Analysis and Interpretation of High Transverse Entanglement in Optical Parametric Down Conversion

Abstract

Quantum entanglement associated with transverse wave vectors of down conversion photons is investigated based on the Schmidt decomposition method. We show that transverse entanglement involves two variables: orbital angular momentum and transverse frequency. We show that in the monochromatic limit high values of entanglement are closely controlled by a single parameter resulting from the competition between (transverse) momentum conservation and longitudinal phase matching. We examine the features of the Schmidt eigenmodes, and indicate how entanglement can be enhanced by suitable mode selection methods.

Experimental Demonstration of Fractional Orbital Angular Momentum Entanglement of Two Photons

“…The dimensionality D of the subspace probed in the experiment is either limited by the number of entangled modes emitted by the BBO crystal, expressed by the Schmidt number K [14,15], or by the (spatial) modal bandwidth of the analyzers, N. To estimate K, we follow Law and Eberly's approximate analytical theory [16],…”

Spatial, spectral, and temporal coherence of ultraintense twin beams

“…It quantifies the number of paired modes found in a twin beam. We note that formula (18) reduces to the usual Schmidt number [19] for weak twin beams. We also note that several quantifiers of entanglement dimensionality have been compared in [13,38,39].…”

“…We decompose the twin beam together with the pump beam into multiple triplets of individual spatio-spectral modes defined in the signal, idler and pump beams. We adopt the signal and idler spatio-spectral Schmidt modes defined for weak twin beams [17][18][19][20] following the approach elaborated in [13]. The presented theory represents a generalization of the theory given in [13] that assumes un-depleted pump beams.…”

Quantum properties of counterpropagating two-photon states generated in a planar waveguide

“…Entanglement between the signal-and idler-field frequencies can be conveniently quantified using entropy of entanglement [43,44]. To determine entropy S e of entanglement we have to decompose a two-photon spectral amplitude Φ into Schmidt decomposition [45]:…”