Centre for Quantum and Optical Science

We investigate theoretically radio-frequency spectroscopy of weakly bound molecules in an ultracold spinorbit-coupled atomic Fermi gas. We consider two cases with either equal Rashba and Dresselhaus coupling or pure Rashba coupling. The former system has been realized very recently at Shanxi University [Wang et al., Phys. Rev. Lett. 109, 095301 (2012)] and MIT [ Cheuk et al., Phys. Rev. Lett. 109, 095302 (2012)]. We predict realistic radiofrequency signals for revealing the unique properties of anisotropic molecules formed by spin-orbit coupling.

We develop a variational approach to calculate the density response function at finite temperatures of the lowest-lying two-fluid modes in a trapped two-component Fermi superfluid close to a Feshbach resonance. The out-of-phase oscillations, which are the analogue in trapped gases of second sound in uniform superfluids, have so far not been observed in cold-atom experiments. At unitarity, we show that these modes are observable at finite temperatures via two-photon Bragg scattering, whose spectrum is related to the imaginary part of density response function. This provides direct evidence for superfluidity and a promising way to test microscopic results for thermodynamics at unitarity.

For 2 years, a baseline investigation was carried out to collect reference information of the present environmental status in the Fehmarn Belt and adjacent area. The temporal and spatial variability of phytoplankton was monitored by a combination of monitoring buoys, pigment analysis and fast screening microscopy. The overall phytoplankton succession in the Fehmarn Belt area was found to be influenced primarily by the seasonal changes, where various diatoms dominated the spring and autumn blooms and flagellates like Chrysochromulina sp., Dictyocha speculum and various dinoflagellates were occasionally abundant in late spring and summer. The phytoplankton groups were remarkably uniform horizontally in the investigation area while large differences in both biomasses and composition of individual phytoplankton groups were seen vertically in the water column, especially in the summer periods, in which the two-layer exchange flow between the North Sea and the Baltic Sea is showing a particularly strong stratification in the Fehmarn Belt. The chlorophyll a concentrations ranged continuously from 1 to 3 μg/L at the three permanent buoy stations during the 2 years of monitoring, except for the spring and autumn blooms where chlorophyll a increased up to 18 μg/L in the spring of 2010 and up to 8 μg/L in the autumn of 2009. Recurrent blooms of filamentous cyanobacteria are common during the summer period in the Baltic Sea and adjacent areas, but excessive blooms of cyanobacteria did not occur in 2009 and 2010 in the Fehmarn Belt area. The combination of the HPLC pigment analysis method and monitoring buoys continuously measuring fluorescence at selected stations with fast screening of samples in the microscope proved advantageous for obtaining information on both the phytoplankton succession and dynamic and, at the same time, getting information on duration and intensity of the blooms as well as specific information on the dominant species present both temporally and spatially in the large Fehmarn Belt area.

We theoretically investigate the static structure factor of an interacting Fermi gas near the BEC-BCS crossover at large momenta. Due to short-range two-body interactions, we show that the structure factor of unlike spin correlations S ↑↓ (q) falls off as 1/q in a universal scaling region with large momentumhq and large scattering length. The scaling coefficient is determined by the celebrated Tan's contact parameter, which links the short-range behavior of many-body systems to their universal thermodynamic properties. By implementing this structure-factor Tan relation together with the random-phase approximation and the virial expansion theory in various limiting cases, we show how to calculate S ↑↓ (q) at zero and finite temperatures for arbitrary interaction strengths, at momentum transfer higher than the Fermi momentum. Our results provide a way to experimentally confirm one of the Tan relations and to accurately measure the value of contact parameter.

ABSTRACT In this paper, the momentum-resolved radio-frequency spectra of a unitary Fermi gas in the normal phase are presented and analyzed on the basis of the framework of the non-self-consistent T-matrix approximation with the extended Gorkov and Melik-Barkhudarov (GMB) approximation. We report the calculated occupied spectral intensity and energy distribution curves for different temperatures above Tc. Our results indicate the existence of pseudogap phenomenon which would be helpful for further understanding of the pseudogap in high-temperature superconductivity.

We theoretically investigate the inhomogeneous Fulde-Ferrell (FF) superfluidity in a three dimensional atomic Fermi gas with Rashba spin-orbit coupling near a broad Feshbach resonance. We show that within mean-field theory the FF superfluid state is always more favorable than the standard Bardeen-Cooper-Schrieffer (BCS) superfluid state when an in-plane Zeeman field is applied. We present a qualitative finite-temperature phase diagram near resonance and argue that the predicted FF superfluid is observable with experimentally attainable temperatures (i.e., T ∼ 0.2TF , where TF is the characteristic Fermi degenerate temperature).

The recently discovered universal thermodynamic behaviour of dilute, strongly interacting Fermi gases also implies a universal structure in the many-body pair-correlation function at short distances, as quantified by the contact I. This quantity is an excellent indicator of the presence of strong correlations in these systems, which provide a highly accessible physical model for other strongly correlated quantum fluids. Here we theoretically calculate the temperature dependence of this universal contact for a Fermi gas in free space and in a harmonic trap. At high temperatures above the Fermi degeneracy temperature, T TF , we obtain a reliable non-perturbative quantum virial expansion up to third order. At low temperatures we compare different approximate strong coupling theories. These make different predictions, which need to be tested either by future experiments or advanced quantum Monte Carlo simulations. We conjecture that in the universal unitarity limit, the contact or correlation decreases monotonically with increasing temperature, unless the temperature is significantly lower than the critical temperature, T ≪ Tc ∼ 0.2TF . We also discuss briefly how to measure the universal contact either in homogeneous or harmonically trapped Fermi gases.

We examine theoretically the visualization of Majorana fermions in a two-dimensional trapped ultracold atomic Fermi gas with spin-orbit coupling. By increasing an external Zeeman field, the trapped gas transits from non-topological to topological superfluid, via a mixed phase in which both types of superfluids coexist. We show that the zero-energy Majorana fermion, supported by the topological superfluid and localized at the vortex core, is clearly visible through (i) the core density and (ii) the local density of states, which are readily measurable in experiment. We present a realistic estimate on experimental parameters for ultracold 40 K atoms.

We investigate theoretically Bose-Einstein condensation of an ideal, trapped Bose gas in the presence of Rashba spin-orbit coupling. Analytic results for the critical temperature and condensate fraction are derived, based on a semi-classical approximation to the single-particle energy spectrum and density of states, and are compared with exact results obtained by explicitly summing discrete energy levels for small number of particles. We find a significant decrease of the critical temperature and of the condensate fraction due to a finite spin-orbit coupling. For large coupling strength and finite number of particles N , the critical temperature scales as N 2/5 and N 2/3 in three and two dimensions, respectively, contrasted to the predictions of N 1/3 and N 1/2 in the absence of spin-orbit coupling. Finite size corrections in three dimensions are also discussed.

We investigate theoretically the prospect of realizing a topological superfluid in one-dimensional spin-orbit coupled atomic Fermi gases under Zeeman field in harmonic traps. In the absence of spin-orbit coupling, it is well-known that the system is either a Bardeen-Cooper-Schrieffer (BCS) superfluid or an inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid. Here we show that with spin-orbit coupling it could be driven into a topological superfluid, which supports zeroenergy Majorana modes. However, in the weakly interacting regime the spin-orbit coupling does not favor the spatially oscillating FFLO order parameter. As a result, it seems difficult to create an inhomogeneous topological superfluid in current cold-atom experiments.