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

Abstract

Photon-number-resolving (PNR) detection allows for the direct measurement of the Wigner quasi-probability distribution of an optical mode without the need for numerically processing an inverse Radon transform [Phys. Rev. Lett.76, 4344 (1996)10.1103/PhysRevLett.76.4344PRLTAO0031-9007]. In this work, we reproduced the seminal experiment of Banaszek et al. [Phys. Rev. A60, 674 (1999)10.1103/PhysRevA.60.674PLRAAN1050-2947] 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 zero to five photons at 1064 nm, at ∼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.