2009/12/30 by Viktor Bollen, Yong Meng Sua, Kim Fook Lee · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Coherent states #Field (mathematics) #Laser-Matter Interactions and Applications #Mathematics #Optical phase space #Optics #Physics #Position (finance) #Quantum #Quantum Information and Cryptography #Quantum imaging #Quantum information #Quantum mechanics #Quantum network #Quantum optics and atomic interactions #Quantum state #Quantum tomography #Squeezed coherent state #Wigner distribution function #quant-ph
paper · pdf · doi:10.1103/physreva.81.063826
27 pages, 14 figures
arxiv created 2009/12/30 · openalex publication_date 2010/06/25 · arxiv updated 2015/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a direct measurement of the Kirkwood-Rihaczek (KR) distribution for spatial properties of a 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 the distribution of the transverse position and momentum of a light beam. The two-LO BHD can measure the KR distribution for any complex wave field (including quantum mechanical wave function) without applying tomography methods (inverse Radon transformation). The transformation of the KR distribution to the Wigner, Glauber-Sudarshan P, and Husimi or Q distributions in spatial coordinates are illustrated through experimental data. The KR distribution can provide the local information of a wave field, which is suitable for studying particle properties of a quantum system. Meanwhile, the 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 the spatial quantum state for information processing and optical phase-space imaging for biomedical applications.