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We consider spin-1/2 fermionic atoms with isotropic Rashba spin-orbit coupling in three directions. The interatomic potential is modeled by a square-well potential. We derive the analytic form of the asymptotic wave functions at short range for two fermions in the subspace of zero net momentum and zero total angular momentum. We show that the spin-orbit coupling has perturbative effects on the short-range asymptotic behavior of the wave functions away from resonances. We argue that our conclusion should hold generally. [ABSTRACT FROM AUTHOR]

For two-dimensional (2D) atomic Fermi gases in harmonic traps, the SO(2,l) symmetry is broken by the interatomic interaction explicitly via the contact correlation operator. Consequently, the frequency of the breathing mode ωB of the 2D Fermi gas can be different from 2ω0, with ω0 the trapping frequency of harmonic potentials. At zero temperature, we use the sum rules of density correlation functions to yield upper bounds for ωΒ. We further calculate ωΒ through the Euler equations in the hydrodynamic regime. The obtained value of ωΒ satisfies the upper bounds and shows deviation from 2ω0, which can be as large as about 8%. [ABSTRACT FROM AUTHOR]

We study the effective one-dimensional (ID) scattering of two distinguishable atoms confined individually by separated transverse harmonic traps. With equal trapping frequency for two s-wave interacting atoms, we find that by tuning the trap separations, the system can undergo double ID scattering resonance, named as the separation-induced resonance (SIR), when the ratio between the confinement length and s-wave scattering length is within (0.791.1.46). Near SIR, the scattering property shows unique dependence on the resonance position. The universality of a many-body system on scattering branch near SIR is demonstrated by studying the interaction effect of a localized impurity coupled with a Fermi sea of light atoms in a quasi-1D trap. [ABSTRACT FROM AUTHOR]

A class of universal "three-body" bound states has been recently predicted theoretically for identical fermions interacting at p-wave resonance in two dimensions. This phenomenon is called the super Efimov effect since the binding energies of the states follow a intriguing double exponential scaling. However, experimental resolution of this scaling is expected to meet formidable challenges. In this work, we introduce a thermodynamic quantity, the three-body contact Cθ, to quantify three-body correlations in a two-dimensional gas composed of the resonantly interacting fermions; the contact Cθ is the consequence of the underlying universal super Efimov effect in the many-body context. We show how Cθ affects physical observables such as the radio-frequency spectrum, the momentum distribution, and the atom loss rate. The signature of the elusive super Efimov effect can be pinned down by the detection of the three-body contact Cθ via these observables in the many-body system. [ABSTRACT FROM AUTHOR]

The superfluid to Mott insulator transition and the superradiant transition are textbook examples of quantum phase transition and coherent quantum optics, respectively. Recent experiments in ETH and Hamburg have succeeded in loading degenerate bosonic atomic gases in optical lattices inside a cavity, which enables the first experimental study of the interplay between these two transitions. In this Rapid Communication we present the theoretical phase diagram for the ETH Zurich experimental setup, and determine the phase boundaries and the orders of the phase transitions between the normal superfluid phase, the superfluid with superradiant light, the normal Mott insulator, and the Mott insulator with superradiant light. We find that in contrast to the second-order superradiant transition in a weakly interacting Bose condensate, strong correlations in the superfluid nearby a Mott transition can render the superradiant transition to a first-order one. Our results will stimulate further experimental studies of interactions between cavity light and strongly interacting quantum matter. [ABSTRACT FROM AUTHOR]

Super Efimov states are new kinds of universal three-body bound states predicted for three identical fermions with p-wave resonant interactions in two dimensions (2D) by a recent field-theoretic calculation [Phys. Rev. Lett. 110, 235301 (2013)]. The binding energies of these states obey a dramatic double exponential scaling En = E*exp(--2eπn/s0+θ) with universal scaling, s0 = 4/3 and three-body parameters E* and θ. We use the hyperspherical formalism and show that the super Efimov states originate from an emergent effective potential --l/4p² -- (s0² + 1/4) / p² In² (p) at large hyperradius p. Moreover, for pairwise interparticle potentials with van der Waals tails, our numerical calculation indicates that the three-body parameters E* and θ are also universal and the ground super Efimov state shall cross the threshold when the 2D p-wave scattering area is about --42.0/vdW², with lvdw the van der Waals length. [ABSTRACT FROM AUTHOR]

We consider the superradiant phase transition of a two-component Fermi gas in a cavity across a Feshbach resonance. It is known that quantum statistics plays a crucial role for the superradiant phase transition in atomic gases; in contrast to bosons, in a Fermi gas this transition exhibits strong density dependence. We show that across a Feshbach resonance, while the two-component Fermi gas passes through the BEC-BCS crossover, the supenradiant phase transition undergoes a corresponding crossover from a fermionic behavior on the weakly interacting BCS side, to a bosonic behavior on the molecular Bose-Einstein condensate (BEC) side. This intricate statistics crossover makes the superradiance maximally enhanced either in the unitary regime for low densities, in the BCS regime for moderate densities close to Fermi surface nesting, or in the BEC regime for high densities. [ABSTRACT FROM AUTHOR]

In this work, we present an effective-field theory to describe a two-component Fermi gas near a d-wave-interaction resonance. The effective-field theory is renormalizable by matching with the low-energy d-wave scattering phase shift. Based on the effective-field theory, we derive universal properties of the Fermi gas by the operator-product-expansion method. We find that beyond the contacts defined by adiabatic theorems, the asymptotic expressions of the momentum distribution and the Raman spectroscopy involve two extra contacts which provide additional information on correlations of the system. Our formalism sets the stage for further explorations of many-body effects in a d-wave resonant Fermi gas. Finally, we generalize our effective-field theory for interaction resonances of arbitrary higher partial waves. [ABSTRACT FROM AUTHOR]