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arXiv:1209.5935 · Physical Review A

Significance of dressed molecules in a quasi-two-dimensional Fermi gas with spin-orbit coupling

Ren Zhang, Fan Wu, Jun-Rong Tang, Guang‐Can Guo, Wei Yi, Wei Zhang

Published Mar 27, 2013• 5 citations
arXivHTMLPDF

Abstract

We investigate the properties of a spin-orbit coupled quasi-two-dimensional Fermi gas with tunable $s$-wave interaction between the two spin species. By analyzing the two-body bound state, we find that the population of the excited states in the tightly confined axial direction can be significant when the two-body binding energy becomes comparable to or exceeds the axial confinement. Since the Rashba spin-orbit coupling that we study here tends to enhance the two-body binding energy, this effect can become prominent at unitarity or even on the BCS side of the Feshbach resonance. To study the impact of these excited modes along the third dimension, we adopt an effective two-dimensional Hamiltonian in the form of a two-channel model, where the dressed molecules in the closed channel consist of the conventional Feshbach molecules as well as the excited states occupation in the axial direction. With properly renormalized interactions between atoms and dressed molecules, we find that both the density distribution and the phase structure in the trap can be significantly modified near a wide Feshbach resonance. In particular, the stability region of the topological superfluid phase is increased. Our findings provide a proper description for a quasi-two-dimensional Fermi gas under spin-orbit coupling, and are helpful for the experimental search for the topological superfluid phase in ultracold Fermi gases.

DOI
10.1103/physreva.87.033629

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We investigate the properties of a spin-orbit coupled quasi-two-dimensional Fermi gas with tunable sss-wave interaction between the two spin species. By analyzing the two-body bound state, we find that the population of the excited states in the tightly confined axial direction can be significant when the two-body binding energy becomes comparable to or exceeds the axial confinement. Since the Rashba spin-orbit coupling that we study here tends to enhance the two-body binding energy, this effect can become prominent at unitarity or even on the BCS side of the Feshbach resonance. To study the impact of these excited modes along the third dimension, we adopt an effective two-dimensional Hamiltonian in the form of a two-channel model, where the dressed molecules in the closed channel consist of the conventional Feshbach molecules as well as the excited states occupation in the axial direction. With properly renormalized interactions between atoms and dressed molecules, we find that both the density distribution and the phase structure in the trap can be significantly modified near a wide Feshbach resonance. In particular, the stability region of the topological superfluid phase is increased. Our findings provide a proper description for a quasi-two-dimensional Fermi gas under spin-orbit coupling, and are helpful for the experimental search for the topological superfluid phase in ultracold Fermi gases.
One of the most dynamic directions in ultracold atomic gas research is the study of low-dimensional physics in quasi-low-dimensional geometries, where atoms are confined in strongly anisotropic traps. Recently, interest has significantly intensified with the realization of synthetic spin–orbit coupling (SOC). As a first step toward understanding the SOC effect in quasi-low-dimensional systems, the solution of two-body problems in different trapping geometries and different types of SOC has attracted great attention in the past few years. In this review, we discuss both the scattering-state and the bound-state solutions of two-body problems in quasi-one and quasi-two dimensions. We show that the degrees of freedom in tightly confined dimensions, in particular with the presence of SOC, may significantly affect system properties. Specifically, in a quasi-one-dimensional atomic gas, a one-dimensional SOC can shift the positions of confinement-induced resonances whereas, in quasitwo- dimensional gases, a Rashba-type SOC tends to increase the two-body binding energy, such that more excited states in the tightly confined direction are occupied and the system is driven further away from a purely two-dimensional gas. The effects of the excited states can be incorporated by adopting an effective low-dimensional Hamiltonian having the form of a two-channel model. With the bare parameters fixed by two-body solutions, this effective Hamiltonian leads to qualitatively different many-body properties compared to a purely low-dimensional model.
We derive one-dimensional effective Hamiltonians for spin-orbit-coupled Fermi gases confined in quasi-one-dimensional trapping potentials. For an energy regime around the two-body bound-state energy, the effective Hamiltonian takes a two-channel form, where the populations in transverse excited levels are described by dressed molecules in the closed channel. For an energy regime slightly above the continuum threshold, the effective Hamiltonian takes a single-channel form, where low-energy physics is governed by the one-dimensional interacting strength determined by three-dimensional scattering length and transverse confinement. We further discuss the effect of spin-orbit coupling and effective Zeeman field on the position of confinement-induced resonances and show that these resonances can be understood as Feshbach resonances between the threshold of the transverse ground state and the two-body bound state associated with the transverse excited states. We expect that the shift of confinement-induced resonances can be observed under present experimental technology at attainable temperatures.
We study the superfluid transition in a quasi-two-dimensional Fermi gas with a magnetic field tuning through a Feshbach resonance. Using an effective two-dimensional Hamiltonian with renormalized interaction between atoms and dressed molecules, we investigate the Berezinskii-Kosterlitz-Thouless transition temperature by studying the phase fluctuation effect. We also take into account the trapping potential in the radial plane and discuss the number and superfluid density distributions. These results can be compared to experimental outcomes for gases prepared in one-dimensional optical lattices.
We present a detailed analysis of the two-channel atom-molecule effective Hamiltonian for an ultracold two-component homogeneous Fermi gas interacting near a Feshbach resonance. We particularly focus on the two-body and many-body properties of the dressed molecules in such a gas. An exact result for the many-body T matrix of the two-channel theory is derived by both considering coupled vertex equations and functional-integral methods. Making use of this result allows us to incorporate exactly into the many-body theory the two-body physics of the Feshbach scattering by means of simple analytical formulas without any fitting parameters. New interesting many-body effects are discussed in the case of narrow resonances. We give also a description of the BEC-BCS crossover above and below TC{T}_{C}TC​. The effects of different approximations for the self-energy of the dressed molecules are discussed. The single-channel results are derived as a special limit for broad resonances. Moreover, through an analytic analysis of the BEC limit, the relation between the composite boson of the single-channel model and the dressed-molecule of the two-channel model is established.
We theoretically investigate a Rashba spin-orbit-coupled Fermi gas near Feshbach resonances, by using mean-field theory and a two-channel model that takes into account explicitly Feshbach molecules in the closed channel. In the absence of spin-orbit coupling, when the channel coupling ggg between the closed and the open channels is strong, it is widely accepted that the two-channel model is equivalent to a single-channel model that excludes Feshbach molecules. This is the so-called broad resonance limit, which is well satisfied by ultracold atomic Fermi gases of 6{}^{6}6Li atoms and 40{}^{40}40K atoms in current experiments. Here, with Rashba spin-orbit coupling we find that the condition for equivalence becomes much more stringent. As a result, the single-channel model may already be insufficient to describe properly an atomic Fermi gas of 40{}^{40}40K atoms at a moderate spin-orbit coupling. We determine a characteristic channel coupling strength gc{g}_{c}gc​ as a function of the spin-orbit-coupling strength, above which the single-channel and two-channel models are approximately equivalent. We also find that for narrow resonance with small-channel coupling, the pairing gap and molecular fraction are strongly suppressed by SO coupling. Our results can be readily tested in 40{}^{40}40K atoms by using optical molecular spectroscopy.
We study the effects of induced interactions on the pairing gap, transition temperature, and chemical potential of a quasi-two-dimensional Fermi gas of atoms with spin-orbit coupling. We find that these mean-field parameters are significantly modified when induced interactions are taken into account. We also investigate the implications of induced interaction corrections for the BEC-BCS crossover driven by spin-orbit coupling, which happens even for small (compared to the Fermi energy) values of the binding energy.