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

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.

27 pages, 14 figures

References in corpus (5)

• Continuous-variable optical quantum state tomography
• Photon wave functions, wave-packet quantization of light, and coherence theory
• Sub-Planck phase-space structures and Heisenberg-limited measurements
• Factorization of Numbers with the temporal Talbot effect: Optical implementation by a sequence of shaped ultrashort pulses
• Measurement of the transverse spatial quantum state of light at the single-photon level

Cited by in corpus (6)

• The quasiprobability behind the out-of-time-ordered correlator
• Properties and Applications of the Kirkwood-Dirac Distribution
• Entropic uncertainty relations for quantum information scrambling
• Kirkwood-Dirac representations beyond quantum states (and their relation to noncontextuality)
• Compressive Direct Imaging of a Billion-Dimensional Optical Phase-Space
• Optical Phase-Space-Time-Frequency Tomography