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arXiv:1512.06669 · Physical Review A

Interplay between exotic superfluidity and magnetism in a chain of four-component ultracold atoms

E. Szirmai, Gergely Barcza, Jenő Sólyom, Örs Legeza

Published Jan 12, 2017• 9 citations
arXivHTMLPDF

Abstract

We investigate the spin-polarized chain of ultracold alkaline-earth-metal atoms with spin-3/2 described by the fermionic Hubbard model with SU(4) symmetric attractive interaction. The competition of bound pairs, trions, quartets, and unbound atoms is studied analytically and by density-matrix renormalization-group simulations. We find several distinct states where bound particles coexist with the ferromagnetic state of unpaired fermions. In particular, an exotic inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-type superfluid of quartets in a magnetic background of uncorrelated atoms is found for weaker interactions. We show that the system can be driven from this quartet-FFLO state to a molecular state of localized quartets where spatial segregation between molecular crystals and ferromagnetic liquids emerges, and this transition is reflected in the static structure factor.

DOI
10.1103/physreva.95.013610

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We investigate the spin-polarized chain of ultracold alkaline-earth-metal atoms with spin-3/2 described by the fermionic Hubbard model with SU(4) symmetric attractive interaction. The competition of bound pairs, trions, quartets, and unbound atoms is studied analytically and by density-matrix renormalization-group simulations. We find several distinct states where bound particles coexist with the ferromagnetic state of unpaired fermions. In particular, an exotic inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-type superfluid of quartets in a magnetic background of uncorrelated atoms is found for weaker interactions. We show that the system can be driven from this quartet-FFLO state to a molecular state of localized quartets where spatial segregation between molecular crystals and ferromagnetic liquids emerges, and this transition is reflected in the static structure factor.
By analyzing vortex lattices, re-entrant Cooper pairing, and Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states in a single theoretical framework, we explore how vortices and spin textures join to protect superconductivity against large magnetic fields. We use a rapidly rotating ultracold gas of fermionic atoms near unitarity as a model system amenable to experimental exploration and discover a hierarchy of spin-polarized and FFLO phases in which a metal or a band insulator of unpaired particles coexists with a spatially modulated superfluid hosting a vortex lattice. Quantum fluctuations can transform these phases into strongly correlated ``vortex-liquid'' metals and insulators, respectively. We argue that vortex lattices significantly enhance the stability of FFLO states and discuss prospects for observing these states in cold-atom experiments.
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.
We present a detailed study of the population imbalanced three-component Hubbard chain with attractive interactions. Such a system can be realized experimentally with three different hyperfine states of ultra cold 6^66Li atoms in an optical lattice. We find that there are different phases that compete with each other in this system: A molecular superfluid phase in which the three fermion species pair up to form molecules (trions), a usual pairing phase involving two species with exactly opposite momenta, and a more exotic generalized Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase consisting of three competing pairing tendencies with different non-zero center-of-mass momenta. At large attractive interactions the system exhibits strong tendencies towards collapse and phase separation. Employing the density-matrix-renormalization-group-method (DMRG) to determine the decay exponents of the various correlators we establish the phase diagram of this model for different fillings and interactions. We also discuss the experimentally relevant situation in a trap and report the existence of an additional region where two species are dynamically balanced.
We study the properties of a one-dimensional (1D) gas of fermions trapped in a lattice by means of the density matrix renormalization group method, focusing on the case of unequal spin populations, and strong attractive interaction. In the low-density regime, the system phase separates into a well-defined superconducting core and a fully polarized metallic cloud surrounding it. We argue that the superconducting phase corresponds to a 1D analog of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, with a quasicondensate of tightly bound bosonic pairs with a finite center-of-mass momentum that scales linearly with the magnetization. In the large density limit, the system allows for four phases: in the core, we either find a Fock state of localized pairs or a metallic shell with free spin-down fermions moving in a fully filled background of spin-up fermions. As the magnetization increases, the Fock state disappears to give room for a metallic phase, with a partially polarized superconducting FFLO shell and a fully polarized metallic cloud surrounding the core.
The formation of bound states of fermions in one dimension has always been one of the key topics in condensed matter physics. Motivated by recent experimental progresses in Prof. Jeremy Levy's group, we study the interplay of both species (spin and transverse band index) and mass imbalance in a mixture of two or more species of fermions with attractive interactions in one dimension. Previous theoretical and experimental efforts have shown the existence of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase for the case of two species with equal mass, in addition to the fully paired and fully polarized phases. For the unequal mass case, there are signatures of trion phases as well. We use DMRG to explore the rich possibilities of quantum phases and their transport signatures for the cases of two and more species of Fermions as we vary the interaction strengths and mass imbalances. With this we can gain insights into ongoing experiments with sketched nanowires in LAO/STO and ultracold atoms confined to one-dimensional tubes. We also study the formation of bound states in a single component Fermi chain with attractive interactions. The phase diagram, computed from DMRG (density matrix renormalization group), shows not only a superfluid of paired fermions (pair phase) and a liquid of fermion triplets (trion phase), but also a phase with two gapless modes. We show that the latter phase is described by a 2-component Tomonaga-Luttinger liquid (TLL) theory, consisting of one charged and one emergent neutral mode. We argue based on our numerical data, that the single, pair, and trion phases are descendants of the 2-component TLL theory. We speculate on the nature of the phase transitions amongst these phases.
Leveraging cutting-edge numerical methodologies, we study the ground state of the two-dimensional spin-polarized Fermi gas in an optical lattice. We focus on systems at high density and small spin polarization, corresponding to the parameter regime believed to be most favorable to the formation of the elusive Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid phase. Our systematic study of large lattice sizes, hosting nearly 500 atoms, provides strong evidence of the stability of the FFLO state in this regime, as well as a high-accuracy characterization of its properties. Our results for the density correlation function reveal the existence of density order in the system, suggesting the possibility of an intricate coexistence of long-range orders in the ground state. The ground-state properties are seen to differ significantly from the standard mean-field description, providing a compelling avenue for future theoretical and experimental explorations of the interplay between spin imbalance, strong interactions, and superfluidity in an exotic phase of matter.