arXiv subjects

H. T. C. Stoof

Publications and source records attributed to H. T. C. Stoof.

At least 163 records · Page 9Linked to original sources

arXiv1998

Growth and Collapse of a Bose Condensate with Attractive Interactions

We consider the dynamics of a quantum degenerate trapped gas of Li-7 atoms. Because the atoms have a negative s-wave scattering length, a Bose condensate of Li-7 becomes mechanically unstable when the number of condensate atoms approaches a maximum value. We calculate the dynamics of the collapse that occurs when the unstable point is reached. In addition, we use the quantum Boltzmann equation to investigate the nonequilibrium kinetics of the atomic distribution during and after evaporative cooling. The condensate is found to undergo many cycles of growth and collapse before a stationary state is reached.

cond-mat.stat-mech↗

arXiv1997

Elastic and inelastic collisions of 6Li in magnetic and optical traps

We use a full coupled channels method to calculate collisional properties of magnetically or optically trapped ultracold 6Li. The magnetic field dependence of the s-wave scattering lengths of several mixtures of hyperfine states are determined, as are the decay rates due to exchange collisions. In one case, we find Feshbach resonances at B=0.08 T and B=1.98 T. We show that the exact coupled channels calculation is well approximated over the entire range of magnetic fields by a simple analytical calculation.

cond-mat.stat-mech↗

arXiv1997

The Superfluid State of Atomic Li6 in a Magnetic Trap

We report on a study of the superfluid state of spin-polarized atomic Li6 confined in a magnetic trap. Density profiles of this degenerate Fermi gas, and the spatial distribution of the BCS order parameter are calculated in the local density approximation. The critical temperature is determined as a function of the number of particles in the trap. Furthermore we consider the mechanical stability of an interacting two-component Fermi gas, both in the case of attractive and repulsive interatomic interactions. For spin-polarized Li6 we also calculate the decay rate of the gas, and show that within the mechanically stable regime of phase space, the lifetime is long enough to perform experiments on the gas below and above the critical temperature if a bias magnetic field of about 5 T is applied. Moreover, we propose that a measurement of the decay rate of the system might signal the presence of the superfluid state.

cond-mat.supr-con↗

arXiv1997

Collective Modes in Supersolid 4He

We derive the hydrodynamic equations of motion of solid and supersolid 4He, that describe the collective modes of these phases. In particular, the usual hydrodynamics is modified in such a way that it leads to the presence of a propagating instead of a diffusive defect mode. The former is appropriate for a quantum crystal and observed in recent experiments. Furthermore, we find that in supersolid helium there are two additional modes associated with the superfluid degrees of freedom. The observation of these additional modes is a clear experimental signature of the supersolid phase.

cond-mat↗

arXiv1997

Microscopic Treatment of Binary Interactions in the Non-Equilibrium Dynamics of Partially Bose-condensed Trapped Gases

In this paper we use microscopic arguments to derive a nonlinear Schrödinger equation for trapped Bose-condensed gases. This is made possible by considering the equations of motion of various anomalous averages. The resulting equation explicitly includes the effect of repeated binary interactions (in particular ladders) between the atoms. Moreover, under the conditions that dressing of the intermediate states of a collision can be ignored, this equation is shown to reduce to the conventional Gross-Pitaevskii equation in the pseudopotential limit. Extending the treatment, we show first how the occupation of excited (bare particle) states affects the collisions, and thus obtain the many-body T-matrix approximation in a trap. In addition, we discuss how the bare particle many-body T-matrix gets dressed by mean fields due to condensed and excited atoms. We conclude that the most commonly used version of the Gross-Pitaevskii equation can only be put on a microscopic basis for a restrictive range of conditions. For partial condensation, we need to take account of interactions between condensed and excited atoms, which, in a consistent formulation, should also be expressed in terms of the many-body T-matrix. This can be achieved by considering fluctuations around the condensate mean field beyond those included in the conventional finite temperature mean field, i.e. Hartree-Fock-Bogoliubov (HFB), theory.

cond-mat.stat-mech↗

arXiv1997

Collective Excitations, NMR, and Phase Transitions in Skyrme Crystals

At Landau level filling factors near nu =1, quantum Hall ferromagnets form a Skyrme crystal state with quasi-long-range translational and non-collinear magnetic order. We develop an effective low energy theory which explains the presence in these systems of magnetic excitations at low energies below the Larmor gap (Delta) and which predicts a dramatic enhancement of the nuclear spin relaxation rate by a factor of 1000. The effective theory predicts a rich set of quantum and classical phase transitions. Based in part on accurate time-dependent Hartree-Fock calculations of the ordered state collective excitation spectrum, we discuss aspects of the T-nu-Delta crystal phase diagram.

cond-mat.mes-hall↗

arXiv1996

Critical Temperature of a Trapped Bose Gas: Mean-Field Theory and Fluctuations

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 are much larger than those predicted by the mean-field theory.

cond-mat.stat-mech↗

arXiv1996

Initial Stages of Bose-Einstein Condensation

We present the quantum theory for the nucleation of Bose-Einstein condensation in a dilute atomic Bose gas. This quantum theory comfirms the results of the semiclassical treatment, but has the important advantage that both the kinetic and coherent stages of the nucleation process can now be described in a unified way by a single Fokker-Planck equation.

