Optimal generation of Fock states in a weakly nonlinear oscillator

TL;DR

This paper uses optimal control theory to efficiently generate Fock states in a weakly nonlinear oscillator, revealing pulse shapes and scaling laws that outperform simple models.

Contribution

It introduces a method to find the shortest control pulses for Fock state preparation in weakly nonlinear oscillators, improving upon previous Landau-Zener estimates.

Findings

Optimal pulses involve beatings at transition frequencies.

Shortest pulse time scales as a power law with nonlinearity parameter.

Power law exponent found to be approximately -0.73.

Abstract

We apply optimal control theory to determine the shortest time in which an energy eigenstate of a weakly anharmonic oscillator can be created under the practical constraint of linear driving. We show that the optimal pulses are beatings of mostly the transition frequencies for the transitions up to the desired state and the next leakage level. The time of a shortest possible pulse for a given nonlinearity scale with the nonlinearity parameter delta as a power law of alpha with alpha=-0.73 +/-0.029. This is a qualitative improvement relative to the value alpha=1 suggested by a simple Landau-Zener argument.