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

TL;DR

This paper investigates how optimal control techniques can manipulate a qubit interacting with a structured bosonic environment, revealing the limits and characteristics of control in such open quantum systems.

Contribution

It introduces a numerical method to determine the set of reachable qubit states under fixed control constraints and explores control strategies for two qubits with specific bath interactions.

Findings

Reachable qubit states depend on system-environment coupling strength.

Optimal control laws can be approximated by sinusoidal functions in certain regimes.

Control mechanisms significantly influence qubit relaxation and population dynamics.

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 set of reachable states 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.