Coherent coupling generated by laser light between the hyperfine states of atoms, loaded in a one-dimensional (1D) optical lattice, gives rise to the synthetic dimension'' system which is equivalent to a Hofstadter model in a finite strip of square lattice. An SU($M$) symmetric attractive interaction in conjunction with the synthetic gauge field present in this system gives rise to unusual effects. We study the two-body problem of the system using the $T$-matrix formalism. We show that the two-body ground states pick up a finite momentum and can transform into two-body resonancelike features in the scattering continuum with a large change in the phase shift. As a result, even for this 1D system, a critical amount of attraction is needed to form bound states. These phenomena have spectacular effects on the many-body physics of the system analyzed using the numerical density matrix renormalization group technique. We show that the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states form in the system even for a balanced'' gas and the FFLO momentum of the pairs scales linearly with flux. Considering suitable measures, we investigate interesting properties of these states. We also discuss a possibility of realization of a generalized interesting topological model, called the Creutz ladder.
Spin-polarized attractive Fermi gases in one-dimensional (1D) optical lattices are expected to be remarkably good candidates for the observation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We model these systems with an attractive Hubbard model with population imbalance. By means of the density-matrix renormalization-group method, we compute the pairing correlations as well as the static spin and charge structure factors in the whole range from weak to strong coupling. We demonstrate that pairing correlations exhibit quasi-long-range order and oscillations at the wave number expected from the FFLO theory. However, we also show by numerically computing the mixed spin-charge static structure factor that charge and spin degrees of freedom appear to be coupled already for a small imbalance. We discuss the consequences of this coupling for the observation of the FFLO phase, as well as for the stabilization of the quasi-long-range order into long-range order by coupling many identical 1D systems, such as in quasi-1D optical lattices.
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 consider the quasi-one-dimensional (quasi-1D) system realized by an array of weakly coupled parallel one-dimensional ``tubes'' in a two-dimensional lattice which permits free motion of atoms in an axial direction in the presence of a Zeeman field, Rashba type spin-orbit coupling (SOC), and an
s-wave attractive interaction, while the radial motion is tightly confined. We solve the zero-temperature (
T=0) Bogoliubov--de Gennes (BdG) equations for the quasi-1D Fermi gas with the dispersion modified by tunneling between the tubes and show that the
T=0 phase diagram hosts the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase with nonzero center-of-mass momentum Cooper pairs for small values of the SOC while for larger values of the SOC and high Zeeman fields the uniform superfluid phase with zero center-of-mass momentum Cooper pairs has an instability towards the topological uniform superfluid phase with Majorana fermions at the tube ends. Also, we show that tuning the two-dimensional optical lattice strength in this model allows one to explore the crossover behaviors of the phases during the transition between the three-dimensional and 1D systems and in general the FFLO (for small SOC) and the topological uniform superfluid phase (for large SOC) are favored as the system becomes more one dimensional. We also find evidence of the existence of a Zeeman-tuned topological quantum phase transition (TQPT) within the FFLO phase itself and, for large values of the Zeeman field and small SOC, the TQPT gives rise to a topologically distinct FFLO phase.
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.
We present a full phase diagram for the one-dimensional (1D) to three-dimensional (3D) crossover of the Fulde-Ferrell--Larkin-Ovchinnikov (FFLO) state in an attractive Hubbard model of 3D-coupled chains in a harmonic trap. We employ real-space dynamical mean-field theory which describes full local quantum fluctuations beyond the usual mean-field and local density approximation. We find strong dimensionality effects on the shell structure undergoing a crossover between distinctive quasi-1D and quasi-3D regimes. We predict an optimal regime for the FFLO state that is considerably extended to intermediate interchain couplings and polarizations, directly realizable with ultracold atomic gases. We find that the 1D-like FFLO feature is vulnerable to thermal fluctuations, while the FFLO state of mixed 1D-3D character can be stabilized at a higher temperature.
The ``synthetic dimension'' proposal [A. Celi et al., Phys. Rev. Lett. 112, 043001 (2014)] uses atoms with
M internal states (``flavors'') in a one-dimensional (1D) optical lattice, to realize a hopping Hamiltonian equivalent to the Hofstadter model (tight-binding model with a given magnetic flux per plaquette) on an
M-sites-wide square lattice strip. We investigate the physics of
SU(M) symmetric interactions in the synthetic dimension system. We show that this system is equivalent to particles [with
SU(M) symmetric interactions] experiencing an
SU(M) Zeeman field at each lattice site and a non-Abelian
SU(M) gauge potential that affects their hopping. This equivalence brings out the possibility of generating nonlocal interactions between particles at different sites of the optical lattice. In addition, the gauge field induces a flavor-orbital coupling, which mitigates the ``baryon breaking'' effect of the Zeeman field. For
M particles, concomitantly, the
SU(M) singlet baryon which is site localized in the usual 1D optical lattice, is deformed to a nonlocal object (``squished baryon''). We conclusively demonstrate this effect by analytical arguments and exact (numerical) diagonalization studies. Our study promises a rich many-body phase diagram for this system. It also uncovers the possibility of using the synthetic dimension system to laboratory realize condensed-matter models such as the
SU(M) random flux model, inconceivable in conventional experimental systems.