Optimizing for an arbitrary Schr\"odinger cat state

TL;DR

This paper develops a flexible optimal control framework to generate and optimize arbitrary Schrödinger cat states in various quantum systems, including dissipative environments, demonstrating its effectiveness and adaptability.

Contribution

It introduces a set of functionals for optimizing complex quantum states, extends them to open systems, and applies them to different models like Kerr and Jaynes-Cummings, showcasing versatility.

Findings

Control strategies vary with dissipation and cat size.

Optimal control can achieve complex quantum states efficiently.

The framework adapts to different quantum models and conditions.

Abstract

We derive a set of functionals for optimization towards an arbitrary cat state and demonstrate their application by optimizing the dynamics of a Kerr-nonlinear Hamiltonian with two-photon driving. The versatility of our framework allows us to adapt our functional towards optimization of maximally entangled cat states, applying it to a Jaynes-Cummings model. We identify the strategy of the obtained control fields and determine the quantum speed limit as a function of the cat state's excitation. Finally, we extend our optimization functionals to open quantum system dynamics and apply it to the Jaynes-Cummings model with decay on the oscillator. For strong dissipation and large cat radii, we find a change in the control strategy compared to the case without dissipation. Our results highlight the power of optimal control with functionals specifically crafted for complex physical tasks and the versatility of the quantum optimal control toolbox for practical applications in the quantum technologies.