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Register a new userCoexistence of pairing gaps in three-component Fermi gases
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We study a three-component superfluid Fermi gas in a spherically symmetric harmonic trap using the Bogoliubov-deGennes method. We predict a coexistence phase in which two pairing field order parameters are simultaneously nonzero, in stark contrast to studies performed for trapped gases using local density approximation. We also discuss the role of atom number conservation in the context of a homogeneous system.
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The superfluidity and pairing phenomena in ultracold atomic Fermi gases have been of great interest in recent years, with multiple tunable parameters. Here we study the BCS-BEC crossover behavior of balanced two-component Fermi gases in a one-dimensional optical lattice, which is distinct from the simple three-dimensional (3D) continuum and a fully 3D lattice often found in a condensed matter system. We use a pairing fluctuation theory which includes self-consistent feedback effects at finite temperatures, and find widespread pseudogap phenomena beyond the BCS regime. As a consequence of the lattice periodicity, the superfluid transition temperature $T_c$ decreases with pairing strength in the BEC regime, where it approaches asymptotically $T_c = pi an/2m$, with $a$ being the $s$-wave scattering length, and $n$ ($m$) the fermion density (mass). In addition, the quasi-two dimensionality leads to fast growing (absolute value of the) fermionic chemical potential $mu$ and pairing gap $Delta$, which depends exponentially on the ratio $d/a$. Importantly, $T_c$ at unitarity increases with the lattice constant $d$ and hopping integral $t$. The effect of the van Hove singularity on $T_c$ is identified. The superfluid density exhibits $T^{3/2}$ power laws at low $T$, away from the extreme BCS limit. These predictions can be tested in future experiments.
In this paper, we study the effect of population imbalance and its interplay with pairing strength and lattice effect in atomic Fermi gases in a one-dimensional optical lattice. We compute various phase diagrams as the system undergoes BCS-BEC crossover, using the same pairing fluctuation theory as in Part I. We find widespread pseudogap phenomena beyond the BCS regime and intermediate temperature superfluid states for relatively low population imbalances. The Fermi surface topology plays an important role in the behavior of $T_text{c}$. For large $d$ and/or small $t$, which yield an open Fermi surface, superfluidity can be readily destroyed by a small amount of population imbalance $p$. The superfluid phase, especially in the BEC regime, can exist only for a highly restricted volume of the parameter space. Due to the continuum-lattice mixing, population imbalance gives rise to a new mechanism for pair hopping, as assisted by excessive majority fermions, which may lead to significant enhancement of $T_text{c}$ on the BEC side of the Feshbach resonance, and also render $T_text{c}$ approaching a constant asymptote in the BEC limit, when it exists. Furthermore, we find that not all minority fermions will be paired up in BEC limit, unlike the 3D continuum case. These predictions can be tested in future experiments.
We review the status of cooling techniques aimed at achieving the deepest quantum degeneracy for atomic Fermi gases. We first discuss some physical motivations, providing a quantitative assessment of the need for deep quantum degeneracy in relevant physics cases, such as the search for unconventional superfluid states. Attention is then focused on the most widespread technique to reach deep quantum degeneracy for Fermi systems, sympathetic cooling of Bose-Fermi mixtures, organizing the discussion according to the specific species involved. Various proposals to circumvent some of the limitations on achieving the deepest Fermi degeneracy, and their experimental realizations, are then reviewed. Finally, we discuss the extension of these techniques to optical lattices and the implementation of precision thermometry crucial to the understanding of the phase diagram of classical and quantum phase transitions in Fermi gases.
We study the collisionless dynamics of two classes of nonintegrable pairing models. One is a BCS model with separable energy-dependent interactions, the other - a 2D topological superconductor with spin-orbit coupling and a band-splitting external field. The long-time quantum quench dynamics at integrable points of these models are well understood. Namely, the squared magnitude of the time-dependent order parameter $Delta(t)$ can either vanish (Phase I), reach a nonzero constant (Phase II), or periodically oscillate as an elliptic function (Phase III). We demonstrate that nonintegrable models too exhibit some or all of these nonequilibrium phases. Remarkably, elliptic periodic oscillations persist, even though both their amplitude and functional form change drastically with integrability breaking. Striking new phenomena accompany loss of integrability. First, an extremely long time scale emerges in the relaxation to Phase III, such that short-time numerical simulations risk erroneously classifying the asymptotic state. This time scale diverges near integrable points. Second, an entirely new Phase IV of quasiperiodic oscillations of $|Delta|$ emerges in the quantum quench phase diagrams of nonintegrable pairing models. As integrability techniques do not apply for the models we study, we develop the concept of asymptotic self-consistency and a linear stability analysis of the asymptotic phases. With the help of these new tools, we determine the phase boundaries, characterize the asymptotic state, and clarify the physical meaning of the quantum quench phase diagrams of BCS superconductors. We also propose an explanation of these diagrams in terms of bifurcation theory.
Some thoughts regarding pairing in atomic Fermi gases were considered, meant for starting discussion on the topic.
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