Nonadiabatic coherent evolution of two-level systems under spontaneous decay

TL;DR

This paper demonstrates how to engineer nonadiabatic, nonstationary superposition states in a two-level ion system within a cavity, enabling controlled geometric phase observation despite decoherence.

Contribution

It introduces a time-dependent master equation for reservoir engineering, allowing nonadiabatic control of superposition states in ion-cavity systems.

Findings

Engineered effective Hamiltonians couple ion states with cavity mode.

Achieved decoherence-free, nonadiabatic superposition evolution.

Observed geometric phases in protected nonstationary states.

Abstract

In this paper we extend current perspectives in engineering reservoirs by producing a time-dependent master equation leading to a nonstationary superposition equilibrium state that can be nonadiabatically controlled by the system-reservoir parameters. Working with an ion trapped inside a nonindeal cavity we first engineer effective Hamiltonians that couple the electronic states of the ion with the cavity mode. Subsequently, two classes of decoherence-free evolution of the superposition of the ground and decaying excited levels are achieved: those with time-dependent azimuthal or polar angle. As an application, we generalise the purpose of an earlier study [Phys. Rev. Lett. 96, 150403 (2006)], showing how to observe the geometric phases acquired by the protected nonstationary states even under a nonadiabatic evolution.