Topological excitations in normal and superfluid Fermi gases
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.
Localized mid-gap states are expected to occur whenever the mass term changes sign.
A system that similarly supports such mid-gap states is the strongly interacting atomic Fermi gas near a Feshbach resonance. Topological excitations, such as vortices or solitons in a fermionic superfluid 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 step in the order parameter. The solitons are found to be stable for many seconds, allowing us to track their oscillatory motion in the trapped superfluid. Their oscillation period increases dramatically as the interactions are tuned from the Bose-Einstein condensation (BEC) to the Bardeen-Cooper Schrieffer (BCS) superfluidity regime. At the Feshbach resonance, the measured effective mass of a soliton is about 50 times larger than expectations from mean-field Bogoliubov-de Gennes theory, signaling strong effects of pair quantum fluctuations and filling of Andreev bound states. In the presence of spin imbalance, a single soliton is one limit of the long-sought Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state.
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