Onset Of Bose-Einstein Condensation Research Articles

Critical exponents and fluctuations at BEC in a 2D harmonically trapped ideal gas

The critical properties displayed by an ideal 2D Bose gas trapped in a harmonic potential are determined and characterized in an exact numerical fashion. Beyond thermodynamics, addressed in terms of the global pressure and volume which are the appropriate variables of a fluid confined in a non-uniform harmonic potential, the density-density correlation function is also calculated and the corresponding correlation length is found. Evaluation of all these quantities as Bose–Einstein condensation (BEC) is approached manifest its critical continuous phase transition character. The divergence of the correlation length as the critical temperature is reached, unveils the expected spatial scale invariance proper of a critical transition. The logarithmic singularities of this transition are traced back to the non-analytic behavior of the thermodynamic variables at vanishing chemical potential, which is the onset of BEC. The critical exponents associated with the ideal BEC transition in the 2D inhomogeneous fluid reveals its own universality class.

Accurate analytic solution for ideal boson gases in a highly anisotropic two-dimensional harmonic trap

Motivated by quantum statistical mechanics, we propose an accurate analytical solution to the problem of Bose–Einstein condensation (BEC) of ideal bosons in a two-dimensional anisotropic harmonic trap. The study reveals that the number of noncondensed bosons is characterized by an analytical function, which relates to a series expansion of q-digamma functions in mathematics. The q-digamma function is a function of temperature, boson number, and anisotropic parameter. The analytical solution describes fully the experimental results of the BEC of ideal bosons in a two-dimensional anisotropic harmonic trap. We derive the analytical expressions of the critical temperature and the condensate fraction in the thermodynamic limit. The first main conclusion is that for a fixed temperature and boson number, there is a critical anisotropic parameter, which is the precise onset of BEC in this harmonically trapped two-dimensional system. The second main conclusion is that the critical temperature in a two-dimensional anisotropic harmonic trap is larger than that in a two-dimensional isotropic harmonic trap.

Simple method for producing Bose–Einstein condensates of metastable helium using a single-beam optical dipole trap

We demonstrate a simple scheme to reach Bose-Einstein condensation (BEC) of metastable triplet helium atoms using a single beam optical dipole trap with moderate power of less than 3 W. Our scheme is based on RF-induced evaporative cooling in a quadrupole magnetic trap and transfer to a single beam optical dipole trap that is located below the magnetic trap center. We transfer 1x10^6 atoms into the optical dipole trap, with an initial temperature of 14 \mu K, and observe efficient forced evaporative cooling both in a hybrid trap, in which the quadrupole magnetic trap operates just below the levitation gradient, and in the pure optical dipole trap, reaching the onset of BEC with 2x10^5 atoms and a pure BEC of 5x10^4 atoms. Our work shows that a single beam hybrid trap can be applied for a light atom, for which evaporative cooling in the quadrupole magnetic trap is strongly limited by Majorana spin-flips, and the very small levitation gradient limits the axial confinement in the hybrid trap.

Signatures of Bose-Einstein condensation in an optical lattice

We discuss typical experimental signatures for the Bose-Einstein condensation (BEC) of an ultracold Bose gas in an inhomogeneous optical lattice at finite temperature. Applying the Hartree-Fock-Bogoliubov-Popov formalism, we calculate quantities such as the momentum-space density distribution, visibility and peak width as the system is tuned through the superfluid to normal phase transition. Different from previous studies, we consider systems with fixed total particle number, which is of direct experimental relevance. We show that the onset of BEC is accompanied by sharp features in all these signatures, which can be probed via typical time-of-flight imaging techniques. In particular, we find a two-platform structure in the peak width across the phase transition. We show that the onset of condensation is related to the emergence of the higher platform, which can be used as an effective experimental signature.

Second-Order Time Correlations within a Polariton Bose-Einstein Condensate in a CdTe Microcavity

Second-order time correlations of polaritons have been measured across the condensation threshold in a CdTe microcavity. The onset of Bose-Einstein condensation is marked by the disappearance of photon bunching, demonstrating the transition from a thermal-like state to a coherent state. Coherence is, however, degraded with increasing polariton density, most probably as a result of self-interaction within the condensate and scatterings with noncondensed excitons and polaritons. Such behavior clearly differentiates polariton Bose condensation from photon lasing.

Thermodynamics of ideal quantum gas with fractional statistics inDdimensions

We present exact and explicit results for the thermodynamic properties (isochores, isotherms, isobars, response functions, velocity of sound) of a quantum gas in dimensions D > or = 1 and with fractional exclusion statistics 0 < or = g < or =1 connecting bosons (g=0) and fermions (g=1) . In D=1 the results are equivalent to those of the Calogero-Sutherland model. Emphasis is given to the crossover between bosonlike and fermionlike features, caused by aspects of the statistical interaction that mimic long-range attraction and short-range repulsion. A phase transition along the isobar occurs at a nonzero temperature in all dimensions. The T dependence of the velocity of sound is in simple relation to isochores and isobars. The effects of soft container walls are accounted for rigorously for the case of a pure power-law potential.

