[Paper Review] Imbalanced thee-component Fermi gas with attractive interactions: Multiple FFLO-pairing, Bose-Fermi and Fermi-Fermi mixtures versus collapse and phase separation

Andreas Lüscher, Andreas Laeuchli|ArXiv.org|Jun 4, 2009

Cold Atom Physics and Bose-Einstein Condensates1 references3 citations

TL;DR

This study investigates the phase diagram of an imbalanced three-component Fermi gas with attractive interactions in a one-dimensional optical lattice using the density-matrix renormalization group (DMRG) method. It identifies competing pairing phases—trion superfluidity, conventional pairing, and multiple FFLO states with distinct center-of-mass momenta—while revealing collapse and phase separation at strong attraction, with trap-induced dynamical balancing of two species at the trap center.

ABSTRACT

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 $^6$Li 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.

Motivation & Objective

• To understand the interplay of trion formation, multiple FFLO pairing, and phase separation in an imbalanced three-component Fermi gas with attractive interactions.
• To determine the stability and nature of pairing phases in a one-dimensional Hubbard model with three fermionic species and unequal population.
• To investigate the effects of strong attractive interactions, including collapse and phase separation, and their signatures in correlation functions.
• To explore the impact of harmonic trapping on the phase diagram, particularly the emergence of dynamically balanced species at the trap center.
• To compare the non-integrable lattice model with previous results from integrable continuum models, highlighting richer physics due to multi-particle composites and instabilities.

Proposed method

• The study employs the density-matrix renormalization group (DMRG) method to compute correlation functions and decay exponents in the three-component attractive Hubbard chain.
• The model Hamiltonian includes nearest-neighbor hopping (t = 1) and SU(3)-invariant on-site attractive interactions (U < 0) for three fermionic hyperfine states.
• Correlation functions such as Green's functions, pair correlations (Pαβ), and trion correlations (Tαβγ) are computed to identify dominant pairing tendencies.
• Phase boundaries are determined by analyzing the decay exponents ν of correlation functions, with the slowest-decaying correlation defining the dominant phase.
• The trap potential is introduced as H_trap = V Σ(l - (L+1)/2)^2 n_i to simulate experimental harmonic confinement and study inhomogeneous density profiles.
• The analysis compares single-particle Green's functions with two-particle correlations to assess dimensional crossover and the onset of FFLO or Fermi liquid behavior.

Experimental results

Research questions

• RQ1 What are the dominant pairing phases in a three-component Fermi gas with population imbalance and attractive interactions in one dimension?
• RQ2 How do multiple FFLO pairing states with different center-of-mass momenta compete, and which dominates under varying imbalance and interaction strength?
• RQ3 What is the role of trion formation and multi-particle composite states in stabilizing superfluidity away from the symmetric point?
• RQ4 How do strong attractive interactions lead to collapse and phase separation, and what are the signatures of these instabilities in correlation functions?
• RQ5 How does harmonic trapping modify the phase diagram, particularly in inducing dynamical balance between two species at the trap center?

Key findings

• Multiple FFLO pairing modes with distinct non-zero center-of-mass momenta coexist and compete in the imbalanced three-component Fermi gas, especially near the symmetric point.
• Trion superfluidity dominates only near the centroid of the density triangle; otherwise, it is suppressed by stronger pairing correlations.
• At strong attractive interactions (|U|/t > 1), the system exhibits strong tendencies toward collapse and phase separation, with multi-particle composite liquids forming near the instability boundary.
• In the presence of a harmonic trap, the system reorganizes such that two species achieve equal density at the trap center, leading to BCS-like pairing with zero momentum and loss of FFLO signatures.
• The phase diagram is richer than in integrable continuum models due to the formation of multi-particle composites and instabilities not present in the integrable limit.
• At intermediate coupling, the dominant correlation boundaries align with lines of equal density difference, indicating a strong influence of population imbalance on pairing stability.