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Spin-orbit coupling is an essential mechanism underlying quantum phenomenasuch as the spin Hall effect and topological insulators. It has been widelystudied in well-isolated Hermitian systems, but much less is known about therole dissipation plays in spin-orbit-coupled systems. Here, we implementdissipative spin-orbit-coupled bands filled with ultracold fermions, andobserve parity-time symmetry breaking as a result of the competition betweenthe spin-orbit coupling and dissipation. Tunable dissipation, introduced bystate-selective atom loss, enables us to tune the energy gap and close it atthe critical dissipation value, the so-called exceptional point. In thevicinity of the critical point, the state evolution exhibits a chiral response,which enables us to tune the spin-orbit coupling and dissipation dynamically,revealing topologically robust chiral spin transfer when the quantum stateencircles the exceptional point. This demonstrates that we can explorenon-Hermitian topological states with spin-orbit coupling.

Chiral control of quantum states in non-Hermitian spin-orbit-coupled fermions