We show that recently suggested subwavelength lattices offer remarkable prospects for the observation of novel superfluids of fermionic polar molecules. It becomes realistic to obtain a topological $p$-wave superfluid of microwave-dressed polar molecules in 2D lattices at temperatures of the order of tens of nanokelvins, which is promising for topologically protected quantum information processing. Another foreseen novel phase is an interlayer $p$-wave superfluid of polar molecules in a bilayer geometry.
Non-analyticities in the logarithm of the Loschmidt echo, known as dynamical quantum phase transitions [DQPTs], are a recently introduced attempt to classify the myriad of possible phenomena which can occur in far from equilibrium closed quantum systems. In this work, we analytically investigate the Loschmidt echo in nonequilibrium $s$-wave and topological $p_x+ip_y$ fermionic superfluids. We find that the presence of non-analyticities in the echo is not invariant under global rotations of the superfluid phase. We remedy this deficiency by introducing a more general notion of a grand canonical Loschmidt echo. Overall, our study shows that DQPTs are not a good indicator for the long time dynamics of an interacting system. In particular, there are no DQPTs to tell apart distinct dynamical phases of quenched BCS superconductors. Nevertheless, they can signal a quench induced change in the topology and also keep track of solitons emerging from unstable stationary states of a BCS superconductor.
We show that s-wave scattering resonances induced by dipolar interactions in a polar molecular gas have a universal large and positive effective range, which is very different from Feshbach resonances realized in cold atoms before, where the effective range is either negligible or negative. Such a difference has important consequence in many-body physics. At high temperature regime, a positive effective range gives rise to stronger repulsive interaction energy for positive scattering length, and weaker attractive interaction energy for negative scattering length. While at low-temperatures, we study polaron problem formed by single impurity molecule, and we find that the polaron binding energy increases at the BEC side and decreases at the BCS side. All these effects are in opposite to narrow Feshbach resonances where the effective range is negative.
Understanding superfluidity with higher order partial waves is crucial for the understanding of high-$T_c$ superconductivity. For the realization of a superfluid with anisotropic order parameter, spin-polarized fermionic lithium atoms with strong p-wave interaction are the most promising candidates to date. We apply rf-spectroscopy techniques that do not suffer from severe final-state effects cite{Perali08} with the goal to perform photoemission spectroscopy on a strongly interacting p-wave Fermi gas similar to that recently applied for s-wave interactions cite{Stewart08}. Radiofrequency spectra of both quasibound p-wave molecules and free atoms in the vicinity of the p-wave Feshbach resonance located at 159.15,G cite{Schunck05} are presented. The observed relative tunings of the molecular and atomic signals in the spectra with magnetic field confirm earlier measurements realized with direct rf-association cite{Fuchs08}. Furthermore, evidence of bound molecule production using adiabatic ramps is shown. A scheme to observe anisotropic superfluid gaps, the most direct proof of p-wave superfluidity, with 1d-optical lattices is proposed.
Fermionic superfluids provide a new realization of quantum turbulence, accessible to both experiment and theory, yet relevant to phenomena from both cold atoms to nuclear astrophysics. In particular, the strongly interacting Fermi gas realized in cold-atom experiments is closely related to dilute neutron matter in neutron star crusts. Unlike the liquid superfluids 4He (bosons) and 3He (fermions) where quantum turbulence has been studied in the laboratory, superfluid Fermi gases stand apart for a number of reasons. They admit a reliable theoretical description based on a DFT called the TDSLDA that describes both static and dynamic phenomena. Cold atom experiments demonstrate exquisite control over particle number, spin polarization, density, temperature, and interaction strength. Topological defects such as domain walls and quantized vortices, which lie at the heart of quantum turbulence, can be created and manipulated with time-dependent external potentials, and agree with the time-dependent theoretical techniques. While similar experimental and theoretical control exists for weakly interacting Bose gases, the unitary Fermi gas is strongly interacting. The resulting vortex line density is extremely high, and quantum turbulence may thus be realized in small systems where classical turbulence is suppressed. Fermi gases also permit the study of exotic superfluid phenomena such as a 3D LOFF supersolid, and a finite temperature pseudo-gap in the regime of classical turbulence. The dynamics associated with these phenomena has only started to be explored. Finally, superfluid mixtures have recently been realized, providing experimental access to phenomena like Andreev-Bashkin entrainment. Superfluid Fermi gases thus provide a rich forum for addressing phenomena related to quantum turbulence with applications ranging from terrestrial superfluidity to astrophysical dynamics in neutron stars.
We show that, near a Feshbach resonance, a strong p-wave resonance is present at low energy in atom-dimer scattering for $^6$Li-$^{40}$K fermionic mixtures. This resonance is due to a virtual bound state, in the atom-dimer system, which is present at this low energy. When the mass ratio between the two fermionic elements is increased, this virtual bound state goes to a known real bound state which appears when the mass ratio reaches 8.17. This resonance should affect a number of physical properties. These include the equation of state of unbalanced mixtures at very low temperature but also the equation of state of balanced mixtures at moderate or high temperature. The frequency and the damping of collective modes should also provide a convenient way to evidence this resonance. Finally it should be possible to modify the effective mass of one the fermionic species by making use of an optical lattice. This would allow to study the strong dependence of the resonance as a function of the mass ratio of the two fermionic elements.