Session J3 - Focus Session: Theory of Bose-Einstein Condensates.
MIXED session, Thursday afternoon, June 15
PB36,

[J3.01] Making Vortices in Multicomponent Bose-Einstein Condensates

Ever since the first observations of Bose-Einstein condensation in a dilute atomic gas, experimenters have sought a method to create vortices in these systems. We recently discovered a scheme for generating vortices (which have a nontrivial topology) through utilizing the rich spin-structure possible when multicomponent condensates are simultaneously present. Our method for vortex engineering can be generalized, in principle, to allow generation of many other interesting designer quantum states, such as vortices with multiple circulation and quadrupole states. The basic theoretical idea has been implemented experimentally at JILA with the expected signatures of a single quantized vortex flow clearly visible.

Inducing this kind of motion into a Bose-Einstein Condensate should help us to elucidate the properties of the dilute gas condensates, and the relationship to superfluid flow (such as persistent currents) seen in dense quantum liquids.

[J3.02] Dynamics of vortex formation in rotating Bose-Einstein condensates

The nucleation and subsequent dynamics of vortices in dilute trapped Bose-Einstein condensates is investigated numerically using the Gross-Pitaevskii equation. Vortices are generated by rotating a three-dimensional, anisotropic harmonic trap. In the presence of a small amount of noise, pairs of vortices with the same circulation first appear at a rotation frequency significantly larger than the critical frequency for their thermodynamic stability. The vortices exhibit Kelvin-mode oscillations that damp rapidly. As the rotation increases, additional pairs of vortices enter the cloud from the surface at well-defined angular frequencies, forming vortex arrays whose structures are sensitive to the trap geometry. The results are compared with recent experimental data [K.W. Madison et al., Phys. Rev. Lett. 84, 806 (2000)].

[J3.03] The Moment of Inertia of a Bose-Einstein Condensate

One evidence of superfluidity in a rotating gaseous Bose-Einstein condensate (BEC) is a moment of inertia that is reduced below the classical rigid-body value. We have studied the expansion of such a rotating condensate for the case where the rotation frequency, Ømega, lies below the critical frequency, Ømega_c, required for vortex formation. Such a condensate can be formed by spinning an anisotropic harmonic trap. If a condensate is brought to a steady rotational state by adiabatically ramping up the rotation frequency where Ømega < Ømega_c and then released from the magnetic trap, then the more narrowly confined direction (in the plane perpendicular to Ømega) will expand more rapidly than the less narrowly confined direction. One would expect that the aspect ratio (\delta \equiv \left|\langle x^2 - y^2\rangle/\langle x^2 + y^2\rangle\right|) of the expanding cloud would, at some moment, become equal to zero. However, because both energy and the z-component of the angular momentum are conserved in the expansion and because of the irrotational flow of the initial condensate, the aspect ratio can never reach this value. Thus the resulting behavior of the expanding BEC can be used to extract the moment of inertia of the initial confined cloud.

[J3.04] Kinetic equation for the thermal cloud in a trapped Bose gas at low temperatures

Recently the authors used the Kadanoff-Baym non-equilibrium Green's function formalism to derive kinetic equation for the non-condensate atoms, in conjunction with a consistent generalization of the Gross-Pitaevskii equation for the Bose condensate wavefunction [1]. This work was limited to high temperatures, where the excited atoms could be described by a Hartree-Fock particle-like spectrum. We present the generalization of this work to low temperatures, where the single-particle spectrum is now described by the Bogoliubov-Popov approximation. We obtain a kinetic equation for the quasiparticle Bose distribution function with collision integrals describing scattering between quasiparticles and the condensate atoms. For a uniform Bose gas, our kinetic equation reduces to that found by Kirkpatrick and Dorfman [2].

[1] M. Imamovic-Tomasovic and A. Griffin, cond-mat/9911402.

[2] T.R. Kirkpatrick and J.R. Dorfman, J. Low Temp. Phys. 58, 301 (1985).

[J3.05] The Partition Function of a Spinor Gas

For a spinor gas, a mixture of identical particles with different internal degrees of freedom, we derive the partition function in terms of the Feynman--Kac functionals of polarized components. As an example a spin-1 Bose gas with the spins subjected to an external magnetic field and confined in a parabolic potential is studied. From the analysis of the free energy obtained for a finite number of particles, we find that the specific heat of this ideal spinor gas has two maxima: one is a Schottky anomaly, due to the lifting of the spin degeneracy by the external field, the other is the signature of Bose--Einstein condensation.

