Session G40: Spin-Orbit Coupling in Ultracold Atom Systems

Synthetic gauge fields for ultracold atoms

Ultracold atoms represent a unique system in which to investigate quantum many-body physics with unprecedented experimental control. The properties of these systems can be tailored to realize model many-particle Hamiltonians, familiar from condensed matter physics, in their most pure and essential form. Magnetic fields, and gauge fields in general, play an important role in collective phenomena in electronic systems, leading to iconic phenomena such as the fractional quantum Hall effect. More complex, matrix valued, gauge fields can be used to describe spin-orbit coupling: itself an essential ingredient in many topological insulators, and in spintronic devices. Given the charge neutrality of ultracold atoms it is not immediately obvious how such physics could be explored in a cold atom context. In this talk I will describe the experimental techniques we use to engineer artificial gauge fields for ultracold neutral atoms using Raman transitions. I will also describe the latest results from the NIST group.   

Search for Majorana fermions in Spin-Orbit Coupled Ultra-cold Fermi Gases

Topological quantum matter has been an active research field in physics in the past three decades with numerous celebrated examples, including quantum Hall effect, chiral superconductor, topological insulator, etc. In topological materials, Majorana fermions, first envisioned by Majorana in 1935 to describe neutrinos, often emerge as topological quasiparticle excitations of the systems. Majorana fermions are intriguing because they can be construed as their own anti-particles and follow non-Abelian anyonic statistics under a pair-wise exchange of the many-particle wave function, unlike Dirac fermions where electrons and positrons (holes) are distinct. Although the emergence of Majorana fermions in any condensed matter or atomic system is by itself an extraordinary phenomenon, they have also come under a great deal of recent attention due to their potential use in fault tolerant quantum computation. Motivated by the recent experimental realization of spin-orbit coupling for cold atoms, in this talk, I will discuss the emergence of Majorana fermions in spin-orbit coupled Fermi cold atomic superfluids. I will talk about various experimental relevant issues for the observation of Majorana fermions in such cold atomic systems.\\[4pt] [1] C. Zhang, S. Tewari, R. Lutchyn, and S. Das Sarma, Phys. Rev. Lett. 101, 160401 (2008).\\[0pt] [2] M. Gong, S. Tewari, C. Zhang, Phys. Rev. Lett. 107, 195303 (2011).\\[0pt] [3] M. Gong, G. Chen, S. Jia, C. Zhang, Phys. Rev. Lett. 109, 105302 (2012)\\[0pt] [4] G. Chen, M. Gong, and C. Zhang, Phys. Rev. A 85, 013601 (2012).   

Majorana fermions in one-dimensional spin-orbit coupled Fermi gases

We theoretically study trapped one-dimensional Fermi gases in the presence of spin-orbit coupling induced by Raman lasers. The gas changes from a conventional (non-topological) superfluid to a topological superfluid as one increases the intensity of the Raman lasers above a critical chemical-potential dependent value. Solving the Bogoliubov-de Gennes equations self-consistently, we calculate the density of states in real and momentum space at finite temperatures. We study Majorana fermions (MFs) which appear at the boundaries between topologically trivial and topologically non-trivial regions. We linearize the trap near the location of a MF, finding an analytic expression for the localized MF wavefunction and the gap between the MF state and other edge states.   

Phase diagram of 1D spin-orbit coupled Fermi gases in optical lattices

We consider a one dimensional spin-orbit coupled Fermi gas in optical lattices with open boundary condition. This system belongs to the BDI symmetry class because the Hamiltonian can be made real when the Zeeman field is assumed to be along the z direction, thus the topological superfluid is characterized by $Z$, instead of $Z_2$ class. In the optical lattice system, each site admits at most two fermions. The system can host plenty of phases depending on the filling factor and the Zeeman field. At finite Zeeman field we observe a strong competition between the topological superfluid phase and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. The latter phase is more likely to be observed near the half filling. The spin-orbit coupling plays the role of enhancing the topological superfluid phase and suppressing the FFLO phase, which the Hartree shift plays an utterly opposite role. The possible observation of topological phase is also discussed in the presence of a harmonic trap.   

Topological Quantum Phase Transition of Fermi Gases and its Detections in a Synthetic Non-Abelian Gauge Potential

We investigate the topological quantum phase transition of Fermi gases trapped in a honeycomb lattice in the presence of a synthetic non-Abelian gauge potential. We develop a systematic fermionic effective field theory to describe a topological quantum phase transition tuned by the non-Abelian gauge potential and explore its various important experimental consequences. We obtain the critical exponents at zero temperature, dynamic compressibility, uniform compressibility, specific heat and Wilson ratio at finite temperatures. We analyze the effects of atom-atom interactions and possible disorders in generating the non-Abelian gauge fields. We also perform direct numerical calculations on the lattice scale and compare with the results achieved from the fermionic effective field theory. When discussing various feasible experimental detections of the topological quantum phase transition, we stress the important roles of the gauge invariance to distinguish gauge invariant quantities from non-gauge invariant ones.   

