Jami J. Kinnunen

Pairing Gap and In-Gap Excitations in Trapped Fermionic Superfluids

We consider trapped atomic Fermi gases with Feshbach-resonance enhanced interactions in pseudogap and superfluid temperatures. We calculate the spectrum of radio-frequency (or laser) excitations for transitions that transfer atoms out of the superfluid state. The spectrum displays the pairing gap and also the contribution of unpaired atoms, that is, in-gap excitations. The results support the conclusion that a superfluid, in which pairing is a manybody effect, was observed in recent experiments on radio-frequency spectroscopy of the pairing gap.

Strongly interacting Fermi gases with density imbalance.

We consider density-imbalanced Fermi gases of atoms in the strongly interacting, i.e., unitarity, regime. The Bogoliubov-de Gennes equations for a trapped superfluid are solved. They take into account the finite size of the system, as well as give rise to both phase separation and Fulde-Ferrel-Larkin-Ovchinnikov-type oscillations in the order parameter. We show how radio-frequency spectroscopy reflects the phase separation, and can provide direct evidence of the FFLO-type oscillations via observing the nodes of the order parameter.

Fermion pairing with spin-density imbalance in an optical lattice

We consider pairing in a two-component atomic Fermi gas, in a three-dimensional optical lattice, when the components have unequal densities, i.e. the gas is polarized. We show that a superfluid where the translational symmetry is broken by a finite Cooper pair momentum, namely a Fulde–Ferrel–Larkin–Ovchinnikov (FFLO)-type state, minimizes the Helmholtz free energy of the system. We demonstrate that such a state is clearly visible in the observable momentum distribution of the atoms, and analyse the dependence of the order parameter and the momentum distribution on the filling fraction and the interaction strength.

Signatures of superfluidity for Feshbach-Resonant Fermi gases

We consider atomic Fermi gases where Feshbach resonances can be used to study the whole BCS-Bose-Einstein condensate crossover. We show how a probing field transferring atoms out of the superfluid can be used to detect the onset of the superfluid transition in the high-T(c) and BCS regimes. The number of transferred atoms, as a function of the energy given by the probing field, peaks at the gap energy. The shape of the peak is asymmetric due to the single particle excitation gap. Since the excitation gap also includes a pseudogap contribution, the asymmetry alone is not a signature of superfluidity. The incoherent nature of the noncondensed pairs leads to broadening of the peak. The broadening decays below the critical temperature, causing a drastic increase in the asymmetry. This provides a signature of the transition.

The Fulde-Ferrell-Larkin-Ovchinnikov state for ultracold fermions in lattice and harmonic potentials: A review

We review the concepts and the present state of theoretical studies of spin-imbalanced superfluidity, in particular the elusive Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, in the context of ultracold quantum gases. The comprehensive presentation of the theoretical basis for the FFLO state that we provide is useful also for research on the interplay between magnetism and superconductivity in other physical systems. We focus on settings that have been predicted to be favourable for the FFLO state, such as optical lattices in various dimensions and spin-orbit coupled systems. These are also the most likely systems for near-future experimental observation of the FFLO state. Theoretical bounds, such as Blochs and Luttingers theorems, and experimentally important limitations, such as finite-size effects and trapping potentials, are considered. In addition, we provide a comprehensive review of the various ideas presented for the observation of the FFLO state. We conclude our review with an analysis of the open questions related to the FFLO state, such as its stability, superfluid density, collective modes and extending the FFLO superfluid concept to new types of lattice systems.

Sound velocity and dimensional crossover in a superfluid Fermi gas in an optical lattice

We study the sound velocity in cubic and noncubic three-dimensional optical lattices. We show how the van Hove singularity of the free Fermi gas is smoothed by interactions and eventually vanishes when interactions are strong enough. For noncubic lattices, we show that the speed of sound (Bogoliubov-Anderson phonon) shows clear signatures of dimensional crossover both in the one- and two-dimensional limits.

Induced interactions in a superfluid Bose-Fermi mixture

We analyse a Bose-Einstein condensate (BEC) mixed with a superfluid two-component Fermi gas in the whole BCS-BEC cross-over. Using a quasiparticle random phase approximation combined with Beliaev theory to describe the Fermi superfluid and the BEC respectively, we show that the single particle and collective excitations of the Fermi gas give rise to an induced interaction between the bosons, which varies strongly with momentum and frequency. It diverges at the sound mode of the Fermi superfluid, resulting in a sharp avoided crossing feature and a corresponding sign change of the interaction energy shift in the excitation spectrum of the BEC. In addition, the excitation of quasiparticles in the Fermi superfluid leads to damping of the excitations in the BEC. Besides studying induced interactions themselves, these prominent effects can be used to systematically probe the strongly interacting Fermi gas.

Exotic superfluid states of lattice fermions in elongated traps

We present real-space dynamical mean-field theory calculations for attractively interacting fermions in three-dimensional lattices with elongated traps. The critical polarization is found to be 0.8, regardless of the trap elongation. Below the critical polarization, we find unconventional superfluid structures where the polarized superfluid and Fulde-Ferrell-Larkin-Ovchinnikov-type states emerge across the entire core region.

One-dimensional Fermi polaron in a combined harmonic and periodic potential

We study an impurity in a one-dimensional potential consisting of a harmonic and a periodic part using both the time-evolving block decimation (TEBD) algorithm and a variational ansatz. Attractive and repulsive contact interactions with a sea of fermions are considered. We find excellent agreement between TEBD and variational results and use the variational ansatz to investigate higher lattice bands. We conclude that the lowest band approximation fails at sufficiently strong interactions and develop a new method for computing the Tan contact parameter.

Coexistence of pairing gaps in three-component Fermi gases

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 non-zero, 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.