Dynamics of a two-level system under strong driving: quantum gate optimization based on floquet theory

摘要

We consider the dynamics of a two-level system (qubit) driven by strong andshort resonant pulses in the framework of Floquet theory. First we deriveanalytical expressions for the quasienergies and Floquet states of the drivensystem. If the pulse amplitude varies very slowly, the system adiabaticallyfollows the instantaneous Floquet states, which acquire dynamical phases thatdepend on the evolution of the quasienergies over time. The difference betweenthe phases acquired by the two Floquet states corresponds to a qubit staterotation, generalizing the notion of Rabi oscillations to the case of largedriving amplitudes. If the pulse amplitude changes very fast, the evolution isnon-adiabatic, with transitions taking place between the Floquet states. Wequantify and analyze the nonadiabatic transitions during the pulse by employingadiabatic perturbation theory and exact numerical simulations. We find that,for certain combinations of pulse rise and fall times and maximum drivingamplitude, a destructive interference effect leads to a remarkably strongsuppression of transitions between the Floquet states. This effect provides thebasis of a quantum control protocol, which we name Floquet InterferenceEfficient Suppression of Transitions in the Adiabatic basis (FIESTA), that canbe used to design ultra-fast high-fidelity single-qubit quantum gates.