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arXiv:1610.03352 · Physical Review A

Topological superfluidity of lattice fermions inside a Bose-Einstein condensate

Jonatan Melkær Midtgaard, Zhigang Wu, Georg M. Bruun

Published Dec 22, 2016• 20 citations
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Abstract

We calculate the phase diagram of identical fermions in a two-dimensional lattice immersed in a three-dimensional Bose-Einstein condensate (BEC). The fermions exchange density fluctuations in the BEC, which gives rise to an attractive induced interaction. The resulting zero-temperature phase diagram exhibits topological ${p}_{x}+i{p}_{y}$ superfluid phases as well as a phase separation region. We show how to use the flexibility of the Bose-Fermi mixture to tune the induced interaction, so that it maximizes the pairing between nearest-neighbor sites, whereas phase separation originating from long-range interactions is suppressed. Finally, we calculate the Berezinskii-Kosterlitz-Thouless critical temperature of the topological superfluid in the lattice and discuss experimental realizations.

DOI
10.1103/physreva.94.063631

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We show that a 2D spin-polarized Fermi gas immersed in a 3D Bose-Einstein condensate constitutes a very promising system for realizing a p_{x}+ip_{y} superfluid. The fermions attract each other via an induced interaction mediated by the bosons, and the resulting pairing is analyzed with retardation effects fully taken into account. This is further combined with Berezinskii-Kosterlitz-Thouless (BKT) theory to obtain reliable results for the superfluid critical temperature. We show that both the strength and the range of the induced interaction can be tuned experimentally, which can be used to make the critical temperature approach the maximum value allowed by general BKT theory. Moreover, this is achieved while keeping the Fermi-Bose interaction weak so that three-body losses are small. Our results show that realizing a topological superfluid with atomic Fermi-Bose mixtures is within experimental reach.
We analyze the stability of inhomogeneous superfluid phases in a system consisting of identical fermions confined in two layers that are immersed in a Bose-Einstein condensate (BEC). The fermions in the two layers interact via an induced interaction mediated by the BEC, which gives rise to pairing. We present zero-temperature phase diagrams varying the chemical potential difference between the two layers and the range of the induced interaction, and show that there is a large region where an inhomogeneous superfluid phase is the ground state. This region grows with increasing range of the induced interaction and it can be much larger than for a corresponding system with a short-range interaction. The range of the interaction is controlled by the healing length of the BEC, which makes the present system a powerful tunable platform to stabilize inhomogeneous superfluid phases. We furthermore analyze the melting of the superfluid phases in the layers via phase fluctuations as described by the Berezinskii-Kosterlitz-Thouless mechanism and show that the normal, homogeneous, and inhomogeneous superfluid phases meet in a tricritical point. The superfluid density of the inhomogeneous superfluid phase is reduced by inherent gapless excitations, and we demonstrate that this leads to a significant suppression of the critical temperature as compared to the homogeneous superfluid phase.
Using the Gaussian pair fluctuation theory, we investigate quantum fluctuations of a strongly interacting two-dimensional chiral ppp-wave Fermi superfluid at the transition from a Bose-Einstein condensate (BEC) to a topologically nontrivial Bardeen-Cooper-Schrieffer superfluid. Near the topological phase transition at zero chemical potential, $\ensuremath{\mu}=0$, we observe that quantum fluctuations strongly renormalize the zero-temperature equations of state, sound velocity, pair-breaking velocity, and Berezinskii-Kosterlitz-Thouless (BKT) critical temperature of the Fermi superfluid, all of which can be nonanalytic functions of the interaction strength. The indication of nonanalyticity is particularly evident in the BKT critical temperature, which also exhibits a pronounced peak near the topological phase transition. Across the transition and towards the BEC limit we find that the system quickly becomes a trivial interacting Bose liquid, whose properties are less dependent on the interparticle interaction. The qualitative behavior of composite bosons in the BEC limit remains to be understood.
We analyze the phase diagram of superfluidity for two-species fermion mixtures from the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) limit as a function of scattering parameter, population imbalance, and mass anisotropy. We identify regions corresponding to normal, or uniform or nonuniform superfluid phases, and discuss topological quantum phase transitions in the BCS, unitarity, and BEC limits. We derive the Ginzburg-Landau equation near the critical temperature, and show that it describes a dilute mixture of paired and unpaired fermions in the BEC limit. We also obtain the zero temperature low frequency and long wavelength collective excitation spectrum, and recover the Bogoliubov relation for weakly interacting dilute bosons in the BEC limit. Lastly, we discuss the effects of harmonic traps and the resulting density profiles in the BEC regime.
A mixed dimensional system of fermions in two layers immersed in a Bose-Einstein condensate (BEC) is shown to be a promising setup to realize topological superfluids with time-reversal symmetry (TRS). The induced interaction between the fermions mediated by the BEC gives rise to a competition between ppp-wave pairing within each layer and sss-wave pairing between the layers. When the layers are far apart, intralayer pairing dominates and the system forms a topological superfluid either with or without TRS. With decreasing layer separation or increasing BEC coherence length, interlayer pairing sets in. We show that this leads either to a second-order transition breaking TRS where the edge modes gradually become gapped or to a first-order transition to a topologically trivial sss-wave superfluid. Our results provide a realistic road map for experimentally realizing a topological superfluid with TRS in a cold atomic system.
We propose to use a one-dimensional system consisting of identical fermions in a periodically driven lattice immersed in a Bose gas, to realise topological superfluid phases with Chern numbers larger than 1. The bosons mediate an attractive induced interaction between the fermions, and we derive a simple formula to analyse the topological properties of the resulting pairing. When the coherence length of the bosons is large compared to the lattice spacing and there is a significant next-nearest neighbour hopping for the fermions, the system can realise a superfluid with Chern number ±2. We show that this phase is stable in a large region of the phase diagram as a function of the filling fraction of the fermions and the coherence length of the bosons. Cold atomic gases offer the possibility to realise the proposed system using well-known experimental techniques.