Sympathetic cooling and growth of a Bose-Einstein condensate

We study two sets of rate equations for sympathetic cooling of harmonically trapped Bose gases. Calculations for mixtures of Na-Rb and Li-Cs show that both sets yield similar results for the cooling times. The equilibration rates are in fair agreement with each other and differ considerably from classical rates. The onset of Bose-Einstein condensation is rather sudden and non-exponential in time, and the growth of the condensate differs for the two different mixtures we studied.

Bose-Einstein condensation of a finite number of particles confined to harmonic traps

The onset of Bose-Einstein condensation in a sample of N atoms confined to harmonic traps is critically examined. The monotonic growth of the condensate fraction f and the nonmonotic variation of the specific heat C of the sample are studied in fine detail. While no temperature is truly critical, our analysis does provide a strong theoretical basis for recognizing a temperature ${T}^{*},$ that has been identified and advocated by previous authors, as the transition temperature of the system. The specific-heat maximum ${T}_{m}$ (which happens to be another important ``marker'' in this transition), the value of the specific heat at ${T=T}_{m},$ and the ``jump'' in the specific heat of the system when the number N becomes very large are all explicitly evaluated. Wherever comparison is possible, our analytical results are found to be in perfect agreement with the ones obtained numerically by Kirsten and Toms [Phys. Rev. A 54, 4188 (1996)] and by Haugerud, Haugest, and Ravndal [Phys. Lett. A 225, 18 (1997)].

Canonical Bose-Einstein condensation of interacting bosons in two dimensions

The onset of Bose-Einstein condensation in a 2D gas of bosons in a parabolic confinement potential is investigated. For such a system of non-interacting bosons, both the grand-canonical and the canonical partition function are calculated. The canonical partition function of a system of harmonically interacting bosons in 2D is obtained analytically. Both in the case of interacting and of non-interacting bosons, a distinct peak in the specific heat is found at a critical temperature and the dependence of this critical temperature on the number of particles and on the interparticle interaction strength is investigated.

Collective Excitations of a Bose-Einstein Condensate in a Magnetic Trap.

Collective excitations of a dilute Bose condensate have been observed. These excitations are analogous to phonons in superfluid helium. Bose condensates were created by evaporatively cooling magnetically trapped sodium atoms. Excitations were induced by a modulation of the trapping potential, and detected as shape oscillations in the freely expanding condensates. The frequencies of the lowest modes agreed well with theoretical predictions based on mean-field theory. Before the onset of Bose-Einstein condensation, we observed sound waves in a dense ultracold gas.

Bose-Einstein condensation in an Einstein universe

Taking into account the possibility of particle-antiparticle pair production, the authors have investigated the onset of Bose-Einstein condensation in an ideal relativistic Bose gas confined to an Einstein universe. Through an extensive use of the Poisson summation formula, they have carried out an explicit evaluation of the summations-over-states appearing in the problem, to derive rigorously the condensate fraction, rho 0/ rho , and the specific heat at constant volume, crho , of the system as smooth functions of temperature-from T>or=Tc down to T=0K. A detailed asymptotic analysis of the growth of the condensate and of the specific-heat maximum is then carried out and, in each case, finite-size corrections to the standard bulk results are obtained in explicit terms. Special cases of the non-relativistic and extreme relativistic versions of the model are examined at some length and, wherever possible, a comparison is made with the findings of the previous authors.

Criteria for the onset of Bose-Einstein condensation in ideal systems confined to restricted geometries

Several authors have proposed criteria for the onset of Bose-Einstein condensation in finite systems. Using mathematical techniques developed by Pathria and collaborators (1972) these various proposals are systematically examined by applying them to an ideal Bose gas confined to a cuboidal enclosure under periodic boundary conditions. The 'transition points' thus obtained have been subjected to a comparative study, which indicates that the most useful general criterion is the macroscopic one based on the maximum of the specific heat Cv.

Evaluation of lattice sums using Poisson's summation formula. II

For pt.I see J. Math. Phys., vol.16, p.1457 of 1975. Application of Poisson's summation formula for the analytic evaluation of a class of lattice sums in arbitrary dimensions is extended to a more generalized class of sums. The resulting formulae are applicable to a variety of problems such as electronic-structure studies of crystalline solids, the onset of Bose-Einstein condensation in finite systems, the analysis of stability of quantized vortex arrays in extreme type-II superconductors and in rotating superfluid helium, plasma oscillations in an array of filamentary conductors, etc. They also provide an alternative approach for the determination of Madelung constants and other related sums that appear in the theory of cubic lattices.