Open physical systems with balanced loss and gain, described by non-Hermitian parity-time $$\left( {{\cal P}{\cal T}} \right)$$P T reflection symmetric Hamiltonians, exhibit a transition which could engender modes that exponentially decay or grow with time, and thus spontaneously breaks the $${\cal P}{\cal T}$$P T -symmetry. Such $${\cal P}{\cal T}$$P T -symmetry-breaking transitions have attracted many interests because of their extraordinary behaviors and functionalities absent in closed systems. Here we report on the observation of $${\cal P}{\cal T}$$P T -symmetry-breaking transitions by engineering time-periodic dissipation and coupling, which are realized through state-dependent atom loss in an optical dipole trap of ultracold ⁶Li atoms. Comparing with a single transition appearing for static dissipation, the time-periodic counterpart undergoes $${\cal P}{\cal T}$$P T -symmetry breaking and restoring transitions at vanishingly small dissipation strength in both single and multiphoton transition domains, revealing rich phase structures associated to a Floquet open system. The results enable ultracold atoms to be a versatile tool for studying $${\cal P}{\cal T}$$P T -symmetric quantum systems.

We study the dynamics of a driven non-Hermitian superconducting qubit which is perturbed by quantum jumps between energy levels, a purely quantum effect with no classical correspondence. The quantum jumps mix the qubit states leading to decoherence. We observe that this decoherence rate is enhanced near the exceptional point, owing to the cube-root topology of the non-Hermitian eigenenergies. Together with the effect of non-Hermitian gain or loss, quantum jumps can also lead to a breakdown of adiabatic evolution under the slow-driving limit. Our study shows the critical role of quantum jumps in generalizing the applications of classical non-Hermitian systems to open quantum systems for sensing and control.

Open quantum systems interacting with an environment exhibit dynamics described by the combination of dissipation and coherent Hamiltonian evolution. Taken together, these effects are captured by a Liouvillian superoperator. The degeneracies of the (generically non-Hermitian) Liouvillian are exceptional points, which are associated with critical dynamics as the system approaches steady state. We use a superconducting transmon circuit coupled to an engineered environment to observe two different types of Liouvillian exceptional points that arise either from the interplay of energy loss and decoherence or purely due to decoherence. By dynamically tuning the Liouvillian superoperators in real time we observe a non-Hermiticity-induced chiral state transfer. Our study motivates a new look at open quantum system dynamics from the vantage of Liouvillian exceptional points, enabling applications of non-Hermitian dynamics in the understanding and control of open quantum systems.

We study the phase diagram of a parity- and time-reversal- (PT-) symmetric tight-binding chain with N sites and hopping energy J in the presence of two impurities with imaginary potentials \ifmmode\pm\else\textpm\fi{}i$\gamma${} located at arbitrary (P-symmetric) positions (m,m\ifmmode \bar{}\else \={}\fi{}=N+1-m) on the chain where m$\leqslant${}N/2. We find that except in the two special cases where impurities are either the farthest or the closest, the PT-symmetric region is algebraically fragile. We analytically and numerically obtain the critical impurity potential $\gamma${}PT and show that $\gamma${}PT$\propto${}1/N$\rightarrow${}0 as N$\rightarrow${}$\infty${} except in the two special cases. When the PT symmetry is spontaneously broken, we find that the maximum number of complex eigenvalues is given by 2m. When the two impurities are the closest, we show that $\gamma${}PT in the limit N$\rightarrow${}$\infty${} approaches J (J/2) provided that N is even (odd). For an even N, the PT symmetry is maximally broken, whereas for an odd N, it is sequentially broken. Our results show that the phase diagram of a PT-symmetric tight-binding chain is extremely rich and that, in the continuum limit, this model may give rise to hitherto unexplored PT-symmetric Hamiltonians.