Spin-orbit Coupled Fermi Gases and Heavy Solitons in Fermionic Superfluids

The coupling of the spin of electrons to their motional state lies at the heart of topological phases of matter. We have created and detected spin-orbit coupling in an atomic Fermi gas via spin-injection spectroscopy, which characterizes the energy-momentum dispersion and spin composition of the quantum states. For energies within the spin-orbit gap, the system acts as a spin diode. To fully inhibit transport, we open an additional spin gap with radio-frequency coupling, thereby creating a spin-orbit coupled lattice whose spinful band structure we probe. In the presence of s-wave interactions, spin-orbit coupled fermion systems should display induced p-wave pairing and consequently topological superfluidity. Such systems can be described by a relativistic Dirac theory with a mass term that can be made to vary spatially. Topologically protected edge states are expected to occur whenever the mass term changes sign. A system that similarly supports edges states is the strongly interacting atomic Fermi gas near a Feshbach resonance. Topological excitations, such as vortices - line defects - or solitons - planar defects - have been described theoretically for decades in many different physical contexts. In superconductivity and superfluidity they represent a defect in the order parameter and give rise to localized bound states. We have created and directly observed solitons in a fermionic superfluid by imprinting a phase step into the superfluid wavefunction. These are found to be stable for many seconds, allowing us to track their oscillatory motion in the trapped superfluid. Their trapping period increases dramatically as the interactions are tuned from the BEC to the BCS regime. At the Feshbach resonance, their period is an order of magnitude larger than expectations from mean-field Bogoliubov-de Gennes theory, signaling strong effects of bosonic quantum fluctuations and possible filling of Andreev bound states. Our work opens the study of fermionic edge states in ultracold gases. In the presence of spin imbalance, the solitons created here represent one limit of the long-sought Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state of mobile Cooper pairs.\\[4pt] Additional Authors: Ariel Sommer, Massachusetts Institute of Technology; Mark Ku, Massachusetts Institute of Technology; Wenjie Jie, Massachusetts Institute of Technology; Zoran Hadzibabic, University of Cambridge; Tarik Yefsah, Massachusetts Institute of Technology; Waseem Bakr, Massachusetts Institute of Technology; Martin Zwierlein, Massachusetts Institute of Technology