Marijan Kostrun

A fast algorithm for the solution of the time-independent Gross--Pitaevskii equation

A new efficient numerical method for the solution of the time-independent Gross-Pitaevskii partial differential equation in three spatial variables is introduced. This equation is converted into an equivalent fixed-point form and is discretized using the collocation method at zeros of Legendre polynomials. Numerical comparisons with a state-of-the-art method based on propagating the solution of the time-dependent Gross-Pitaevskii equation in imaginary time are presented.

Collective molecule formation in a degenerate Fermi gas via a Feshbach resonance

We model collisionless collective conversion of a degenerate Fermi gas of atoms into bosonic molecules via a Feshbach resonance, treating the bosonic molecules as a classical field and seeding the pairing amplitudes with random phases. A dynamical instability of the Fermi sea against association with molecules drives the conversion. The model qualitatively reproduces several experimental observations [Regal et al., Nature (London), (2003)]. We predict that the initial temperature of the Fermi gas sets the limit for the efficiency of atom-molecule conversion.

Instability of a mixed atom-molecule condensate under photoassociation

Using the counterpart of the Gross-Pitaevskii equation, we study a system of atomic and molecular condensates in equilibrium in the presence of photoassociating light. All equilibria except a special case with only molecules are prone to an analog of the modulational instability in second-harmonic generation. The nature of the instability is such that the atoms and molecules aggregate in dense clumps.

Simple Mean-Field Theory for a Zero-Temperature Fermionic Gas at a Feshbach Resonance

We present a simple two-channel mean-field theory for a zero-temperature two-component Fermi gas in the neighborhood of a Feshbach resonance. Our results agree with recent experiments on the bare-molecule fraction as a function of magnetic field [Partridge, Phys. Rev. Lett. 95, 020404 (2005)]. Even in this strongly coupled gas of 6Li, the experimental results depend on the structure of the molecules formed in the Feshbach resonance and, therefore, are not universal.

Pulsating Instability of a Bose-Einstein Condensate in an Optical Lattice

We find numerically that in the limit of weak atom-atom interactions a Bose-Einstein condensate in an optical lattice may develop a pulsating dynamical instability in which the atoms nearly periodically form a peak in the occupation numbers of the lattice sites, and then return to the unstable initial state. Multiple peaks behaving similarly are also found. Simple arguments show that the pulsating instability is a remnant of integrability, and give a handle on the relevant physical scales.

Spectroscopic temperature determination of degenerate Fermi gases

We suggest a simple method for measuring the temperature of ultracold gases made of fermions. We show that by using a two-photon Raman probe, it is possible to obtain line shapes which reveal properties of the degenerate sample, notably its temperature T. The proposed method could be used with identical fermions in different hyperfine states interacting via s-wave scattering or identical fermions in the same hyperfine state via p-wave scattering. We illustrate the applicability of the method in realistic conditions for {sup 6}Li prepared in two different hyperfine states. We find that temperatures down to 0.05T{sub F} can be determined by this in situ method.

Stability of an atom-molecule Bose-Einstein condensate against collapse

We investigate the coupled atom-molecule Bose-Einstein condensate, as would ensue in an attempt to control the scattering length by means of either the Feshbach resonance or coherent photoassociation. In a mean-field model with a photoassociative coupling between the condensates, we demonstrate that the system is structurally stable. The sign of the effective scattering length notwithstanding, neither condensate will collapse.