- 16/07/2014, 1pm, C/2.07, Queen's Buildings, Cardiff University, 5 The Parade, CF24 3AA
- On the Control of Open Quantum Systems in the Weak Coupling Limit
- E. JonckheereUniversity of Southern California, Los Angeles, USA
- (joint work with Domenico D'Alessandro and Raffaele Romano,Iowa State University, Ames, IA, USA)
- When dealing with the control of quantum systems in interaction with an external environment, one of the most commonly used models is the Lindblad-Kossakowski equation for the density matrix. Its derivation relies on various approximations, which are usually justified in terms of weak interaction between the system and its surroundings and special properties of the bath interacting with the system. This equation contains dissipative corrections, accounting for the interaction with the environment, whose expression strongly depends on the adopted Markov approximation. In the case of coherently controlled Lindblad-Kossakowski equation, it is usually assumed that this correction is independent of the control Hamiltonian. However, this procedure is not consistent with the rigorous derivation of the Markov approximation in the standard case, the so-called weak coupling limit, in which the dissipative contribution depends on the coherent part of the dynamics.
- In this talk, we will discuss the rigorous derivation of the Lindblad-Kossakowski equation in the weak coupling limit regime, following the original derivation of Davies, in the case where the control is present, and explicitly displaying the dependence of the model on the control. We will then consider the special case of a 2-level system in a bosonic bath, and show explicitly how the model depends on the parameters in the Hamiltonian which contains the control.
- We will also discuss the impact of this more rigorous modeling procedure in the current research on methods to find controls that decouple the system from the environment. Finally, we will indicate directions and problems for further research.