Viscous relaxation and collective oscillations in a trapped Fermi gas near the unitarity limit

The viscous relaxation time of a trapped two-component gas of fermions in its normal phase is calculated as a function of temperature and scattering length, with the collision probability being determined by an energy-dependent s-wave cross section. The result is used for calculating the temperature dependence of the frequency and damping of collective modes studied in recent experiments, starting from the kinetic equation for the fermion distribution function with mean-field effects included in the streaming terms.Comment: 10 pages, 9 figures; proof version, corrected typo in Eq. (23); accepted for publication in PR

Collective excitations of a trapped Bose-Einstein condensate in the presence of a 1D optical lattice

We study low-lying collective modes of a horizontally elongated 87Rb condensate produced in a 3D magnetic harmonic trap with the addition of a 1D periodic potential which is provided by a laser standing-wave along the horizontal axis. While the transverse breathing mode results unperturbed, quadrupole and dipole oscillations along the optical lattice are strongly modified. Precise measurements of the collective mode frequencies at different height of the optical barriers provide a stringent test of the theoretical model recently introduced [M.Kraemer et al. Phys. Rev. Lett. 88 180404 (2002)].Comment: 4 pages, 4 figure

A strongly interacting Bose gas: Nozi\`eres and Schmitt-Rink theory and beyond

We calculate the critical temperature for Bose-Einstein condensation in a gas of bosonic atoms across a Feshbach resonance, and show how medium effects at negative scattering lengths give rise to pairs reminiscent of the ones responsible for fermionic superfluidity. We find that the formation of pairs leads to a large suppression of the critical temperature. Within the formalism developed by Nozieres and Schmitt-Rink the gas appears mechanically stable throughout the entire crossover region, but when interactions between pairs are taken into account we show that the gas becomes unstable close to the critical temperature. We discuss prospects of observing these effects in a gas of ultracold Cs133 atoms where recent measurements indicate that the gas may be sufficiently long-lived to explore the many-body physics around a Feshbach resonance.Comment: 8 pages, 8 figures, RevTeX. Significantly expanded to include effects beyond NS

Twin peaks in rf spectra of Fermi gases at unitarity

We calculate the radio-frequency spectrum of balanced and imbalanced ultracold Fermi gases in the normal phase at unitarity. For the homogeneous case the spectrum of both the majority and minority components always has a single peak even in the pseudogap regime. We furthermore show how the double-peak structures observed in recent experiments arise due to the inhomogeneity of the trapped gas. The main experimental features observed above the critical temperature in the recent experiment of Schunck et al. [Science 316, 867, (2007)] are recovered with no fitting parameters.Comment: v3: version accepted for publication as a Rapid Communication in PRA. With respect to v2, minor changes in the text and in the inset of Fig.

Spin polarons and molecules in strongly-interacting atomic Fermi gases

We examine pairing and molecule formation in strongly-interacting Fermi gases, and we discuss how radio-frequency (RF) spectroscopy can reveal these features. For the balanced case, the emergence of stable molecules in the BEC regime results in a two-peak structure in the RF spectrum with clearly visible medium effects on the low-energy part of the molecular wavefunction. For the highly-imbalanced case, we show the existence of a well-defined quasiparticle (a spin polaron) on both sides of the Feshbach resonance, we evaluate its lifetime, and we illustrate how its energy may be measured by RF spectroscopy.Comment: 4 pages, 5 figures. Revised version accepted for publication: minor changes to Fig. 2 (added inset with the chemical potential at unitarity), to Fig. 3 (experimental data updated), and to the notatio

Energy-dependent effective interactions for dilute many-body systems

We address the issue of determining an effective two-body interaction for mean-field calculations of energies of many-body systems. We show that the effective interaction is proportional to the phase shift, and demonstrate this result in the quasiclassical approximation when there is a trapping potential in addition to the short-range interaction between a pair of particles. We calculate numerically energy levels for the case of an interaction with a short-range square-well and a harmonic trapping potential and show that the numerical results agree well with the analytical expression. We derive a generalized Gross--Pitaevskii equation which includes effective range corrections and discuss the form of the electron--atom effective interaction to be used in calculations of Rydberg atoms and molecules.Comment: 6 pages, 2 figure

Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons

Topological insulators are fascinating states of matter exhibiting protected edge states and robust quantized features in their bulk. Here, we propose and validate experimentally a method to detect topological properties in the bulk of one-dimensional chiral systems. We first introduce the mean chiral displacement, and we show that it rapidly approaches a multiple of the Zak phase in the long time limit. Then we measure the Zak phase in a photonic quantum walk, by direct observation of the mean chiral displacement in its bulk. Next, we measure the Zak phase in an alternative, inequivalent timeframe, and combine the two windings to characterize the full phase diagram of this Floquet system. Finally, we prove the robustness of the measure by introducing dynamical disorder in the system. This detection method is extremely general, as it can be applied to all one-dimensional platforms simulating static or Floquet chiral systems.Comment: 10 pages, 7 color figures (incl. appendices) Close to the published versio

A Hybrid Lagrangian Variation Method for Bose-Einstein Condensates in Optical Lattices

Solving the Gross--Pitaevskii (GP) equation describing a Bose--Einstein condensate (BEC) immersed in an optical lattice potential can be a numerically demanding task. We present a variational technique for providing fast, accurate solutions of the GP equation for systems where the external potential exhibits rapid varation along one spatial direction. Examples of such systems include a BEC subjected to a one--dimensional optical lattice or a Bragg pulse. This variational method is a hybrid form of the Lagrangian Variational Method for the GP equation in which a hybrid trial wavefunction assumes a gaussian form in two coordinates while being totally unspecified in the third coordinate. The resulting equations of motion consist of a quasi--one--dimensional GP equation coupled to ordinary differential equations for the widths of the transverse gaussians. We use this method to investigate how an optical lattice can be used to move a condensate non--adiabatically.Comment: 16 pages and 1 figur

Metastability in spin polarised Fermi gases and quasiparticle decays

We investigate the metastability associated with the first order transition from normal to superfluid phases in the phase diagram of two-component polarised Fermi gases.We begin by detailing the dominant decay processes of single quasiparticles.Having determined the momentum thresholds of each process and calculated their rates, we apply this understanding to a Fermi sea of polarons by linking its metastability to the stability of individual polarons, and predicting a region of metastability for the normal partially polarised phase. In the limit of a single impurity, this region extends from the interaction strength at which a polarised phase of molecules becomes the groundstate, to the one at which the single quasiparticle groundstate changes character from polaronic to molecular. Our argument in terms of a Fermi sea of polarons naturally suggests their use as an experimental probe. We propose experiments to observe the threshold of the predicted region of metastability, the interaction strength at which the quasiparticle groundstate changes character, and the decay rate of polarons

Atomic wave packet dynamics in finite time-dependent optical lattices

Atomic wave packets in optical lattices which are both spatially finite and time-dependent exhibit many striking similarities with light pulses in photonic crystals. We analytically characterize the transmission properties of such a potential geometry for an ideal gas in terms of a position-dependent band structure. In particular, we find that at specific energies, wave packets at the center of the finite lattice may be enclosed by pairs of band gaps. These act as mirrors between which the atomic wave packet is reflected, thereby effectively yielding a matter wave cavity. We show that long trapping times may be obtained in such a resonator and investigate the collapse and revival dynamics of the atomic wave packet by numerical evaluation of the Schr\"odinger equation