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:0811.0555 · Physical Review A

Three-component Fermi gas in a one-dimensional optical lattice

P. Azaria, Sylvain Capponi, P. Lecheminant

Published Oct 19, 2009• 47 citations
arXivHTMLPDF

Abstract

We investigate the effect of the anisotropy between the $s$-wave scattering lengths of a three-component atomic Fermi gas loaded into a one-dimensional optical lattice. We find four different phases which support trionic instabilities made of bound states of three fermions. These phases distinguish themselves by the relative phases between the $2{k}_{F}$ atomic density wave fluctuations of the three species. At small enough densities and strong anisotropies we give further evidences for a decoupling and the stabilization of more conventional BCS phases. Finally, our results are discussed in light of a recent experiment on $^{6}\text{L}\text{i}$ atoms.

DOI
10.1103/physreva.80.041604

Related papers

Fractionalization in Three-Components Fermionic Atomic Gases in a One-Dimensional Optical Lattice

P. Azaria

We study a three-components fermionic gas loaded in a one-dimensional optical trap at half-filling. We find that the system is fully gapped and may order into 8 possible phases: four 2$k_F$ atomic density wave and spin-Peierls phases with all possible relative $π$ phases shifts between the three species. We find that trionic excitations are unstable toward the decay into pairs of kinks carrying a {\it fractional} number, $Q=3/2$, of atoms. These sesquions eventually condense upon small doping and are described by a Luttinger liquid. We finally discuss the phase diagram of a three component mixture made of three hyperfine level of $^6$Li as a function of magnetic field.

arXiv:1011.2944•Nov 12, 2010•0 citations

BCS-BEC crossover and effects of density fluctuations in a two-component Fermi gas loaded on an optical lattice

Hiromasa Tamaki, Yoji Ohashi, Miyake, K.

We investigate the superfluid phase transition in a gas of Fermi atoms loaded on a three-dimensional optical lattice. When the lattice potential is strong, this system can be well described by an attractive Hubbard model. In this model, we calculate the superfluid phase transition temperature Tc, including both superfluid and (spin and charge) density fluctuations within the self-consistent t-matrix theory and fluctuation exchange approximation, respectively. Since we treat these fluctuations in a consistent manner, our theory satisfies the required particle-hole symmetry over the entire BCS-BEC crossover region. We show that charge density fluctuations compete against superfluid fluctuations near the half-filling, leading to the suppression of Tc. As a result, the maximum Tc is obtained away the half-filling. Since the strong density fluctuations originate from the nesting property of the Fermi surface at the half filling (which is absent in a uniform gas with no lattice potential), our results would be useful in considering lattice effects on strong-coupling superfluidity.

arXiv:0803.2084•Mar 14, 2008•1 citation

Superfluidity and pairing phenomena in ultracold atomic Fermi gases in one-dimensional optical lattices. I. Balanced case

Jibiao Wang, Leifeng Zhang, Yi Yu +2 more

The superfluidity and pairing phenomena in ultracold atomic Fermi gases have been of great interest in recent years, with multiple tunable parameters. Here we study the BCS-BEC crossover behavior of balanced two-component Fermi gases in a one-dimensional optical lattice, which is distinct from the simple three-dimensional (3D) continuum and a fully 3D lattice often found in a condensed matter system. We use a pairing fluctuation theory which includes self-consistent feedback effects at finite temperatures and find widespread pseudogap phenomena beyond the BCS regime. As a consequence of the lattice periodicity, the superfluid transition temperature ${T}_{\mathrm{c}}$ decreases with pairing strength in the BEC regime, where it approaches asymptotically ${T}_{\mathrm{c}}=\ensuremath{\pi}an/2m$, with $a$ being the $s$-wave scattering length, and $n$ ($m$) the fermion density (mass). In addition, the quasi-two dimensionality leads to fast-growing (absolute value of the) fermionic chemical potential $\ensuremath{\mu}$ and pairing gap $\mathrm{\ensuremath{\Delta}}$, which depends exponentially on the ratio $d/a$. Importantly, ${T}_{\mathrm{c}}$ at unitarity increases with the lattice constant $d$ and hopping integral $t$. The effect of the van Hove singularity on ${T}_{\mathrm{c}}$ is identified. The superfluid density exhibits ${T}^{3/2}$ power laws at low $T$, away from the extreme BCS limit. These predictions can be tested in future experiments.

