Pulsed characteristic-function measurement of a thermalizing harmonic oscillator

TL;DR

This paper introduces a method to directly measure the Wigner characteristic function of a thermalizing harmonic oscillator, even when it cannot be directly controlled or measured, by extending a probe-based pulsed control scheme to include thermalization effects.

Contribution

It generalizes a probe-measurement scheme to account for nonunitary evolution due to thermalization, enabling direct measurement of the characteristic function under realistic decoherence conditions.

Findings

Derived analytical expressions for the measurement process.

Extended the scheme to include thermalization effects.

Validated the approach with theoretical analysis.

Abstract

We present a method for the direct measurement of the Wigner characteristic function of a thermalizing harmonic oscillator that is completely inaccessible for control or measurement. The strategy employs a recently proposed probe-measurement-based scheme [Phys. Rev. Lett. 122, 110406 (2019)] which relies on the pulsed control of a two-level probe. We generalize this scheme to the case of a nonunitary time evolution of the target harmonic oscillator, describing its thermalization through contact to a finite-temperature environment, given in the form of a Lindblad master equation. This generalization is achieved using a superoperator formalism and yields analytical expressions for the direct measurement of the characteristic function, accounting for the decoherence during the measurement process.