π phases in balanced fermionic superfluids on spin-dependent optical lattices

Unconventional pairing in few-fermion systems at finite temperature

Attractively interacting two-component mixtures of fermionic particles confined in a one-dimensional harmonic trap are investigated. Properties of balanced and imbalanced systems are systematically explored with the exact diagonalization approach, focusing on the finite-temperature effects. Using single- and two-particle density distributions, specific non-classical pairing correlations are analyzed in terms of the noise correlations—quantity directly accessible in state-of-the-art experiments with ultra-cold atoms. It is shown that along with increasing temperature, any imbalanced system hosting Fulde–Ferrel–Larkin–Ovchinnikov pairs crossovers to a standard Bardeen-Cooper-Schrieffer one characterized by zero net momentum of resulting pairs. By performing calculations for systems with different imbalances, the approximate boundary between the two phases on a phase diagram is determined.

Creating State-Dependent Lattices for Ultracold Fermions by Magnetic Gradient Modulation

We demonstrate a versatile method for creating state-dependent optical lattices by applying a magnetic field gradient modulated in time. This allows for tuning the relative amplitude and sign of the tunneling for different internal states. We observe substantially different momentum distributions depending on the spin state of fermionic ^{40}K atoms. Using dipole oscillations, we probe the spin-dependent band structure and find good agreement with theory. In situ expansion dynamics demonstrate that one state can be completely localized while others remain itinerant. A systematic study shows negligible heating and lifetimes of several seconds in the Hubbard regime.

Mobile magnetic impurities in a Fermi superfluid: a route to designer molecules

A magnetic impurity in a fermionic superfluid hosts bound quasiparticle states known as Yu-Shiba-Rusinov states. We argue here that, if the impurity is mobile (i.e., has a finite mass), the impurity and its bound Yu-Shiba-Rusinov quasiparticle move together as a midgap molecule, which has an unusual "Mexican-hat" dispersion that is tunable via the fermion density. We map out the impurity dispersion, which consists of an "atomic" branch (in which the impurity is dressed by quasiparticle pairs) and a "molecular" branch (in which the impurity binds a quasiparticle). We discuss the experimental realization and detection of midgap Shiba molecules, focusing on Li-Cs mixtures, and comment on the prospects they offer for realizing exotic many-body states.

Topological transitions of gapless paired states in mixed-geometry lattices

We propose a mixed-geometry system of fermionic species selectively confined in lattices of different geometry. We investigate how such asymmetry can lead to exotic multiband fermion pairing in an example system of honeycomb and triangular lattices. A rich phase diagram of interband pairing with gapped and gapless excitations is found at zero temperature. We find that the two-band contribution of the honeycomb lattices to the paired state helps to stabilize the gapless phase with one or two Fermi surfaces. We also show that the Fermi surface topology further divides the gapless phase into subclasses between which the system undergoes density-driven Lifshitz transitions.

Triplet pair correlations in s-wave superfluids as a signature of the Fulde-Ferrell-Larkin-Ovchinnikov state

We show that antiparallel triplet pairing correlations are generated in superfluids with purely s-wave interactions whenever population imbalance enforces anisotropic Fulde-Ferrell (FF) or inhomogeneous Larkin-Ovchinikov (LO) states. These triplet correlations appear in the Cooper pair wave function, while the triplet part of the gap remains zero. The same set of quasiparticle states contributes to the triplet component and to the polarization, thus spatially correlating them. In the LO case, this set forms a narrow band of Andreev states centered on the nodes of the s-wave order parameter. This picture naturally provides a unifying explanation of previous findings that attractive p-wave interaction stabilizes FFLO states. We also study a similar triplet mixing which occurs when a balanced two-component system displays FFLO-type oscillations due to a spin-dependent optical lattice. We discuss how this triplet component can be measured in systems of ultracold atoms using a rapid ramp across a p-wave Feshbach resonance. This should provide a smoking gun signature of FFLO states.