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arXiv:0901.2783 · Physical Review Letters

Continuous Variable Entanglement and Squeezing of Orbital Angular Momentum States

Mikael Lassen, Gerd Leuchs, Ulrik L. Andersen

Published Apr 23, 2009• 113 citations
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Abstract

We report the first experimental characterization of the first-order continuous variable orbital angular momentum states. Using a spatially nondegenerate optical parametric oscillator (OPO) we produce quadrature entanglement between the two first-order Laguerre-Gauss modes. The family of orbital angular momentum modes is mapped on an orbital Poincaré sphere, where the mode's position on the sphere is spanned by the three orbital parameters. Using a nondegenerate OPO we produce squeezing of these parameters, and as an illustration, we reconstruct the "cigar-shaped" uncertainty volume on the orbital Poincaré sphere.

DOI
10.1103/physrevlett.102.163602

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We report the first experimental characterization of the first-order continuous variable orbital angular momentum states. Using a spatially nondegenerate optical parametric oscillator (OPO) we produce quadrature entanglement between the two first-order Laguerre-Gauss modes. The family of orbital angular momentum modes is mapped on an orbital Poincaré sphere, where the mode's position on the sphere is spanned by the three orbital parameters. Using a nondegenerate OPO we produce squeezing of these parameters, and as an illustration, we reconstruct the "cigar-shaped" uncertainty volume on the orbital Poincaré sphere.
Spatially structured quantum states, such as orbital angular momentum (OAM) squeezing and entanglement, is currently a popular topic in quantum optics. The method of generating and manipulating spatial quantum states on demand needs to be explored. In this paper, we generated OAM mode squeezed states of −5.4 dB for the L G 0 + 1 mode and −5.3 dB for the L G 0 − 1 mode directly by an optical parametric oscillator (OPO) for the first time. Additionally, we demonstrated that the OAM mode squeezed and entangled states were respectively generated by manipulating the nonlinear process of the OPO by controlling the relative phase of two beams of different modes, thus making two different spatial multimode pump beams. We characterized the Laguerre-Gaussian (LG) entangled states by indirectly measuring the squeezing for the H G 10 ( 45 ∘ ) mode and H G 10 ( 135 ∘ ) mode, and directly measuring the entanglement between the L G 0 + 1 and L G 0 − 1 modes. The effective manipulation of the OAM quantum state provides a novel insight into the continuous variable quantum state generation and construction on demand for high-dimensional quantum information and quantum metrology.
We have generated a new quantum state of light composed of quadrature entangled Laguerre-Gaussian (LG) modes. For the generation we used an OPO operating in a new regime where all field parameters are degenerate except for its spatial degree of freedom for which it is two-fold degenerate. The entanglement is manifested in the squeezing of the rotated modes in the Hermite-Gauss (HG) basis, measured with a specially tailored local oscillator. The most promising application of CV orbital angular momentum (OAM) states is their compatibility with atoms, thus allowing for storage of CV quantum information.
Abstract We demonstrate experimentally a measurement scheme for the Stokes operators for the continuous-variable squeezed states of orbital angular momentum (OAM). An OAM squeezed state is generated by coupling a dim Hermite-Gauss HG01-mode quadrature-squeezed light beam with a bright HG10-mode coherent light beam on a 98/2 beam splitter. Using an asymmetric Mach–Zehnder interferometer with an extra Dove prism in one arm, we measured the three orbital Stokes operators of the OAM squeezed states with a self-homodyne detection and finally characterized their positions and noise on the orbital Poincaré sphere.
We report on the generation of continuous-variable hyperentanglement of polarization and orbital angular momentum with a type II optical parametric oscillator. By compensating for the astigmatism between spatial modes, we produce an entangled pair of Hermite-Gauss beams. From correlations measurements, we verify the existence of continuous-variable hyperentanglement by the general entanglement criterion as well as by the continuous-variable version of the Peres-Horodecki criterion visualized on an equivalent Poincaré sphere.
We describe continuous-variable hyperentanglement in polarization and orbital angular momentum modes of an optical parametric oscillator. The quantum stochastic equations for the multimode parametric interaction are derived and solved allowing for calculation of the quadrature noise spectra that characterize continuous-variable entanglement. As a main result, we predict simultaneous entanglement between different combinations of amplitude and phase quadratures of the interacting modes. We also propose experimental setups to access the different kinds of entanglement.