Explorations into quantum state diffusion beyond the Markov approximation

The non-Markovian quantum state diffusion equation is rapidly becoming a powerful tool for both theoretical and numerical investigations into non-trivial problems in quantum optical QED. It has been used to rederive the exact master equation for quantum Brownian motion, as well as an optical cavity or a two-level atom which is either damped or dephased under the rotating wave approximation [1]. The exact quantum state diffusion equations for the spin-1 system have also been found [2], and general theorems have now been derived for solving the N-cavity, N-qubit, and N-level systems [3]. Here, we build upon the results of Ref.~[3] to explore other problems from quantum optical QED using the non-Markovian quantum state diffusion equation. [1] L. Diosi, N. Gisin, and W.T. Strunz, Phys. Rev. A {\bf 58}, 1699 (1998). T. Yu, L. Diosi, N. Gisin, and W. T. Strunz, Phys. Rev. A {\bf 60}, 91 (1999). [2] J. Jing and T. Yu, Phys. Rev. Lett. {\bf 105}, 240403 (2010). [3] J. Jing, X. Zhao, J. Q. You, and T. Yu, arXiv:1012.0364v1. Research supported by ARO W911NF-09-1-0385, NSF PHY-0855701, and NSF PHY-0925174.