Quantum-dynamical phase transition and Fisher information in a non-Hermitian Bose-Hubbard dimer

Abstract

We study the dynamical properties in a non-Hermitian Bose-Hubbard dimer and show that the steady state consists mostly of the eigenstate whose eigenvalue has the largest imaginary part. A sharp phase transition occurs in the steady state and the phase transition occurs for a finite particle number, not for infinite ones, in contrast to the Hermitian system. We also investigate the quantum Fisher information and entanglement in two different phases. The results show that the steady state in the Josephson oscillation regime is fully N-particle entangled and the corresponding parameter sensitivity approaches the Heisenberg limit. In the self-trapping regime, the parameter sensitivity just scales as the shot-noise limit. Moreover, quantum Fisher information of the steady state is robust to the initial state, which indicates that the non-Hermitian dynamics takes more advantage than the Hermitian one for quantum metrology.