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Journal of the Optical Society of America A

Detection of polarization-spatial classical optical entanglement in partially coherent light fields using intensity measurements

S. Asokan, J. Solomon Ivan

Published Jan 11, 2023• 0 citations
Publisher

Abstract

Detection of polarization-spatial classical optical entanglement through implementation of partial transpose on measured intensities is explored. A sufficient criterion for polarization-spatial entanglement in partially coherent light fields based on intensities measured at various orientations of the polarizer, as implied through partial transpose, is outlined. Detection of polarization-spatial entanglement using the outlined method is demonstrated experimentally through a Mach-Zehnder interferometer setup.

DOI
10.1364/josaa.477383

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Detection of polarization-spatial classical optical entanglement through implementation of partial transpose on measured intensities is explored. A sufficient criterion for polarization-spatial entanglement in partially coherent light fields based on intensities measured at various orientations of the polarizer, as implied through partial transpose, is outlined. Detection of polarization-spatial entanglement using the outlined method is demonstrated experimentally through a Mach-Zehnder interferometer setup.
The problem of bipartite entanglement in partially coherent paraxial vector light fields is addressed. A generalized uncertainty principle suited for the polarization-spatial degrees of freedom is introduced. Partial transpose is implemented through the obtained generalized uncertainty principle. Partial transpose is shown to be necessary and sufficient in detecting entanglement for a class of partially coherent vector light fields which have a spatial part to be Gaussian. An experimental realization of the studied entangled states using classical optical interferometry is outlined.
Gaussian spatial-polarization entanglement in a coherent vectorial paraxial light field is studied. Detection of spatial-polarization entanglement through fringe movement on rotation of a linear polarizer, with the light field passing through the polarizer, is outlined. The fringe movement is shown to be a sufficient condition for the detection of spatial-polarization entanglement in coherent paraxial vector light fields. Two Gaussian light fields with a small relative tilt but with significant spatial overlap and with orthogonal polarizations are shown to possess close to 1 ebit of spatial-polarization entanglement. Tunable Gaussian spatial-polarization entanglement is experimentally demonstrated in a folded Mach-Zehnder interferometer.
For light fields, the manifestation of correlations between fluctuating electric field components at different space–time points is referred to as coherence, whereas these correlations appearing between orthogonal electric field components at a single space–time point are referred to as polarization. In this context, a natural question is as follows: how are coherence and polarization interconnected? Very recently, a tight equality P2=V2+D2, namely, the “polarization coherence theorem” (PCT) connecting polarization P with interference visibility V (measure of coherence) and distinguishability D (measure of which-path information) has been proposed [Optica4, 1113 (2017)OPTIC82334-253610.1364/OPTICA.4.001113]. We here report a direct observation of the PCT for classical light fields using a Mach–Zehnder interferometer along with a synthesized source producing a complete gamut of degrees of polarizations. Our experimental demonstration could motivate ongoing experimental efforts toward probing the hidden coherences and complementarity features.
A scheme is discussed for measuring NNNth-order coherences of two orthogonally polarized light fields in a single spatial mode at very limited experimental cost. To implement the scheme, the only measurements needed are the NNNth-order intensity moments after the light beam has passed through two quarter-wave plates, one half-wave plate, and a polarizing beam splitter for specific settings of the wave plates. It is shown that this method can be applied for arbitrarily large NNN. A set of explicit values is given for the settings of the wave plates, constituting an optimal measurement of the NNNth-order coherences for any NNN. For Fock states the method introduced here corresponds to a full state tomography. Applications of the scheme to systems other than polarization optics are discussed.