Topological superfluidity with repulsive alkaline-earth atoms in optical lattices

Abstract

We discuss a realization of topological superfluidity with fermionic atoms in an optical lattice. We consider a situation where atoms in two internal states experience different lattice potentials: one species is localized and the other itinerant, and show how quantum fluctuations of the localized fermions give rise to an attraction and spin-orbit coupling in the itinerant band. At low temperature, these effects stabilize a topological superfluid of mobile atoms even if their bare interactions are repulsive. This emergent state can be engineered with alkaline-earth atoms in a superlattice with a dimerized unit cell. To probe its unique properties we describe protocols that use high spectral resolution and controllability of a narrow clock transition, such as momentum-resolved spectroscopy and supercurrent response to a synthetic (laser-induced) magnetic field.

Accurate projective two-band description of topological superfluidity in spin-orbit-coupled Fermi gases

“…(16) and with the chemical potential approximated by the analytical expressions from Eqs. (21) and (23). For the parameter ranges explored in this work, both routines yield practically indistinguishable results for |∆|, thus making it possible to adopt the simpler routine for further exploration of the physical ramifications of the 2×2-projected theory.…”

“…4(b) is an illustration, the approximations Eqs. (21) and (23) are accurate over the entire range of Zeeman energies h, including the critical value h c where both expression yield coinciding values. Thus, from the condition that the right-hand sides of (21) and (23) are equal, we can obtain an approximate expression for the phase boundary in h-λ space, The result (27) is consistent with the expectation that h c ≈ |µ c | for |∆| µ, which follows straightforwardly from (26), in conjunction with the validity of the approximation (23).…”

“…The observation that the exact 4 × 4-theory results for µ/E F and the approximate analytical expressions given in Eqs. (21) and (23) are practically indistinguishable at small-enough magnitude of spin-orbit coupling suggests the possibility to utilize these analytical formulae, for better efficiency and greater insight, as input into the self-consistent calculation of the s-wave pair potential. The analytical expression (23) could also be useful to more accurately represent the chemical potential in the low-h limit where the 2 × 2-projected results deviate significantly from those obtained from the exact 4 × 4 approach.…”

“…We now investigate in greater detail the physical picture provided by the effective two-band approach, where the self-consistency condition (13) is solved using Υ k ≡ Υ ↑ k with (25a) and approximating the chemical potential by Eqs. (21) and (23) as appropriate.…”

“…One of the important technical differences between these two platforms is the way how the Zeeman spin splitting is introduced. For superconductors, the required magnetic-field strengths are typically deleterious to superconductivity, motivating a search for alternative approaches [19][20][21]. Being unencumbered by this drawback, ultracold-atom realizations may offer a more direct avenue towards implementation of topological superfluidity.…”