Fermi gases with generalized Rashba spin orbit coupling inducedby a synthetic gauge field have the potential of realizing many interesting states such as rashbon condensates and topological phases. Here we develop a fluctuation theory of such systems
and demonstrate that beyond-Gaussian effects are essential to capture the physics of such systems. We obtain their phase diagram by constructing an approximate non-Gaussian theory. We conclusively establish that spin-orbit coupling can enhance the exponentially small transition temperature ($T_c$) of a weakly attracting superfluid to the order of Fermi temperature, paving a pathway towards high $T_c$ superfluids.
We investigate few body physics in a cold atomic system with synthetic dimensions (Celi et al., PRL 112, 043001 (2014)) which realizes a Hofstadter model with long-ranged interactions along the synthetic dimension. We show that the problem can be map
ped to a system of particles (with $SU(M)$ symmetric interactions) which experience an $SU(M)$ Zeeman field at each lattice site {em and} a non-Abelian $SU(M)$ gauge potential that affects their hopping from one site to another. This mapping brings out the possibility of generating {em non-local} interactions (interaction between particles at different physical sites). It also shows that the non-Abelian gauge field, which induces a flavor-orbital coupling, mitigates the baryon breaking effects of the Zeeman field. For $M$ particles, the $SU(M)$ singlet baryon which is site localized, is deformed to be a nonlocal object (squished baryon) by the combination of the Zeeman and the non-Abelian gauge potential, an effect that we conclusively demonstrate by analytical arguments and exact (numerical) diagonalization studies. These results not only promise a rich phase diagram in the many body setting, but also suggests possibility of using cold atom systems to address problems that are inconceivable in traditional condensed matter systems. As an example, we show that the system can be adapted to realize Hamiltonians akin to the $SU(M)$ random flux model.
We study the Feshbach resonance of spin-1/2 particles in the presence of a uniform synthetic non-Abelian gauge field that produces spin orbit coupling along with constant spin potentials. We develop a renormalizable quantum field theory that includes
the closed channel boson which engenders the Feshbach resonance, in the presence of the gauge field. By a study of the scattering of two particles in the presence of the gauge field, we show that the Feshbach magnetic field, where the apparent low energy scattering length diverges, depends on the conserved centre of mass momentum of the two particles. For high symmetry gauge fields, such as the one which produces an isotropic Rashba spin orbit coupling, we show that the system supports two bound states over a regime of magnetic fields for a negative background scattering length and resonance width comparable to the energy scale of the spin orbit coupling. We discuss the consequences of these findings for the many body setting, and point out that a broad resonance (width larger than spin orbit coupling energy scale) is most favourable for the realization of the rashbon condensate.
We propose a model to realize a fermionic superfluid state in an optical lattice circumventing the cooling problem. Our proposal exploits the idea of tuning the interaction in a characteristically low entropy state, a band-insulator in an optical bil
ayer system, to obtain a superfluid. By performing a detailed analysis of the model including fluctuations and augmented by a variational quantum Monte Carlo calculations of the ground state, we show that the superfluid state obtained has high transition temperature of the order of the hopping energy. Our system is designed to suppress other competing orders such as a charge density wave. We suggest a laboratory realization of this model via an orthogonally shaken optical lattice bilayer.
