Narrow Results

The bosonic atom–molecule conversion via Feshbach resonance is investigated by a semi-analytical method. The many-particle model is used and the independent crossing approximation (ICA) is utilized in calculation. An explicit formula is obtained for the conversion efficiency. The many-particle simulation supports our formula.

We review the recent experimental and theoretical advances in the generation of matter wave solitons in Bose–Einstein condensates. In particular, the controlled generation and dynamics of stable bright solitons by mean of Feshbach resonance techniques is discussed in details. Several aspects are taking into account, including the variation of the scattering length due to Feshbach resonance, the safe parameters against the collapse and the experimental implications of our scenario.

We study an effective field theory describing cold fermionic atoms near a Feshbach resonance. The effective theory gives a precise description of the dynamics in the limit that the energy of the Feshbach resonance is tuned to be twice that of the Fermi surface. We compute the zero temperature superfluid condensate in this limit, and obtain a critical temperature T_C≃0.43 T_F.

We briefly review our recent work on spatial tuning of Bose-Einstein condensation (BEC). We first study spatially periodic tuning of the s-wave scattering length for controlling the propagation of a BEC matter wave, and find matter wave limiting processing and bistability. Second, we show that a stable BEC with natural attractive interaction could be formed by tuning the s-wave scattering length with a Gaussian optical field, but the condensed atom number should be less than a critical value. Further, we apply Thomas-Fermi approximation to obtain a formula for this critical value.

We explore p-wave pairing in a single-channel two-component Fermi system with unequal population near Feshbach resonance. Our analytical and numerical study reveal a rich superfluid (SF) ground state structure as a function of imbalance. In addition to the state Δ_±1 ∝ Y_1±1, a multitude of “mixed” SF states formed of linear combinations of Y_1m's give global energy minimum under a phase stability condition; these states exhibit variation in energy with the relative phase between the constituent gap amplitudes. States with local energy minimum are also obtained. We provide a geometric representation of the states. A T = 0 polarization vs. p-wave coupling phase diagram is constructed across the BEC-BCS regimes. With increased polarization, the global minimum SF state may undergo a quantum phase transition to the local minimum SF state.

In this review we will discuss the experimental and theoretical progresses in studying spin–orbit coupled degenerate atomic gases during the last two years. We shall first review a series of pioneering experiments in generating synthetic gauge potentials and spin–orbit coupling in atomic gases by engineering atom-light interaction. Realization of spin–orbit coupled quantum gases opens a new avenue in cold atom physics, and also brings out a lot of new physical problems. In particular, the interplay between spin–orbit coupling and inter-atomic interaction leads to many intriguing phenomena. By reviewing recent theoretical studies of both interacting bosons and fermions with isotropic Rashba spin–orbit coupling, the key message delivered here is that spin–orbit coupling can enhance the interaction effects, and make the interaction effects much more dramatic even in the weakly interacting regime.

Exact solitonic solutions of the Gross–Pitaevskii equation with time-modulated nonlinearity of a(t) = a₀ / (t + t₀) are obtained. With help of these solutions, we analyze the properties of Feshbach-managed solitons in Bose–Einstein condensates in details. Our results show that the parameters of atomic matter waves can be manipulated by proper variation of the scattering length. In particular, an exact two-soliton solution is given, from which, it is shown that the separation between the neighboring solitons can be effectively maintained by allowing the solitons to have unequal initial amplitudes.

We study the possibility of the emergence of a spatiotemporal pattern in a gas of ultra bosons, where atomic and molecular condensates can coexist due to the presence of Feshbach resonance and nonlinear interactions in the condensates. These patterns exhibit features which are very similar to those that have been seen in thermohaline convection in salt water. The experimental identification of these patterns in the condensates will be highly interesting.

The dynamics of the coexisting ultracold atomic and molecular condensates in the presence of Feshbach resonance, atom–atom, molecule–molecule and atom–molecule interactions is described in terms of coupled Gross–Pitaevskii equation. We show that the appearence of oscillation or the existence of Josephson-like currents in the condensates is the natural consequence of the Gross–Pitaevskii equation under a suitable approximation regarding the nature of the condensate wave function.

We show that the self-trapped condensate can be dynamically stabilized in two and three dimensional free space by periodic oscillation of the scattering length. The oscillating interaction produces an effective potential that prevents the condensate from collapsing. We take into account the effect of dissipation to simulate realistic situations.

We explore p-wave pairing in a single-channel two-component Fermi system with unequal population near Feshbach resonance. Our analytical and numerical study reveal a rich superfluid (SF) ground state structure as a function of imbalance. In addition to the state Δ_±1 ∝ Y_1±1, a multitude of “mixed” SF states formed of linear combinations of Y_1m's give global energy minimum under a phase stability condition; these states exhibit variation in energy with the relative phase between the constituent gap amplitudes. States with local energy minimum are also obtained. We provide a geometric representation of the states. A T = 0 polarization vs. p-wave coupling phase diagram is constructed across the BEC-BCS regimes. With increased polarization, the global minimum SF state may undergo a quantum phase transition to the local minimum SF state.

We construct an effective field theory for a condensate of cold Fermi atoms whose scattering is controlled by a Feshbach resonance, with particular emphasis on the speed of sound and its hydrodynamic description.

We report on measurements of the excitation spectrum of a strongly interacting Bose-Einstein condensate (BEC). A magnetic-field Feshbach resonance is used to tune atom-atom interactions in the condensate and to reach a regime where quantum depletion and beyond mean-field corrections to the condensate chemical potential are significant. We use two-photon Bragg spectroscopy to probe the condensate excitation spectrum; our results demonstrate the onset of beyond mean-field effects in a gaseous BEC.

Lithium-7 exhibits a broad Feshbach resonance that we exploit to tune the interactions in a Bose-Einstein condensate (BEC). We find that the rate of photoassociation can be enhanced by several orders of magnitude by tuning close to the resonance, and use this effect to observe saturation in the rate of association of a BEC for the first time. We have also used a lithium BEC to explore the effects of disorder on the transport and coherence properties of the condensate. We also show that the scattering length goes through a shallow zero-crossing far from the resonance, where it may be made positive or negative with a magnitude of less than 0.1 a_o, and have made preliminary transport measurements in the regime of weak repulsive and attractive interactions.