Motivated by recent experimental development, we investigate spin-orbit coupled repulsive Fermi atoms in a one-dimensional optical lattice. Using the density-matrix renormalization group method, we calculate momentum distribution function, gap, and spin-correlation function to reveal rich ground-state properties. We find that spin-orbit coupling (SOC) can generate unconventional momentum distribution, which depends crucially on the filling. We call the corresponding phase with zero gap the SOC-induced metallic phase. We also show that SOC can drive the system from the antiferromagnetic to ferromagnetic Mott insulators with spin rotating. As a result, a second-order quantum phase transition between the spin-rotating ferromagnetic Mott insulator and the SOC-induced metallic phase is predicted at the strong SOC. Here the spin rotating means that the spin orientations of the nearest-neighbor sites are not parallel or antiparallel, i.e., they have an intersection angle $theta in (0,pi )$. Finally, we show that the momentum $k_{mathrm{peak}}$, at which peak of the spin-structure factor appears, can also be affected dramatically by SOC. The analytical expression of this momentum with respect to the SOC strength is also derived. It suggests that the predicted spin-rotating ferromagnetic ($k_{mathrm{peak}% }<pi /2$) and antiferromagnetic ($pi /2<k_{mathrm{peak}}<pi $) correlations can be detected experimentally by measuring the SOC-dependent spin-structure factor via the time-of-flight imaging.
The non-Abelian gauge fields play a key role in achieving novel quantum phenomena in condensed-matter and high-energy physics. Recently, the synthetic non-Abelian gauge fields have been created in the neutral degenerate Fermi gases, and moreover, generate many exotic effects. All the previous predictions can be well understood by the microscopic Bardeen-Cooper-Schrieffer theory. In this work, we establish an SU(2) Ginzburg-Landau theory for degenerate Fermi gases with the synthetic non-Abelian gauge fields. We firstly address a fundamental problem how the non-Abelian gauge fields, imposing originally on the Fermi atoms, affect the pairing field with no extra electric charge by a local gauge-field theory,and then obtain the first and second SU(2) Ginzburg-Landau equations. Based on these obtained SU(2) Ginzburg-Landau equations, we find that the superfluid critical temperature of the intra- (inter-) band pairing increases (decreases) linearly, when increasing the strength of the synthetic non-Abelian gauge fields. More importantly, we predict a novel SU(2) non-Abelian Josephson effect, which can be used to design a new atomic superconducting quantum interference device.
In this paper we explore the spin-orbit-induced bound state and molecular signature of the degenerate Fermi gas in a narrow Feshbach resonance based on a generalized two-channel model. Without the atom-atom interactions, only one bound state can be found even if spin-orbit coupling exists. Moreover, the corresponding bound-state energy depends strongly on the strength of spin-orbit coupling, but is influenced slightly by its type. In addition, we find that when increasing the strength of spin-orbit coupling, the critical point at which the molecular fraction vanishes shifts from zero to the negative detuning. In the weak spin-orbit coupling, this shifting is proportional to the square of its strength. Finally, we also show that the molecular fraction can be well controlled by spin-orbit coupling.
