H. T. C. Stoof

Superfluidity of Spin-Polarized 6Li

We study the prospects for observing superfluidity in a spin-polarized atomic gas of 6Li 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. 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 6Li gas are particularly promising for magnetic bias fields larger than 10 T.

Skyrmions in a ferromagnetic Bose-Einstein condensate

Multi-component Bose–Einstein condensates provide opportunities to explore experimentally the wealth of physics associated with the spin degrees of freedom. The ground-state properties and line-like vortex excitations of these quantum systems have been studied theoretically. In principle, nontrivial spin textures consisting of point-like topological excitations, or skyrmions, could exist in a multi-component Bose–Einstein condensate, owing to the superfluid nature of the gas. Although skyrmion excitations are already known in the context of nuclear physics and the quantum-Hall effect, creating these excitations in an atomic condensate would offer an opportunity to study their physical behaviour in much greater detail, while also enabling an ab initio comparison between theory and experiment. Here we investigate theoretically the stability of skyrmions in a fictitious spin-1/2 condensate of 87Rb atoms. We find that skyrmions can exist in such a gas only as a metastable state, but with a lifetime comparable to (or even longer than) the typical lifetime of the condensate itself.

Atom-molecule coherence in Bose gases

Abstract In an atomic gas near a Feshbach resonance, the energy of two colliding atoms is close to the energy of a bound state, i.e., a molecular state, in a closed channel that is coupled to the incoming open channel. Due to the different spin arrangements of the atoms in the open channel and the atoms in the molecular state, the energy difference between the bound state and the two-atom continuum threshold is experimentally accessible by means of the Zeeman interaction of the atomic spins with a magnetic field. As a result, it is in principle possible to vary the scattering length to any value by tuning the magnetic field. This level of experimental control has opened the road for many beautiful experiments, which recently led to the demonstration of coherence between atoms and molecules. This is achieved by observing coherent oscillations between atoms and molecules, analogous to coherent Rabi oscillations that occur in ordinary two-level systems. We review the many-body theory that describes coherence between atoms and molecules in terms of an effective quantum field theory for Feshbach-resonant interactions. The most important feature of this effective quantum field theory is that it incorporates the two-atom physics of the Feshbach resonance exactly, which turns out to be necessary to fully explain experiments with Bose–Einstein condensed atomic gases.

Deformation of a Trapped Fermi Gas with Unequal Spin Populations

The real-space densities of a polarized strongly interacting two-component Fermi gas of 6Li atoms reveal two low-temperature regimes, both with a fully paired core. At the lowest temperatures, the unpolarized core deforms with increasing polarization. Sharp boundaries between the core and the excess unpaired atoms are consistent with a phase separation driven by a first-order phase transition. In contrast, at higher temperatures the core does not deform but remains unpolarized up to a critical polarization. The boundaries are not sharp in this case, indicating a partially polarized shell between the core and the unpaired atoms. The temperature dependence is consistent with a tricritical point in the phase diagram.

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

We use a full coupled channels method to calculate collisional properties of magnetically or optically trapped ultracold 6-Li. 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.

Coherent versus incoherent dynamics during Bose-Einstein condensation in atomic gases

We review and extend the theory of the dynamics of Bose-Einstein condensation in weakly interacting atomic gases. We present in a unified way both the semiclassical theory as well as the full quantum theory. This is achieved by deriving a Fokker-Planck equation that incorporates both the coherent and incoherent effects of the interactions in a dilute Bose gas. In first instance we focus our attention on the nonequilibrium dynamics of a homogeneous Bose gas with a positive interatomic scattering length. After that we discuss how our results can be generalized to the inhomogeneous situation that exists in the present experiments with magnetically trapped alkali gases, and how we can deal with a negative interatomic scattering length in that case as well. We also show how to arrive at a discription of the collective modes of the gas that obeys the Kohn theorem at all temperatures. The theory is based on the many-body T-matrix approximation throughout, since this approximation has the correct physical behavior near the critical temperature and also treats the coherent and incoherent processes taking place in the gas on an equal footing.

Phonon exchange in dilute Fermi-Bose mixtures: tailoring the Fermi-Fermi interaction

We consider a mixture of a single-component Bose gas and a two-component Fermi gas at temperatures where the Bose gas is almost fully condensed. In such a mixture, two fermionic atoms can interact with each other by exchanging a phonon that propagates through the Bose condensate. We calculate the interaction potential due to this mechanism and determine the effective s-wave scattering length for two fermions that interact, both directly by the interatomic potentials, as wel as by the above mentioned exchange mechanism. We find that the effective scattering length is quite sensitive to changes in the condensate density and becomes strongly energy dependent. In addition, we consider the mechanical stability of these mixtures and also calculate the dispersion and the damping of the various collisionless collective modes of the gas.

Superfluid state of atomic 6 Li in a magnetic trap

We report on a study of the superfluid atate of spin-polarized atomic 6-Li 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 6-Li 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 preform 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.

Growth and Collapse of a Bose-Einstein Condensate with Attractive Interactions

We consider the dynamics of a quantum degenerate trapped gas of 7Li atoms. Because the atoms have a negative s-wave scattering length, a Bose condensate of 7Li 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.

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 naΛth2≪1, where the average interaction energy is small compared to the average kinetic energy.