Molecule And Novel Superfluid In Ultracold Fermi Gases

In recent years,ultracold Fermi gases have emerged as an excellent platform for the study of fermion superfluid in the strong-coupling regime via the Feshbach resonance(FR)technique.Fermion superfluid is one of the central research topics in modern physics.The realization of synthetic spin-orbit coupling(SOC),optical lattice in ultracold atomic gases can give rise to a wealth of exotic superfluid phases.They can also be a powerful tool of quantum control.Ever since the pioneering work of Bardeen,Cooper and Schrieffer in the 1950 s,exploring novel pairing mechanisms for fermion superfluids has become one of the central tasks in modern physics.In this thesis,we show the novel pairing physics in a spin-orbit coupling Fermi gases.At the first part,we investigate a three-component Fermi-Fermi mixture,where two constituent fermions are subject to synthetic SOC.The interplay of SOC and the spin-selective interaction,which gives rise to a new type of Fulde-Ferrell(FF)pairing in spin-orbit coupled Fermi systems.The existence of the Fermi sea can also lead to the competition between FF-like pairing states with different center-of-mass momenta,which is alos consistent with the many body system.Optical lattice and also leads to interesting pairing physics,in the second part we study the interplay effect of spin-orbit coupling(SOC)and an optical lattice on the single-particle physics and superfluid-insulator transition in ultracold Fermi gases.We evaluate existing tight-binding models and point out their limitations in predicting the correct single-particle physics due to the missed high-band contributions.Moreover,we show that the Raman field(creating SOC)can induce band-gap closing in a two-dimensional optical lattice,leading to the intriguing phenomenon of superfluidity reentrance for interacting fermions at integer filling.All these results can be directly probed in current cold atoms experiments by the existing experimental techniques.With the knowledge of s-and p-wave Feshbach resonance,we investigate an ultracold spin-1/2 Fermi gas with comparable s-and p-wave interactions near the p-wave resonance.According to the numerical calculation and phase diagram analysis,we find that the co-existence of interactions lead to a new type of fermion superfluid with hybridized s-and p-wave pairings.The hybridized superfluid state is stable over a considerable parameter region on the phase diagram,and can lead to intriguing patterns of spin densities and pairing fields in momentum space.In particular,it can induce a phase-locked p-wave pairing in the fermion species that has no p-wave interactions.The hybridized nature of this novel superfluid can also be confirmed by measuring the s-and p-wave contacts,which can be extracted from the high-momentum tail of the momentum distribution of each spin component.These results enrich our knowledge of pairing superfluidity in Fermi systems,and open theavenue for achieving novel fermion superfluids with multiple partial-wave scatterings in cold atomic gases.Nowadays,confinement-induced resonance(CIR)as one of the most intriguing phenomena in low-dimensional systems has attracted a great deal of interest.We study the induced molecules near p-wave resonance in quasi-one-dimensional atomic gases.We derive the reduced 1D interaction parameters and show that they can well predict the binding energy of shallow molecules in quasi-1D system.Importantly,these shallow molecules are found to be much more spatially extended compared to those in three dimensions without transverse confinement.Our results strongly indicate that a p-wave interacting atomic gas can be much more stable in quasi-1D near the induced p-wave resonance,where most weight of the molecule lies outside the short-range regime and thus the atom loss could be suppressed.