Trapped Fermi gases with Rashba spin-orbit coupling

We use the Bogoliubov-de Gennes formalism to analyze harmonically trapped Fermi gases with Rashba-type spin-orbit coupling in two dimensions. We consider both population-balanced and -imbalanced Fermi gases throughout the BCS-BEC evolution, and study the effects of spin-orbit coupling on the spontaneously induced countercirculating mass currents and the associated intrinsic angular momentum. In particular, we find that even a small spin-orbit coupling destabilizes Fulde-Ferrel-Larkin-Ovchinnikov (FFLO)-type spatially modulated superfluid phases as well as the phase-separated states against the polarized superfluid phase. We also show that the continuum of quasiparticle and quasihole excitation spectrum can be connected by zero, one or two discrete branches of interface modes, depending on the number of interfaces between a topologically trivial phase (e.g. locally unpolarized/low-polarized superfluid or spin-polarized normal) and a topologically nontrivial one (e.g. locally high-polarized superfluid) that may be present in a trapped system.   

Superfluid transition temperature across the BCS-BEC crossover induced by a synthetic non-Abelian gauge field

A non-Abelian gauge field that induces a spin-orbit coupling on the motion of fermions engenders a BCS-BEC crossover even for weakly attracting fermions. The transition temperature at large spin-orbit coupling is known to be determined by the mass of the emergent boson -- the rashbon. We obtain the transition temperature of the system as a function of the spin-orbit coupling by constructing and studying a Gaussian fluctuation (Nozieres-Schmitt-Rink) theory. These results will help guide the upcoming experiments on spin-orbit coupled fermions. In addition, this work suggests a route to enhance the transition temperature of a weakly attracting fermionic system by tuning the spin-orbit coupling.   

Fulde-Ferrell-Larkin-Ovchinnikov Phases in Two-dimensional Spin-Orbit Coupled Degenerate Fermi gas

We examine the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase in two dimensional spin-orbit coupled degenerate Fermi gas using mean-field theory at zero temperature. The FFLO phase has been greatly enhanced due to the deformation of the Fermi surface, which arise from the interplay between spin-orbit coupling and in-plane Zeeman field. The emergence of FFLO phase has been carefully examined from different angles, and the properties of the BCS superfluid, the FFLO phase and normal gas have also been studied. The in-plane Zeeman field break the rotation symmetry thus the eigenvalues no longer appear in pairs. The experimental signatures for the observation of FFLO phase is also discussed.   

FFLO and Topological Superfluid Phases in 2D Spin-Orbit Coupling Fermionic Optical Lattices

We investigate the phase diagram of 2D spin-orbit coupled ultra-cold Fermi atoms confined in a square lattice. By numerically solving the corresponding Bogoliubov-de Gennes equation self-consistently, we show that a finite Zeeman field can induce Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) and /or topological superfluid phases (which support Majorana fermions) in the presence of spin-orbit coupling. We find that the perpendicular Zeeman field favors the topological superfluid phase, while the in-plane Zeeman field favors the FFLO state. A simple physical explanation for the above results is also provided.   

Finite-Momentum Dimer Bound State in Spin-Orbit Coupled Fermi Gas

We investigate the two-body properties of a spin-1/2 Fermi gas subject to a spin-orbit coupling induced by laser fields. When attractive $s$-wave interaction between unlike spins is present, the system may form a dimer bound state. Surprisingly, under proper conditions, the bound state obtains finite center-of-mass momentum, whereas under the same condition but in the absence of the two-body interaction, the system has zero total momentum. This unusual result can be regarded as a consequence of the broken Galilean invariance by the spin-orbit coupling. Such a finite-momentum bound state will have profound effects on the many-body properties of the system.   

Ultra-cold fermions in the flatland: evolution from BCS to Bose superfluidity in two-dimensions with spin-orbit and Zeeman fields

We discuss the evolution from BCS to Bose superfluidity for ultracold fermions in two-dimensions and in the presence of simultaneous spin-orbit and Zeeman fields. We analyze several thermodynamic properties to characterize different superfluid phases including pressure, compressibility, induced polarization, and spin susceptibility. Furthermore, we compute the momentum distribution and construct topological invariants for each of the superfluid phases.   

Flow induced superfluidty and other novel effects in spin orbit coupled fermionic quantum gases

Recent experiments on fermions with synthetic gauge fields produce systems with spin-orbit coupling, detuning and Zeeman fields. We show by theoretical considerations that such systems have many interesting features when the fermions experience a contact attraction. In particular, a flow (finite centre of mass momentum) produces a ``stronger'' superfluid. In addition, we show that such systems can be tuned to have very interesting normal states paving way for studying spin-orbit coupled Fermi liquids.