Observation of the classical entanglement of twisted partially coherent light in phase space

Recently, a new form of classical entanglement between phase space degrees of freedom in twisted partially coherent beams has been theoretically predicted [ Opt. Lett. 46 , 5958 ( 2021 ) 10.1364/OL.445258 ]. Here, we report the first, to our knowledge, experimental observation of such phase-space entanglement (nonseparability) in a twisted Gaussian Schell-model (TGSM) beam via four-dimensional Wigner distribution function measurements, realized through the scanned windowed Fourier transform method. The Wigner distribution measurement enables direct visualization of phase-space nonseparability in the beam. Moreover, we demonstrate that the twist factor of the TGSM beam can be precisely determined from phase-space measurements. Furthermore, the Wigner distribution reveals the nonuniform spatial correlation properties of the TGSM beam and the rotational symmetry of its spatial coherence structure. Our method provides a versatile platform for probing phase-space nonseparability in random light fields.