cond-mat↗

arXiv1996

Renormalization Group Theory of the Three-Dimensional Dilute Bose Gas

We study the three-dimensional atomic Bose gas using renormalization group techniques. Using our knowledge of the microscopic details of the interatomic interaction, we determine the correct initial values of our renormalization group equations and thus obtain also information on nonuniversal properties. As a result, we can predict for instance the critical temperature of the gas and the superfluid and condensate density of the Bose-Einstein condensed phase in the regime $naΛ_{th}^2\ll 1$.

cond-mat↗

arXiv1996

Stability of Bose condensed atomic Li-7

We study the stability of a Bose condensate of atomic $^7$Li in a (harmonic oscillator) magnetic trap at non-zero temperatures. In analogy to the stability criterion for a neutron star, we conjecture that the gas becomes unstable if the free energy as a function of the central density of the cloud has a local extremum which conserves the number of particles. Moreover, we show that the number of condensate particles at the point of instability decreases with increasing temperature, and that for the temperature interval considered, the normal part of the gas is stable against density fluctuations at this point.

cond-mat↗

arXiv1996

Effect of Interactions on the Critical Temperature of a Dilute Bose gas

Due to the observation of Bose-Einstein condensation in dilute atomic $^{87}$Rb and $^{23}$Na vapors last year, there is currently a great interest in the properties of a degenerate Bose gas. One aspect that is not yet understood is the effect of the interatomic interactions on the critical temperature of the phase transition. We present here a renormalization group study of the weakly-interacting Bose gas and predict the critical temperature at which Bose-Einstein condensation occurs as a function of the (positive) scattering length $a$ of the interatomic potential.

cond-mat↗

arXiv1996

Theory of Interacting Quantum Gases

We present a unified picture of the interaction effects in dilute atomic quantum gases. We consider fermionic as well as bosonic gases and, in particular, discuss for both forms of statistics the fundamental differences between a gas with effectively repulsive and a gas with effectively attractive interatomic interactions, i.e.\ between a gas with either a positive or a negative scattering length.

cond-mat↗

arXiv1996

Macroscopic Quantum Tunneling of a Bose Condensate

We study, by means of a variational method, the stability of a condensate in a magnetically trapped atomic Bose gas with a negative scattering length and find that the condensate is unstable in general. However, for temperatures sufficiently close to the critical temperature the condensate turns out to be metastable. For that case we determine in the usual WKB approximation the decay rate of the condensate due to macroscopic quantum fluctuations. When appropriate, we also calculate the decay rate due to thermal fluctuations. An important feature of our approach is that (nonsingular) phase fluctuations of the condensate are taken into account exactly.

cond-mat↗

arXiv1995

Hydrodynamics of Spatially Ordered Superfluids

We derive the hydrodynamic equations for the supersolid and superhexatic phases of a neutral two-dimensional Bose fluid. We find, assuming that the normal part of the fluid is clamped to an underlying substrate, that both phases can sustain third-sound modes and that in the supersolid phase there are additional modes due to the superfluid motion of point defects (vacancies and interstitials).

cond-mat↗

arXiv1995

Superfluidity of spin-polarized 6Li

We study the prospects for observing superfluidity in a spin-polarized atomic gas of $^6$Li atoms, using state-of-the-art interatomic potentials. We determine the spinodal line and show that a BCS transition to the superfluid state can indeed occur in the (meta)stable region of the phase diagram if the densities are sufficiently low. Moreover, for a total density of $10^{12}~cm^{-3}$, which still fulfills this requirement, we find a critical temperature of only $29~nK$. We also discuss the stability of the gas due to exchange and dipolar relaxation and conclude that the prospects for observing superfluidity in a magnetically trapped atomic $^6$Li gas are particularly promising for magnetic bias fields larger than $10~T$.

cond-mat↗

arXiv1995

Variational Approach to the Dilute Bose Gas

We study the weakly-interacting Bose gas in both two and three dimensions using a variational approach. In particular we construct the thermodynamic potential of the gas to within ladder approximation and find by minimization an accurate mean-field description of the dilute Bose gas. Using spin-polarized atomic hydrogen as a specific example, we obtain an improved description of the Bose-Einstein condensed phase in three dimensions and a signature of a phase transition in two dimensions. The latter cannot be found by straightforward application of perturbation theory around the ideal Bose gas.

cond-mat↗

arXiv1994

Condensate Formation in a Bose Gas

Using magnetically trapped atomic hydrogen as an example, we investigate the prospects of achieving Bose-Einstein condensation in a dilute Bose gas. We show that, if the gas is quenched sufficiently far into the critical region of the phase transition, the typical time scale for the nucleation of the condensate density is short and of $O(\hbar/k_{B}T_{c})$. As a result we find that thermalizing elastic collisions act as a bottleneck for the formation of the condensate. In the case of doubly-polarized atomic hydrogen these occur much more frequently than the inelastic collisions leading to decay and we are lead to the conclusion that Bose-Einstein condensation can indeed be achieved within the lifetime of the gas.

cond-mat↗

arXiv1994

Superhexatics

We develop a theory for a novel state of ${}^4$He films, that possesses off diagonal order (as in the superfluid state), as well as hexatic or bond orientational order. Within our description, both the hexatic and superfluid transitions are still of the Kosterlitz-Thouless type, but the superfluid stiffness is sensitive to the hexatic transition. We briefly discuss the possible relevance of this work to recent experiments on submonolayer helium films.

cond-mat↗