[J3.06] The coherent evolution of a condensed bosonic gas

The kinetic evolution of a condensed bosonic gas is determined by two distinct physical regimes: i.e. the coherent and nonlinear motion of the condensate immersed in a cloud of non-condensate, and on the other hand, the collisional dynamics leading towards equilibrium. In most of the present experiments that have achieved BEC with dilute atomic gases, both types of processes occur simultaneously and must be considered. Based on the quantum kinetic theory presented in Ref. [1], we have studied the coherent time-dependent evolution of a condensed bosonic gas interacting dynamically with the non-condensate. In the case of a 3-dimensional isotropic condensate, we present numerical results that illustrate the physics. In particular, we will discuss the collective excitation frequencies and the important constants of motion: energy and number.

[1] R. Walser J. Williams, J. Cooper, M. Holland, Phys. Rev. A, 59, 3878 (1999)

[J3.07] New source of damping of condensate oscillations at finite temperatures in the collisionless limit

We consider the damping of condensate collective modes at finite temperatures arising from collisions between the condensate and the non-condensate atoms. As a first approximation, we ignore the dynamics of the thermal cloud and assume it remains in static thermal equilibrium. Our calculations should be applicable to collective modes of the condensate which are oscillating out-of-phase with the thermal cloud. We obtain a generalized Stringari equation of motion for the condensate at finite temperature, which includes a damping term associated with the fact that the condensate is not in diffusive equilibrium with the thermal cloud. The damping of the condensate modes is calculated perturbatively using the undamped Stringari modes and found to be slightly smaller but comparable to the Landau damping considered in the recent literature. The damping we find in the collisionless region is the analogue of damping recently calculated in the collision-dominated hydrodynamic region in which the dynamics of both condensate and non-condensate are treated.(E. Zaremba, T. Nikuni, and A. Griffin, Journ. Low Temp. Phys. 116, 277 (1999).)

[J3.08] Coffee Break

This abstract not available.

[J3.09] Dynamics of Separating Bose-Einstein Condensates

When a Bragg laser pulse (two counterpropagating beams with slightly different frequencies) is applied to a gaseous Bose-Einstein condensate (BEC), it is possible to transfer momentum to a controllable fraction of the condensate atoms. A Bragg pulse that imparts momentum to half of the condensate atoms is termed a \pi/2 pulse while a pulse that imparts momentum to all of the atoms is called a \pi pulse. Such pulses split the BEC into two clouds that eventually separate. While the clouds are overlapped, however, their interaction alters both the density and phase profiles of the individual clouds in a nontrivial way. While this process can be modeled using the time-dependent Gross-Pitaevskii (GP) equation, the solution of the full three--dimensional GP equation for large momentum transfer can be a challenging computational task. We have studied the dynamics of two separating BEC's using a Lagrangian variational technique that provides equations of motion for time-dependent variational parameters contained in a specified wavefunction ansatz for the GP solution. We compare the results of these models with data from a recent experiment performed at NIST.

[J3.10] Elastic scattering loss of atoms from colliding Bose-Einstein condensate wavepackets

Bragg scattering can be used to create a daughter wavepacket with momentum k from a parent Bose-Einstein condensate, where k is very large compared to the momentum spread of the parent. Elastic collisions between atoms in the moving wavepacket and atoms in the parent results in formation of a shell of elastically scattered atoms with momentum k/2 that are lost from two original wavepackets. We apply a slowly-varying-envelope approximation to calculate the time-dependent dynamics of the two interacting wavepackets and account for the elastic scattering losses. A significant fraction of atoms can be lost this way from the parent and daughter wavepackets, especially if the motion is along the long axis of an asymmetric trap. We show that such elastic collisional losses lowers the output of four-wave mixing by around 20 percent for the experimental configuration in the NIST experimental demonstration of four-wave mixing of matter waves(Deng et al.), Nature 398, 218 (1999).

