Optimizing for an arbitrary Schrödinger cat state. I. Functionals and application to coherent dynamics

Abstract

A key task in the field of quantum optimal control is to encode physical targets into figures of merit to be 
used as optimization functionals. Here we derive a set of functionals for optimization towards an 
arbitrary cat state. We demonstrate the application of the functionals by optimizing the dynamics 
of a Kerr-nonlinear Hamiltonian with two-photon driving. Furthermore, we show the versatility of the 
framework by adapting the functionals towards optimization of maximally entangled cat states, 
applying it to a Jaynes-Cummings model. Finally, we identify the strategy of the obtained control fields 
and determine the quantum speed limit as a function of the cat state's excitation. Our results highlight 
the power of optimal control with functionals specifically crafted for complex physical tasks. 
They allow for optimizing the preparation of entangled cat states in more realistic settings, 
including, e.g., dissipative effects which we investigate in the companion paper.