Universal quantum control over non-Hermitian continuous-variable systems

Current studies about the continuous-variable systems in non-Hermitian quantum mechanics heavily revolved around the singularities in the eigenspectrum by mimicking their discrete-variable counterparts. Discussions over the nonunitary features in time evolution are growing and yet limited in scalability and controllability. We develop here a general theory to control an arbitrary number of bosonic modes under time-dependent non-Hermitian Hamiltonian. Far beyond the subspace of few excitations, our control theory operates in the Heisenberg picture and exploits the gauge potential underlying the instantaneous frames rather than the eigenspectrum. In particular, instantaneous frames are defined by time-dependent ancillary operators as linear combinations of the laboratory-frame operators, while the gauge potential arises from the unitary transformation between the time-dependent and stationary ancillary frames. We find that upper triangularization condition of the non-Hermitian Hamiltonian's coefficient matrix in the stationary ancillary frame yields two nonadiabatic passages in both bra and ket spaces and also the exact solutions of the time-dependent Schr\"odinger equation. At the end of these passages, probability conservation of wave function is automatically restored without brute-force normalization. Our theory is exemplified by perfect and nonreciprocal state transfers in a cavity magnonic system under non-Hermitian Hamiltonian rigorously derived from the Lindblad master equation with all quantum-jump terms retained. Under certain conditions, perfect state transfer holds for arbitrary initial states and is irrelevant to both parity-time symmetry of coefficient matrix and exceptional points of eigenspectrum. The nonreciprocal transfer is consistent with coherent perfect absorption, providing a first-principles route to coherent control of non-Hermitian continuous-variable systems.