Universal quantum control over non-Hermitian continuous-variable systems

Abstract: Although the control of non-Hermitian quantum systems has a growing interest for their nonunitary feature in the time evolution, the existing discussions are not more than two or three dimensions and heavily influenced by the singularity of the energy spectrum. We here develop a general theory to control an arbitrary number of bosonic modes governed by the time-dependent non-Hermitian Hamiltonian. It takes advantage of the gauge potential in the instantaneous frame rather than the energy spectrum of Hamiltonian. In particular, the dynamics of a general non-Hermitian continuous-variable system is analyzed in the instantaneous frame associated with time-dependent ancillary operators that are superpositions of the laboratory-frame operators and irrelevant to the original Hamiltonian. The gauge potential is determined by the unitary transformation between the time-dependent and stationary ancillary frames. The upper triangularization condition for the Hamiltonian's coefficient matrix in the stationary ancillary frame enables two of the time-dependent ancillary operators to be nonadiabatic Heisenberg passages of the non-Hermitian system. The probability conservation of the system wavefunction can be restored at the end of these passages 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 the parity-time symmetry of the Hamiltonian and the exceptional point of the spectra; and the latter is consistent with the unidirectional perfect absorbtion. Our work essentially extends the universal quantum control (UQC) theory to the non-Hermitian continuous-variable systems, providing a promising approach for their coherent control.