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 Bloch's and Luttinger's 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.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 Bloch's and Luttinger's 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.

arXiv:1706.07076Reports on Progress in PhysicsJan 2, 2018137 citations

Fulde-Ferrell-Larkin-Ovchinnikov states in Fermi-Fermi mixtures

Jibiao Wang, Qijin Chen

Bulletin of the American Physical SocietyMar 21, 20130 citations

The Fulde–Ferrell–Larkin–Ovchinnikov State in Quantum Rings

Andrzej Ptok

Journal of Superconductivity and Novel MagnetismApr 25, 201212 citations

Pure Fulde-Ferrell-Larkin-Ovchinnikov state in optical lattices

Ahai Chen, Gao Xianlong

We study the phase diagram of one-dimensional two-component attractive fermions on optical lattices with an off-diagonal confinement. We identify in this system a pure Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state with spatially modulated superfluidity and polarization in a large parameter window, which provides an easier playground in which to detect the FFLO state experimentally. The clear signature of the FFLO state is analyzed in the ground-state properties, the pair correlation function, and the magnetic structure factor, using the density-matrix renormalization-group method.We study the phase diagram of one-dimensional two-component attractive fermions on optical lattices with an off-diagonal confinement. We identify in this system a pure Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state with spatially modulated superfluidity and polarization in a large parameter window, which provides an easier playground in which to detect the FFLO state experimentally. The clear signature of the FFLO state is analyzed in the ground-state properties, the pair correlation function, and the magnetic structure factor, using the density-matrix renormalization-group method.

arXiv:1110.1799Physical Review BApr 10, 201211 citations

Stable Fulde-Ferrell-Larkin-Ovchinnikov pairing states in two-dimensional and three-dimensional optical lattices

Zi Cai, Yupeng Wang, Congjun Wu

We present the study of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing states in the $p$ -orbital bands in both two- and three-dimensional optical lattices. Due to the quasi-one-dimensional band structure which arises from the unidirectional hopping of the orthogonal $p$ orbitals, the pairing phase space is not affected by spin imbalance. Furthermore, interactions build up high-dimensional phase coherence which stabilizes the FFLO states in 2D and 3D optical lattices in a large parameter regime in the phase diagram. These FFLO phases are stable with the imposition of the inhomogeneous trapping potential. Their entropies are comparable to the normal states at finite temperatures.We present the study of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing states in the $p$-orbital bands in both two- and three-dimensional optical lattices. Due to the quasi-one-dimensional band structure which arises from the unidirectional hopping of the orthogonal $p$ orbitals, the pairing phase space is not affected by spin imbalance. Furthermore, interactions build up high-dimensional phase coherence which stabilizes the FFLO states in 2D and 3D optical lattices in a large parameter regime in the phase diagram. These FFLO phases are stable with the imposition of the inhomogeneous trapping potential. Their entropies are comparable to the normal states at finite temperatures.

arXiv:1009.3257Physical Review AJun 16, 201147 citations

We present the study of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing states in the

p

-orbital bands in both two- and three-dimensional optical lattices. Due to the quasi-one-dimensional band structure which arises from the unidirectional hopping of the orthogonal

p

orbitals, the pairing phase space is not affected by spin imbalance. Furthermore, interactions build up high-dimensional phase coherence which stabilizes the FFLO states in 2D and 3D optical lattices in a large parameter regime in the phase diagram. These FFLO phases are stable with the imposition of the inhomogeneous trapping potential. Their entropies are comparable to the normal states at finite temperatures.