Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1204.4187 · Journal of the Physical Society of Japan

Stability of FFLO States in Optical Lattices with Bilayer Structure

康晴 大川内, Akihisa Koga

Published Jun 8, 2012• 5 citations
arXivHTMLPDF

Abstract

We investigate the stability of the superfluid state in a bilayer fermionic optical lattice system with a confining potential, using the Bogoliubov de-Gennes equations. It is clarified that in the imbalanced case, the introduction of the interlayer hopping stabilizes the radial Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, while makes the angular FFLO state unstable. We also discuss the system size dependence of the superfluid ground state. It is clarified that in a certain ring region the A-FFLO state is indeed realized in a large system.

DOI
10.1143/jpsj.81.074001

Related papers

Fulde-Ferrell-Larkin-Ovchinnikov state in bilayer dipolar systems

Hao Lee, Sergey I. Matveenko, Daw-Wei Wang +1 more

We study the phase diagram of fermionic polar molecules in a bilayer system, with an imbalance of molecular densities of the layers. For the imbalance exceeding a critical value, the system undergoes a transition from the uniform interlayer superfluid to the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state with mostly a stripe structure, and at sufficiently large imbalance a transition from the FFLO to normal phase. Compared to the case of contact interactions, the FFLO regime is enhanced by the long-range character of the interlayer dipolar interaction, which can combine the $s$-wave and $p$-wave pairing in the order parameter.

arXiv:1705.06637•Physical Review A•Dec 14, 2017•9 citations

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

J. J. Kinnunen, J. E. Baarsma, J.-P. Martikainen +1 more

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:1706.07076•Reports on Progress in Physics•Jan 2, 2018•137 citations

Exploring exotic superfluidity of polarized ultracold fermions in optical lattices

Yan Chen, Z. D. Wang, Fu‐Chun Zhang +1 more

Superfluidity with imbalanced populations of harmonically trapped ultracold fermions in a two-dimensional optical lattice is investigated by solving the Bogoliubov-de Gennes equations. The intriguing richness of patterns between competing ferromagnetic and superfluid phases for different filling densities has been revealed. At low density, the main experimental features could be reproduced, especially the bimodal distribution of ferromagnetism. The superfluid-pairing gap oscillates radially, demonstrating the realization of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. In the high-density regime, another type of FFLO state with gap oscillation along the angular direction shows up and the accompanying ferromagnetic order modulates accordingly. The square lattice like FFLO state may appear at the intermediate densities. Moreover, we suggest other experimental proposals of observing the unique FFLO features straightforwardly.

arXiv:0710.5484•Physical Review B•Feb 11, 2009•34 citations

Fulde-Ferrell-Larkin-Ovchinnikov oscillations in harmonically trapped optical lattices

M. Iskin, Carl J. Williams

The attractive Fermi-Hubbard Hamiltonian is solved via the Bogoliubov-de Gennes formalism to analyze the ground state phases of population imbalanced two-component fermion mixtures in harmonically trapped optical lattices. In the low density limit, the superfluid order parameter has Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type oscillations in the radial direction towards the trap edges to accommodate the unpaired fermions that are pushed away from the trap center with a single peak in their density. However, in the high density limit, while the order parameter has oscillations in the radial direction towards the trap center for low imbalances, it also has oscillations towards the trap edges with increasing imbalance until the superfluid to normal phase transition occurs beyond a critical imbalance. This leads to a single peak in the density of unpaired fermions for low and high imbalances, but leads to double peaks for intermediate imbalances.

•Feb 27, 2008•0 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.

arXiv:1110.1799•Physical Review B•Apr 10, 2012•11 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.

arXiv:1009.3257•Physical Review A•Jun 16, 2011•47 citations
We investigate the stability of the superfluid state in a bilayer fermionic optical lattice system with a confining potential, using the Bogoliubov de-Gennes equations. It is clarified that in the imbalanced case, the introduction of the interlayer hopping stabilizes the radial Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, while makes the angular FFLO state unstable. We also discuss the system size dependence of the superfluid ground state. It is clarified that in a certain ring region the A-FFLO state is indeed realized in a large system.
We study the phase diagram of fermionic polar molecules in a bilayer system, with an imbalance of molecular densities of the layers. For the imbalance exceeding a critical value, the system undergoes a transition from the uniform interlayer superfluid to the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state with mostly a stripe structure, and at sufficiently large imbalance a transition from the FFLO to normal phase. Compared to the case of contact interactions, the FFLO regime is enhanced by the long-range character of the interlayer dipolar interaction, which can combine the sss-wave and ppp-wave pairing in the order parameter.
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.
Superfluidity with imbalanced populations of harmonically trapped ultracold fermions in a two-dimensional optical lattice is investigated by solving the Bogoliubov-de Gennes equations. The intriguing richness of patterns between competing ferromagnetic and superfluid phases for different filling densities has been revealed. At low density, the main experimental features could be reproduced, especially the bimodal distribution of ferromagnetism. The superfluid-pairing gap oscillates radially, demonstrating the realization of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. In the high-density regime, another type of FFLO state with gap oscillation along the angular direction shows up and the accompanying ferromagnetic order modulates accordingly. The square lattice like FFLO state may appear at the intermediate densities. Moreover, we suggest other experimental proposals of observing the unique FFLO features straightforwardly.
The attractive Fermi-Hubbard Hamiltonian is solved via the Bogoliubov-de Gennes formalism to analyze the ground state phases of population imbalanced two-component fermion mixtures in harmonically trapped optical lattices. In the low density limit, the superfluid order parameter has Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type oscillations in the radial direction towards the trap edges to accommodate the unpaired fermions that are pushed away from the trap center with a single peak in their density. However, in the high density limit, while the order parameter has oscillations in the radial direction towards the trap center for low imbalances, it also has oscillations towards the trap edges with increasing imbalance until the superfluid to normal phase transition occurs beyond a critical imbalance. This leads to a single peak in the density of unpaired fermions for low and high imbalances, but leads to double peaks for intermediate imbalances.
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 present the study of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing states in the ppp-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 ppp 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.