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

Niranjan Sridhar, Reihaneh Shahrokhshahi, Aaron Miller, Thomas Gerrits, Adriana E. Lita, Sae Woo Nam, Olivier Pfister

Published Jan 1, 2015• 1 citation
Publisher

Abstract

We extended the seminal experiment of Banaszek et al. of quantum tomography by photon counting without Radon transform postprocessing to the more general case of photon fluxes with more than one photon per detection time.
DOI
10.1364/cleo_qels.2015.ftu4a.1

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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.
In this work, a continuous variable quantum tomography is presented. This is done using two approaches, one using simulated data and another one using data from measurements performed in the laboratory. The Radon inverse transform, under the approximation of filtered back projection, alongside the details on the implementa- tion of balanced homodyne detection needed to perform the tomography are clearly explained. Density matrices in the quadrature and number representation are also obtained from the Wigner function. Additionally, complete documentation of the computational implementation and a user-friendly interface for the tomography is reported