Direct Observation of Conservation of Orbital Angular Momentum in Collinear Type-I Spontaneous Parametric Down-Conversion

Stephen Patrick Walborn, Antônio Nonato de Oliveira

Carlos Andres Sevilla Gutierrez

"We implement a direct measurement of the spatial modes distribution generated in a collinear type I spontaneous parametric down-conversion (SPDC) process using a triggered intensified CCD camera. This type of experiments have been realized previously. However in those cases the measurement was an indirect one, where both photons were collected into one-pixel detectors. In this thesis, to the best or our knowledge, it is the first time that a direct two dimensional measurement of the spatial modes distribution is made. These are well described by Laguerre-Gaussian modes. In our experiments we could observe up to mode l=+/-10. By exploiting the capabilities of an ICCD camera, it is possible to visualize the orbital angular momentum (OAM) conservation of the unprocessed SPDC bi-photon state. This is performed by observing the diffraction pattern by a triangular aperture. We show the results using this method for modes l=+/-1,+/-2. This conservation of OAM leads to entanglement in OAM, since one photon carries the anti-correlated topological charge with respect to the other one. Therefore, they are conditioned to the state of the other photon."

Sheng Feng, Prem Kumar

Directly contradictory arguments coexist regarding the conservation rule of orbital angular momentum in spontaneous parametric down-conversion. We analytically show how this rule is decided by spatial symmetry. We discover that the down-converted photon pairs can carry non-negligible extrinsic orbital angular momentum in the degrees of relative-movement freedom due to spatial symmetry breaking, leading to nonconservation of total orbital angular momentum in type-II down-conversion. Also, we demonstrate that the traditional technique does not measure the extrinsic orbital angular momentum.

Gabriel Molina‐Terriza, Juan P. Torres, Lluís Torner

F. M. Miatto, D. Giovannini, Jacquiline Romero +3 more

Sheng Feng, Prem Kumar

Experimental observation of the conservation of orbital angular momentum in spontaneous parametric down-conversion has been theoretically attributed to phase-matching, transfer of plane-wave spectrum from pump beam to down-converted beams. However, according to quantum mechanics, the conservation of angular momentum arises from rotational symmetry of the Hamiltonian describing the studied physical process. Recently, experimental evidence has been found which shows that non-conservation of orbital angular momentum can occur in spontaneous parametric down-conversion due to rotational asymmetry of the Hamiltonian. In this paper, we theoretically show that all reported experimental results of conservation of orbital angular momentum in spontaneous parametric down-conversion are determined only by the Hamiltonian symmetry, and not by phase matching, transfer of plane-wave spectrum.