Universal quantum control over non-Hermitian continuous-variable systems
Phys. Rev. A 113, 042452 – Published 24 April, 2026
DOI: https://doi.org/10.1103/6pmb-2ssf
Abstract
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 the 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 the 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, the instantaneous frames are defined by time-dependent ancillary operators as linear combinations of the laboratory-frame operators, while the associated gauge potential arises from the unitary transformation connecting the time-dependent and stationary ancillary frames. We find that the upper triangularization condition of the non-Hermitian Hamiltonian's coefficient matrix in the stationary ancillary frame gives rise to two nonadiabatic passages in both bra and ket spaces and also the exact solutions of the time-dependent Schrödinger equation. At the end of these passages, the probability conservation of the system wave function can be automatically restored without brute-force normalization. Our theory is exemplified by perfect and nonreciprocal state transfers in a cavity magnonic system under the non-Hermitian Hamiltonian rigorously derived from the Lindblad master equation with all quantum-jump terms retained. Under certain conditions, the perfect state transfer holds for arbitrary initial states and is irrelevant to both parity-time symmetry of the coefficient matrix and exceptional points of the eigenspectrum. The nonreciprocal transfer is consistent with the coherent perfect absorption. Our work promises a first-principles approach for the coherent control over non-Hermitian continuous-variable systems.
