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Nonreciprocal elements, such as isolators and circulators, play an importantrole in classical and quantum information processing. Recently, strongnonreciprocal effects have been experimentally demonstrated in cavityoptomechanical systems. In these approaches, the bandwidth of the nonreciprocalphoton transmission is limited by the mechanical resonator linewidth, which isarguably much smaller than the linewidths of the cavity modes in mostelectromechanical or optomechanical devices. In this work, we demonstratebroadband nonreciprocal photon transmission in the \emph{reversed-dissipation}regime, where the mechanical mode with a large decay rate can be adiabaticallyeliminated while mediating anti-$\mathcal{PT}$-symmetric dissipative couplingwith two kinds of phase factors. Adjusting the relative phases allows theobservation of \emph{periodic} Riemann-sheet structures with distributedexceptional points (Eps). At the Eps, destructive quantum interference breaksboth the $\mathcal{T}$- and $\mathcal{P}$-inversion symmetry, resulting inunidirectional and chiral photon transmissions. In the reversed-dissipationregime, the nonreciprocal bandwidth is no longer limited by the mechanical modelinewidth but is improved to the linewidth of the cavity resonance.Furthermore, we find that the direction of the unidirectional and chiral energytransfer could be reversed by changing the \emph{parity} of the Eps. Extendingnon-Hermitian couplings to a three-cavity model, the brokenanti-$\mathcal{PT}$-symmetry allows us to observe high-order Eps, at which aparity-dependent chiral circulator is demonstrated. The driving-phasecontrolled periodical Riemann sheets allow observation of the parity-dependentunidirectional and chiral energy transfer and thus provide a useful cell forbuilding up nonreciprocal array and realizing topological, e.g., isolators,circulators, or amplifiers.

Parity-dependent unidirectional and chiral photon transfer in reversed-dissipation cavity optomechanics