Abstract
We find dynamical invariants for open quantum systems described by the non-Markovian quantum state diffusion (QSD) equation. In stark contrast to closed systems where the dynamical invariant can be identical to the system density operator, these dynamical invariants no longer share the equation of motion for the density operator. Moreover, the invariants obtained with from bi-orthonormal basis can be used to render an exact solution to the QSD equation and the corresponding non-Markovian dynamics without using master equations or numerical simulations. Significantly we show that we can apply these dynamic invariants to reverse-engineering a Hamiltonian that is capable of driving the system to the target state, providing a novel way to design control strategy for open quantum systems.
Highlights
The theory of the open quantum system [1] provides a realistic and complete description that takes into account the often uncontrollable and inevitable interaction between the system under consideration and its environment
We find dynamical invariants for open quantum systems described by the non-Markovian quantum-statediffusion (QSD) equation
We show that for open systems whose dynamics can be described by the QSD equation, the invariants are no longer equivalent to the reduced density operator
Summary
The theory of the open quantum system [1] provides a realistic and complete description that takes into account the often uncontrollable and inevitable interaction between the system under consideration and its environment. The Markovian approximation entails that the open system dynamics is forgetful and is valid only when memory effects of the environment are negligible. A stochastic Schrodinger equation called the non-Markovian quantum state diffusion (QSD) [10,11], which was derived from a microscopic Hamiltonian, has several advantages over other exact master equations and has been proven to be a powerful tool in the study of the system dynamics. A generic tool for deriving a non-Markovian master equation has been developed using QSD [18] which is applicable to a generic open quantum system irrespective of the system-environment coupling strength and the environment frequency distribution. This control protocol allows the spectrum of the state to change, making it more appealing to experimental realizations
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