arXiv:2001.00545•Physical Review A•May 11, 2020•6 citations

Superfluid State of Repulsively Interacting Three-Component Fermionic Atoms in Optical Lattices

Kensuke Inaba, Sei-ichiro Suga

We investigate the superfluid state of repulsively interacting three-component (color) fermionic atoms in optical lattices. When the anisotropy of the three repulsive interactions is strong, atoms of two of the three colors form Cooper pairs and atoms of the third color remain a Fermi liquid. An effective attractive interaction is induced by density fluctuations of the third-color atoms. This superfluid state is stable against changes in filling close to half filling. We determine the phase diagrams in terms of temperature, filling, and the anisotropy of the repulsive interactions.

arXiv:1205.5964•Physical Review Letters•Jun 18, 2012•23 citations

Crystallization of trions in SU(3) cold-atom gases trapped in optical lattices

Rafael A. Molina, J. Dukelsky, Peter Schmitteckert

Cold fermionic atoms with three different hyperfine states confined in optical lattices show pronounced atomic density waves (ADWs). These ADWs are pinned due to the confining potential that traps the atoms in the optical lattice and can be considered a crystal phase of strongly bound trions (CPT). We show that the crystalline phase is incompressible and robust against anisotropic interactions. We also show that it is generic in the presence of the trap due to its incompressibility. Numeric density matrix renormalization group calculations show evidence of a crossover between a trionic superfluid and the CPT state as a function of the strength of the interaction and as a function of the anisotropy of the interaction.

arXiv:0807.1886•Physical Review A•Jul 28, 2009•17 citations

Finite-temperature properties of attractive three-component fermionic atoms in optical lattices

Kensuke Inaba, Sei-ichiro Suga

We investigate the finite-temperature properties of attractive three-component (colors) fermionic atoms in optical lattices using a self-energy functional approach. As the strength of the attractive interaction increases in the low-temperature region, we observe a second-order transition from a Fermi liquid to a color superfluid (CSF), where atoms from two of the three colors form Cooper pairs. In the strong attractive region, we observe a first-order transition from a CSF to a trionic state, where three atoms with different colors form singlet bound states. A crossover between a Fermi liquid and a trionic state is observed in the high-temperature region. We present a phase diagram covering zero to finite temperatures. We demonstrate that the CSF transition temperature is enhanced by the anisotropy of the attractive interaction.

