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Register a new userFulde-Ferrell-Larkin-Ovchinnikov state to topological superfluidity transition in bilayer spin-orbit coupled degenerate Fermi gas
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Recently a scheme has been proposed for generating the 2D Rashba-type spin-orbit coupling (SOC) for ultracold atomic bosons in a bilayer geometry [S.-W. Su et al, Phys. Rev. A textbf{93}, 053630 (2016)]. Here we investigate the superfluidity properties of a degenerate Fermi gas affected by the SOC in such a bilayer system. We demonstrate that a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state appears in the regime of small to moderate atom-light coupling. In contrast to the ordinary SOC, the FFLO state emerges in the bilayer system without adding any external fields or spin polarization. As the atom-light coupling increases, the system can transit from the FFLO state to a topological superfluid state. These findings are also confirmed by the BdG simulations with a weak harmonic trap added.
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We show that in the presence of magnetic field, two superconducting phases with the center-of-mass momentum of Cooper pair parallel to the magnetic field are induced in spin-orbit-coupled superconductor Li$_2$Pd$_3$B. Specifically, at small magnetic field, the center-of-mass momentum is induced due to the energy-spectrum distortion and no unpairing region with vanishing singlet correlation appears. We refer to this superconducting state as the drift-BCS state. By further increasing the magnetic field, the superconducting state falls into the Fulde-Ferrell-Larkin-Ovchinnikov state with the emergence of the unpairing regions. The observed abrupt enhancement of the center-of-mass momenta and suppression on the order parameters during the crossover indicate the first-order phase transition. Enhanced Pauli limit and hence enlarged magnetic-field regime of the Fulde-Ferrell-Larkin-Ovchinnikov state, due to the spin-flip terms of the spin-orbit coupling, are revealed. We also address the triplet correlations induced by the spin-orbit coupling, and show that the Cooper-pair spin polarizations, generated by the magnetic field and center-of-mass momentum with the triplet correlations, exhibit totally different magnetic-field dependences between the drift-BCS and Fulde-Ferrell-Larkin-Ovchinnikov states.
We study the phase diagram in a two-dimensional Fermi gas with the synthetic spin-orbit coupling that has recently been realized experimentally. In particular, we characterize in detail the properties and the stability region of the unconventional Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states in such a system, which are induced by spin-orbit coupling and Fermi surface asymmetry. We identify several distinct nodal FFLO states by studying the topology of their respective gapless contours in momentum space. We then examine the phase structure and the number density distributions in a typical harmonic trapping potential under the local density approximation. Our studies provide detailed information on the FFLO pairing states with spin-orbit coupling and Fermi surface asymmetry, and will facilitate experimental detection of these interesting pairing states in the future.
We propose a two-step experimental protocol to directly engineer Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states in a cold two-component Fermi gas loaded into a quasi-one-dimensional trap. First, one uses phase imprinting to create a train of domain walls in a superfluid with equal number of $uparrow$- and $downarrow$-spins. Second, one applies a radio-frequency sweep to selectively break Cooper pairs near the domain walls and transfer the $uparrow$-spins to a third spin state which does not interact with the $uparrow$- and $downarrow$-spins. The resulting FFLO state has exactly one unpaired $downarrow$-spin in each domain wall and is stable for all values of domain-wall separation and interaction strength. We show that the protocol can be implemented with high fidelity at sufficiently strong interactions for a wide range of parameters available in present-day experimental conditions.
We consider a two-component Fermi gas in the presence of spin imbalance, modeling the system in terms of a one-dimensional attractive Hubbard Hamiltonian initially in the presence of a confining trap potential. With the aid of the time-evolving block decimation method, we investigate the dynamics of the initial state when the trap is switched off. We show that the dynamics of a gas initially in the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state is decomposed into the independent expansion of two fluids, namely the paired and the unpaired particles. In particular, the expansion velocity of the unpaired cloud is shown to be directly related to the FFLO momentum. This provides an unambiguous signature of the FFLO state in a remarkably simple way.
Starting from the Ginzburg-Landau free energy describing the normal state to Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) state transition, we evaluate the free energy of seven most common lattice structures such as stripe, square, triangular,Simple Cubic (SC), Face centered Cubic (FCC),Body centered Cubic (BCC) and Quasi-crystal (QC). We find that the stripe phase which is the original LO state, is the most stable phase. This result maybe relevant to the detection of LOFF state in some heavy fermion compounds and the pairing lattice structure of fermions with unequal populations in the BCS side of Feshbach resonance in ultra-cold atoms.
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