Universal quantum control over non-Hermitian continuous-variable systems

Abstract

Current studies of non-Hermitian continuous-variable systems heavily revolved around the singularities in the eigen-spectrum by mimicking their discrete-variable counterparts. The growing discussions over the nonunitary features in time evolution, however, are limited in scalability and controllability. We here develop 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 full Hilbert space within the Heisenberg framework and exploits the gauge potential underlying the instantaneous frames rather than the eigen-spectrum. In particular, the instantaneous frames are defined by time-dependent ancillary operators as linear combinations of 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 non-Hermitian Hamiltonian's coefficient matrix in the stationary ancillary frame gives rise to nonadiabatic passages of two time-dependent ancillary operators, also leading to exact solutions of the time-dependent Schrödinger equation. At the end of these passages, the probability conservation of the system wavefunction can be automatically restored without artificial normalization. Our theory is exemplified with the perfect and nonreciprocal state transfers in a cavity magnonic system. The former holds for arbitrary initial states and is irrelevant to both parity-time symmetry of the coefficient matrix and exceptional points of eigen-spectrum; and the latter is consistent with the coherent perfect absorbtion. We essentially constructs the universal quantum control (UQC) theory for the non-Hermitian continuous-variable systems, promising a powerful and reliable approach for their coherent control.