arXiv:0910.0648•Physical Review A•Oct 14, 2009•41 citations
We investigate the effect of the anisotropy between the sss-wave scattering lengths of a three-component atomic Fermi gas loaded into a one-dimensional optical lattice. We find four different phases which support trionic instabilities made of bound states of three fermions. These phases distinguish themselves by the relative phases between the 2kF2{k}_{F}2kF​ atomic density wave fluctuations of the three species. At small enough densities and strong anisotropies we give further evidences for a decoupling and the stabilization of more conventional BCS phases. Finally, our results are discussed in light of a recent experiment on 6Li^{6}\text{L}\text{i}6Li atoms.
We study a three-components fermionic gas loaded in a one-dimensional optical trap at half-filling. We find that the system is fully gapped and may order into 8 possible phases: four 2kFk_FkF​ atomic density wave and spin-Peierls phases with all possible relative πππ phases shifts between the three species. We find that trionic excitations are unstable toward the decay into pairs of kinks carrying a {\it fractional} number, Q=3/2Q=3/2Q=3/2, of atoms. These sesquions eventually condense upon small doping and are described by a Luttinger liquid. We finally discuss the phase diagram of a three component mixture made of three hyperfine level of 6^66Li as a function of magnetic field.
We investigate the superfluid phase transition in a gas of Fermi atoms loaded on a three-dimensional optical lattice. When the lattice potential is strong, this system can be well described by an attractive Hubbard model. In this model, we calculate the superfluid phase transition temperature Tc, including both superfluid and (spin and charge) density fluctuations within the self-consistent t-matrix theory and fluctuation exchange approximation, respectively. Since we treat these fluctuations in a consistent manner, our theory satisfies the required particle-hole symmetry over the entire BCS-BEC crossover region. We show that charge density fluctuations compete against superfluid fluctuations near the half-filling, leading to the suppression of Tc. As a result, the maximum Tc is obtained away the half-filling. Since the strong density fluctuations originate from the nesting property of the Fermi surface at the half filling (which is absent in a uniform gas with no lattice potential), our results would be useful in considering lattice effects on strong-coupling superfluidity.
The superfluidity and pairing phenomena in ultracold atomic Fermi gases have been of great interest in recent years, with multiple tunable parameters. Here we study the BCS-BEC crossover behavior of balanced two-component Fermi gases in a one-dimensional optical lattice, which is distinct from the simple three-dimensional (3D) continuum and a fully 3D lattice often found in a condensed matter system. We use a pairing fluctuation theory which includes self-consistent feedback effects at finite temperatures and find widespread pseudogap phenomena beyond the BCS regime. As a consequence of the lattice periodicity, the superfluid transition temperature Tc{T}_{\mathrm{c}}Tc​ decreases with pairing strength in the BEC regime, where it approaches asymptotically ${T}_{\mathrm{c}}=\ensuremath{\pi}an/2m$, with aaa being the sss-wave scattering length, and nnn (mmm) the fermion density (mass). In addition, the quasi-two dimensionality leads to fast-growing (absolute value of the) fermionic chemical potential $\ensuremath{\mu}$ and pairing gap $\mathrm{\ensuremath{\Delta}}$, which depends exponentially on the ratio d/ad/ad/a. Importantly, Tc{T}_{\mathrm{c}}Tc​ at unitarity increases with the lattice constant ddd and hopping integral ttt. The effect of the van Hove singularity on Tc{T}_{\mathrm{c}}Tc​ is identified. The superfluid density exhibits T3/2{T}^{3/2}T3/2 power laws at low TTT, away from the extreme BCS limit. These predictions can be tested in future experiments.
We investigate the superfluid state of repulsively interacting three-component (color) fermionic atoms in optical lattices. When the anisotropy of the three repulsive interactions is strong, atoms of two of the three colors form Cooper pairs and atoms of the third color remain a Fermi liquid. An effective attractive interaction is induced by density fluctuations of the third-color atoms. This superfluid state is stable against changes in filling close to half filling. We determine the phase diagrams in terms of temperature, filling, and the anisotropy of the repulsive interactions.
Cold fermionic atoms with three different hyperfine states confined in optical lattices show pronounced atomic density waves (ADWs). These ADWs are pinned due to the confining potential that traps the atoms in the optical lattice and can be considered a crystal phase of strongly bound trions (CPT). We show that the crystalline phase is incompressible and robust against anisotropic interactions. We also show that it is generic in the presence of the trap due to its incompressibility. Numeric density matrix renormalization group calculations show evidence of a crossover between a trionic superfluid and the CPT state as a function of the strength of the interaction and as a function of the anisotropy of the interaction.
We investigate the finite-temperature properties of attractive three-component (colors) fermionic atoms in optical lattices using a self-energy functional approach. As the strength of the attractive interaction increases in the low-temperature region, we observe a second-order transition from a Fermi liquid to a color superfluid (CSF), where atoms from two of the three colors form Cooper pairs. In the strong attractive region, we observe a first-order transition from a CSF to a trionic state, where three atoms with different colors form singlet bound states. A crossover between a Fermi liquid and a trionic state is observed in the high-temperature region. We present a phase diagram covering zero to finite temperatures. We demonstrate that the CSF transition temperature is enhanced by the anisotropy of the attractive interaction.