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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Transverse quantum Schmidt-mode patterns in down conversion

C. K. Law, Joseph H. Eberly

Published Feb 3, 2004• 0 citations
Publisher

Abstract

We present the transverse patterns for down conversion that are associated with signal and idler entanglement, in the form of the unique Schmidt modes for the photons. We introduce Schmidt analysis and review Schmidt modes in the simpler context of short-pulse down-conversion with frequency entanglement. For the more difficult pattern analysis, we simplify by assuming zero orbital angular momentum for the pump pulse as well as cw pump light. We provide angular momentum labels as well as Schmidt mode labels to categorize the patterns.

DOI
10.1117/12.512453

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We present the transverse patterns for down conversion that are associated with signal and idler entanglement, in the form of the unique Schmidt modes for the photons. We introduce Schmidt analysis and review Schmidt modes in the simpler context of short-pulse down-conversion with frequency entanglement. For the more difficult pattern analysis, we simplify by assuming zero orbital angular momentum for the pump pulse as well as cw pump light. We provide angular momentum labels as well as Schmidt mode labels to categorize the patterns.
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In this article we investigate the orbital angular momentum spectrum of photons produced in parametric down conversion process. We study how the transverse profile of the pump mode affects the spectrum as compared to a gaussian pump beam. We show that using perfect optical vortex mode as pump the spectrum can be highly narrowed down. We further study the entanglement between the two down converted photons in the orbital angular momentum basis. We observe that photons entangled in Laguerre-Gaussian modes exhibit greater higher dimensional entanglement.
Identification of light modes usually requires careful considerations of the collecting geometry. This is particularly true for states carrying orbital angular-momentum modes from spontaneous parametric down-conversion due to the entanglement of the signal and idler fields. A detailed understanding of the generated modes in a general case allows the design of efficient detection setups. This is true for distinct cases, e.g., when multiple samplings are performed by repeated state generation or in single-photon cryptography or quantum computation, where a photon state is generated within a short-time window and a single measurement is performed. Aspects of nonorthogonality of signal and idler modes and effects of restrictions on the collecting geometry are discussed in this work.
Summary form only given. Entangled photons are the workhorse of quantum information technology and cryptography. So far, the emphasis has been on entanglement of the polarization state (for type II down conversion), or of the wave vectors of the degenerate signal and idler pair (for type I down conversion). A subject of current interest is entanglement in the spatial domain, i.e. nontrivial, spatially extended, correlation between signal and idler. A prime example of this being the discussion regarding the conservation and entanglement of orbital angular momentum in spontaneous parametric down conversion. We report our very first measurements of the signal-idler correlation in type I down conversion, employing a frequency-doubled femtosecond Ti:sapphire laser as our source of pump photons, and a fourth generation intensified CCD as our "multi-element single-photon detector" With pump pulses at /spl lambda/ = 400 nm of approximately 2 nJ energy and 250 fs duration directed at a 0.5 mm long BBO crystal we detect roughly one pair in every four frames.
We put forward an approach to estimate the amount of bipartite spatial entanglement of down-converted photon states correlated in orbital angular momentum and the magnitude of the transverse (radial) wave vectors. Both degrees of freedom are properly considered in our framework, which only requires azimuthal local linear optical transformations and mode selection analysis with two fiber detectors. The coincidence distributions predicted by our approach give an excellent fit to the distributions measured in a recent experiment aimed to show the very high-dimensional transverse entanglement of twin photons from a down-conversion source. Our estimate for the Schmidt number is substantially lower but still confirms the presence of high-dimensional entanglement.