[J3.11] Dark soliton states of Bose-Einstein condensates in anisotropic traps

Dark soliton states of Bose-Einstein condensates in anisotropic traps are studied analytically and computationally by the direct solution of the time-dependent Gross-Pitaevskii equation in three dimensions. The ground and self-consistent excited states are found numerically by relaxation in imaginary time. The energy of a stationary soliton in a harmonic trap is shown to be independent of density and geometry for large numbers of atoms. The Bogoliubov excitation spectrum of the soliton state contains complex frequencies, which disappear for sufficiently small numbers of atoms or large transverse confinement. The relationship between these complex modes and the snake instability is investigated numerically by long time propagation in real time.

[J3.12] Bose-Stimulated Raman Adiabatic Passage in Photoassociation.

We present the theory of stimulated Raman adiabatic passage~\mbox(STIRAP) in free-bound-bound photoassociation of a Bose-Einstein condensate~(BEC). Whereas STIRAP is found to be absent in the nondegenerate case(J. Javanainen and M. Mackie, Phys.\ Rev.\ A 58), R789 (1998)., the counter-intuitive scheme is in fact a viable means for converting an atomic condensate to a molecular condensate with near-unit efficiency(M. Mackie, R. Kowalski, and J. Javanainen, arXiv:\,physics/9909060.). Hence, we review the absence of STIRAP in photoassociation of a thermal nondegenerate gas, illustrate Bose-stimulation as the mechanism that enables the benefits of STIRAP for a condensate, and establish the experimental conditions that should allow for adiabatic passage to a BEC of molecules.

[J3.13] Raman spectroscopy of a trapped two component Fermi gas

Recent experiments (B. DeMarco and D. S. Jin, Science 285), 1703 (1999). have produced trapped ^40K atoms at about half the Fermi temperature and observed clear emergence of quantum degeneracy. We report our study of near resonant light scattering from such degenerate fermionic gas. Taking into account the two component nature of these (\Lambda-type level scheme) model atoms, we investigate Raman spectroscopy as a potentially promising tool for probing quantum degeneracy features under experimentally accessible regime. Specifically, we consider the scattering of two far off resonant pulses driving the trapped atoms in a resonant Raman configuration. We found significantly inhibited coherent Raman scattering at certain ratios of two component densities and at appropriate pumping field directions. This allows for optimal detection of quantum statistic signatures as they are contained within the nominally weaker incoherent part of scattering. Detailed numerical results of temperature and density effects will be presented.

[J3.14] Light interactions with trapped atomic fermions

We consider the interaction of light with spin polarized degenerate trapped Fermi atoms. Several issues will be discussed, including the influence of radiative reabsorpton on the emission profiles from highly anisotropic traps, and the use of light scattering to probe quantum properties of the gas.

[J3.15] Influence of degeneracy on the cooling of trapped atomic fermions

We investigate the forced evaporative cooling dynamics of a two species trapped Fermi gas using a semiclassical Boltzmann equation. We study how Fermi blocking influences the rethermalization and cooling efficiency and make comparison with recent experiments. Our results suggest that even though cooling efficiency drops significantly due to Fermi blocking when the gas becomes degenerate, the ratio of temperature to Fermi temperature continues to decrease in essentially the same way as in the classical regime, until eventually a limit is reached. Mean field effects will also be discussed.

[J3.16] Is BEC behind superfluidity/superconductivity in fermions?

In the late 1930's London conjectured that BEC must be behind the superfluid transition in helium-4, a Bose system. What about Fermi systems where boson Cooper pairs (CPs) are formed? CPs in two (2D) and three (3D) dimensions are analyzed for an interaction general enough to mimic either helium-3 or electron- (or hole-) charge-carrier Fermi systems. Bosonic CPs with non-zero center-of-mass momentum (CMM)---usually neglected in BCS theory---are included. The CP binding energy is expanded analytically in 2D in powers of the CMM up to quadratic terms. For either 2D or 3D, in the weak-coupling (so-called BCS) regime of severely-overlapped CPs a term linear in the CMM dominates the pair excitation energy, whereas in the strong-coupling (so-called Bose) regime the quadratic-in-CMM kinetic energy of the strongly-bound, well-separated composite boson pairs dominates. Results are expected to play a nontrivial role in testing a BEC model of superfluid helium-3 or of superconductivity based upon their respective CPs.

Part J of program listing