Direct Measurement of Kirkwood-Rihaczek distribution for spatial properties of coherent light beam

TL;DR

This paper demonstrates a direct measurement technique for the Kirkwood-Rihaczek distribution of a coherent light beam's spatial properties, enabling detailed local phase space analysis without tomography.

Contribution

The authors introduce a two-local oscillator balanced heterodyne detection method to directly measure the KR distribution, applicable to complex wave fields including quantum states.

Findings

KR distribution measured directly without tomography

Transformation to other phase space distributions demonstrated

Method applicable for quantum mapping and biomedical imaging

Abstract

We present direct measurement of Kirkwood-Rihaczek (KR) distribution for spatial properties of coherent light beam in terms of position and momentum (angle) coordinates. We employ a two-local oscillator (LO) balanced heterodyne detection (BHD) to simultaneously extract distribution of transverse position and momentum of a light beam. The two-LO BHD could measure KR distribution for any complex wave field (including quantum mechanical wave function) without applying tomography methods (inverse Radon transformation). Transformation of KR distribution to Wigner, Glauber Sudarshan P- and Husimi or Q- distributions in spatial coordinates are illustrated through experimental data. The direct measurement of KR distribution could provide local information of wave field, which is suitable for studying particle properties of a quantum system. While Wigner function is suitable for studying wave properties such as interference, and hence provides nonlocal information of the wave field. The method developed here can be used for exploring spatial quantum state for quantum mapping and computing, optical phase space imaging for biomedical applications.