We provide a general decomposition of the two-photon state produced by spontaneous parametric down-conversion in Hermite-Gaussian modes, in the case that the pump beam is described by a Hermite-Gaussian beam of any order. We show that the spatial correlations depend explicitly on the order of the pump beam, as well as other experimental parameters. We use the decomposition to demonstrate a few interesting cases. Our results are applicable to the engineering of two-photon spatial entanglement, in particular for non-Gaussian states.We provide a general decomposition of the two-photon state produced by spontaneous parametric down-conversion in Hermite-Gaussian modes, in the case that the pump beam is described by a Hermite-Gaussian beam of any order. We show that the spatial correlations depend explicitly on the order of the pump beam, as well as other experimental parameters. We use the decomposition to demonstrate a few interesting cases. Our results are applicable to the engineering of two-photon spatial entanglement, in particular for non-Gaussian states.

arXiv:1208.4336Journal of Physics B Atomic Molecular and Optical PhysicsJul 23, 201225 citations

Quality of spatial entanglement propagation

Matthew C. Reichert, Xiaohang Sun, Jason W. Fleischer

We explore, both experimentally and theoretically, the propagation dynamics of spatially entangled photon pairs (biphotons). Characterization of entanglement is done via the Schmidt number, which is a universal measurement of the degree of entanglement directly related to the nonseparability of the state into its subsystems. We develop expressions for the terms of the Schmidt number that depend on the amplitude and phase of the commonly used double-Gaussian approximation for the biphoton wave function, and demonstrate migration of entanglement between amplitude and phase upon propagation. We then extend this analysis to incorporate both phase curvature in the pump beam and higher spatial frequency content of more realistic non-Gaussian wave functions. Specifically, we generalize the classical beam quality parameter ${M}^{2}$ to the biphotons, allowing the description of more information-rich beams and more complex dynamics. Agreement is found with experimental measurements using direct imaging and Fourier optics.We explore, both experimentally and theoretically, the propagation dynamics of spatially entangled photon pairs (biphotons). Characterization of entanglement is done via the Schmidt number, which is a universal measurement of the degree of entanglement directly related to the nonseparability of the state into its subsystems. We develop expressions for the terms of the Schmidt number that depend on the amplitude and phase of the commonly used double-Gaussian approximation for the biphoton wave function, and demonstrate migration of entanglement between amplitude and phase upon propagation. We then extend this analysis to incorporate both phase curvature in the pump beam and higher spatial frequency content of more realistic non-Gaussian wave functions. Specifically, we generalize the classical beam quality parameter ${M}^{2}$ to the biphotons, allowing the description of more information-rich beams and more complex dynamics. Agreement is found with experimental measurements using direct imaging and Fourier optics.

arXiv:1611.07967Physical Review AJun 22, 201735 citations

Evolution of Spatial Entanglement of Realistic Biphotons

Matthew C. Reichert, Xiaohang Sun, Jason W. Fleischer

Jan 1, 20170 citations

All-optical mode conversion via spatially multimode four-wave mixing

Onur Danaci, Christian de los Ríos, Ryan T. Glasser

We experimentally demonstrate the conversion of a Gaussian beam to an approximate Bessel–Gauss mode by making use of a non-collinear four-wave mixing (4WM) process in hot atomic vapor. The presence of a strong, spatially non-Gaussian pump both converts the probe beam into a non-Gaussian mode, and generates a conjugate beam that is in a similar non-Gaussian mode. The resulting probe and conjugate modes are compared to the output of a Gaussian beam incident on an annular aperture that is then spatially filtered according to the phase-matching conditions imposed by the 4WM process. We find that the resulting experimental data agrees well with both numerical simulations, as well as analytical formulae describing the effects of annular apertures on Gaussian modes. These results show that spatially multimode gain platforms may be used as a new method of mode conversion.We experimentally demonstrate the conversion of a Gaussian beam to an approximate Bessel–Gauss mode by making use of a non-collinear four-wave mixing (4WM) process in hot atomic vapor. The presence of a strong, spatially non-Gaussian pump both converts the probe beam into a non-Gaussian mode, and generates a conjugate beam that is in a similar non-Gaussian mode. The resulting probe and conjugate modes are compared to the output of a Gaussian beam incident on an annular aperture that is then spatially filtered according to the phase-matching conditions imposed by the 4WM process. We find that the resulting experimental data agrees well with both numerical simulations, as well as analytical formulae describing the effects of annular apertures on Gaussian modes. These results show that spatially multimode gain platforms may be used as a new method of mode conversion.

arXiv:1608.01333New Journal of PhysicsJul 15, 201610 citations

Entanglement in spatially inhomogeneous systems

V. V. França, Klaus Capelle

Oct 10, 20070 citations

{M}^{2}

to the biphotons, allowing the description of more information-rich beams and more complex dynamics. Agreement is found with experimental measurements using direct imaging and Fourier optics.