Optimal control and selectivity of qubits in contact with a structured environment

Abstract

We present a theoretical study of the optimal control of a qubit interacting with a structured 
environment. We consider a model system in which the bath is a bosonic reservoir at zero 
temperature and the qubit frequency is the only control parameter. Using optimal control 
techniques, we show the extent to which qubit population and relaxation effects can be 
manipulated. The reachable qubit states by a shaped control with a fixed maximum intensity 
are found numerically. We analyze the role of standard control mechanisms and the structure 
of the reachable set with respect to the coupling strength between the system and the 
environment. This investigation is used as a starting point to explore the selectivity problem of 
two uncoupled qubits interacting with their own baths and characterized by a specific 
coupling strength. We numerically derive the optimal control solution for a wide range of 
parameters and we show that the control law is close to a sinusoidal function with a specific 
frequency in some peculiar cases.