While spin-orbit coupling (SOC), an essential mechanism underlying quantum phenomena from the spin Hall effect to topological insulators [1, 2], has been widely studied in well-isolated Hermitian systems, much less is known when the dissipation plays a major role in spin-orbit-coupled quantum systems [3]. Here, we realize dissipative spin-orbit-coupled bands filled with ultracold fermions, and observe a parity-time (PT ) symmetrybreaking transition as a result of the competition between SOC and dissipation. Tunable dissipation, introduced by state-selective atom loss, enables the energy gap, opened by SOC, to be engineered and closed at the critical dissipation value, the so-called exceptional point (EP) [4]. The realized EP of the non-Hermitian band structure exhibits chiral response when the quantum state changes near the EP. This topological feature enables us to tune SOC and dissipation dynamically in the parameter space, and observe the state evolution is direction-dependent near the EP, revealing topologically robust spin transfer between different quantum states when the quantum state encircles the EP. This topological control of quantum states for non-Hermitian fermions provides new methods of quantum control, and also sets the stage for exploring non-Hermitian topological states with SOC.
We measure collective excitations of a harmonically trapped two-dimensional (2D) SU(N ) Fermi gas of 173 Yb confined to a stack of layers formed by a one-dimensional optical lattice. Quadrupole and breathing modes are excited and monitored in the collisionless regime |ln(kF a2D)| 1 with tunable spin. We observe that the quadrupole mode frequency decreases with increasing number of spin component N due to the amplification of the interaction effect by N in agreement with theoretical prediction based on 2D kinetic equations. The breathing mode frequency, however, is twice the dipole oscillation frequency. We also follow the evolution of collective excitations in the dimensional crossover from two to three dimensions and characterize the damping rate of quadrupole and breathing modes for tunable SU(N ) fermions, both of which reveal the enhanced inter-particle collisions for large spin. Our result paves the way to investigate the collective property of 2D SU(N ) Fermi liquid with high spin. * Electronic address: gbjo@ust.hk * Electronic address: gbjo@ust.hk[1] D. Guéry-Odelin, Phys. Rev. A 66 033613 (2002).
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