Infinite operator-sum representation of density operator for a dissipative cavity with Kerr medium derived by virtue of entangled state representation

Abstract

By using the thermo entangled state representation we solve the master equation for a dissipative cavity with Kerr medium to obtain density operators' infinite operator-sum representation}$\rho (t)={\sum }_{m,n,l=0}^{\infty }{M}_{m,n,l}{\rho }_0{\mathcal{M}}_{m,n,l}^{†}.$ It is noticeable that}$M_{m,n,l}$ is not hermite conjugate to ${\mathcal{M}}_{m,n,l}^{†}$, nevertheless the normalization}${\sum }_{m,n,l=0}^{\infty }{\mathcal{M}}_{nm,,l}^{†}{M}_{m,n,l}=1$ still holds}, i.e., they are trace-preserving in a general sense. This example may stimulate further studying if general superoperator theory needs modification.

6 pages, comments welcome

References in corpus (1)

• Wigner Function Evolution of Quantum States in Presence of Self-Kerr Interaction

Cited by in corpus (2)

• Solving quantum trajectories for systems with linear Heisenberg-picture dynamics and Gaussian measurement noise
• Wigner function evolution in self-Kerr Medium derived by Entangled state representation