Direct measurement of the Wigner function by photon-number-resolving detection

TL;DR

This paper demonstrates direct measurement of the Wigner function of optical states using photon-number-resolving detection with superconducting sensors, extending quantum tomography to higher photon fluxes and non-Gaussian states.

Contribution

It reproduces and extends previous quantum tomography experiments by employing advanced PNR detection to measure states with higher photon fluxes and discusses future applications.

Findings

Successful measurement of Wigner functions for coherent and mixed states

Extended quantum tomography to states with more than one photon per detection interval

Achieved high detection efficiency (~70%) with superconducting sensors

Abstract

Photon-number-revolving (PNR) detection allows the direct measurement of the Wigner quasiprobability distribution of an optical mode without the need for numerically processing an inverse Radon transform [K. Banaszek and K. W\'odkiewicz, Phys. Rev. Lett. 76, 4344 (1996)]. In this work, we reproduced the seminal experiment of Banaszek et al. [Phys. Rev. A 60, 674 (1999)] of quantum tomography of a pure coherent state, and of a statistical mixture thereof, and extended it to the more general case of photon fluxes with much more than one photon per detection time. This was made possible by the use of a superconducting transition-edge sensor to perform PNR detection from 0 to 5 photons at 1064 nm, at about 70% system efficiency and with no dead time. We detail signal acquisition and detection efficiency and discuss prospects for applying such quantum tomography to non-Gaussian states.