described by converged numerical solution of the Gross-Pitaevskii equation. By solving the system of coupled equations of this model iteratively we obtain converged results for the temperature dependencies of the condensate fraction, chemical potential, and internal energy for the Bose-Einstein condensate of $^7$Li atoms.
According to the adiabatic approximation atoms moving in a magnetic trap keep their magnetic states. We investigate the validity of this approximation for quantum condensates, where a change of field's direction generates effective interactions between hyperfine angular momentum states. Condensates in general traps are found to be stable because they are confined in the vicinity of the trap center. A decay of a condensate is observable in a trap with extremely large field gradient.
In this study, we consider motion of the massive and charged Bose gas trapped in electric and magnetic fields between two parallel plates in the $x-y$ plane that are separated by a distance $d$ in the $z$ direction. We derive analytical expression of the grand canonical potential of the quantum particles by using of Ketterle and van Druten approximation. By evaluating canonical potential, we obtain Casimir potential and force at the Bose-Einstein condensation temperature $T_{c}$. We also show that Casimir force oscillates depends on distance $d$ for fixed parameters.
We consider coupled atomic-molecular Bose-Einstein condensate system in a quasi-one-dimensional trap. In the vicinity of a Feshbach resonance the system can reveal soliton-like behavior. We analyze bright soliton solutions for the system in the trap and in the presence of the interactions between particles. We show that with increasing number of particles in the system two bright soliton solutions start resembling dark soliton profiles known in an atomic Bose-Einstein condensate with repulsive interactions between atoms. We analyze also methods for experimental preparation and detection of the…
The influence of the finite sizes on the coherent properties of 3D Bose systems is considered. As is shown, the correlation functions of a Bose gas in a trap have essential differences from analogous correlation functions in an infinite system. Thus, the anomalous correlation function vanishes due to the divergency of phase fluctuations which destruct the order parameter too. The normal correlation function decays exponentially in time for sufficiently large time interval.
The critical temperature and condensate fraction of a trapped interacting Bose gas are investigated when both atom-atom interaction and finite-size effects are taken into account. Canonical ensemble is used to obtain the equations on the condensate fraction for the trapped interacting Bose gas near and below the critical temperature. In our approaches corrections due to atom-atom interaction and finite-size effects are obtained simultaneously for the critical temperature and condensate fraction of the system. Analytical high-order correction to the condensate fraction is given in this work.
The study of low density, ultracold atomic Fermi gases is a promising avenue to understand fermion superfluidity from first principles. One technique currently used to bring Fermi gases in the degenerate regime is sympathetic cooling through a reservoir made of an ultracold Bose gas. We discuss a proposal for trapping and cooling of two-species Fermi-Bose mixtures into optical dipole traps made from combinations of laser beams having two different wavelengths. In these bichromatic traps it is possible, by a proper choice of the relative laser powers, to selectively trap the two species in such…
We discuss cooling efficiency for different-species Fermi-Bose mixtures in magnetic traps. A better heat capacity matching between the two atomic species is achieved by a proper choice of the Bose cooler and the magnetically trappable hyperfine states of the mixture. When a partial spatial overlap between the two species is also taken into account, the deepest Fermi degeneracy is obtained for an optimal value of the trapping frequency ratio. This can be achieved by assisting the magnetic trap with a deconfining light beam, as shown in the case of fermionic 6Li mixed with 23Na, 87Rb, and 133Cs,…
