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Physical Review A

Indistinguishability of orbital angular-momentum modes in spontaneous parametric down-conversion

Geraldo Alexandre Barbosa

Published May 8, 2009• 1 citation
Publisher

Abstract

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.

DOI
10.1103/physreva.79.055805

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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.
Assuming two quantum states of spontaneous parametric downconversion carrying orbital angular momentum, one may ask the question what is the minimum probability of error in identifying between two of these biphoton states by an arbitrary physical measurement over the biphoton state generated. While correctly chosen geometries may lead to perfect distinguishability of modes, it is worth noticing that experimental subtleties may lead to a poor mode distinguishability. We discuss the case where a restricted range instead of the needed range of wave vectors is collected by the experimental setup. These considerations may be useful for some applications, e.g., cryptography.
We elucidate the paraxial orbital angular momentum of entangled photon pairs generated by spontaneous parametric down-conversion (SPDC) in different non-collinear geometries. To date, most investigations addressed SPDC in nearly collinear phase-matching geometries, where the pump, the signal and idler photons propagate coaxially almost along the same direction. However, non-collinear geometries introduce a variety of new features. The OAM of the entangled photons strongly depend on the propagation direction of the photons. Here we show that locally paraxial measurements of the OAM conducted with entangled photons generated in non collinear geometries, they do not comply with the known selection rules for the spiral index of the pump, signal and idler mode functions (Mair et al., Nature 412, 313 (2001)). In particular, we find the orbital angular momentum of entangled pairs generated in purely transverse-emitting configurations, where the entangled photons counter-propagate perpendicularly to the direction of propagation of the pump beam. In transverse emitting configurations, the spatial shape of the down converted in one transverse dimensions strongly depends on the corresponding spatial shape of the input pump beam, while in the other transverse dimension, the shape is tailored by the longitudinal phase matching. The spatial walk-off of all interacting waves in the parametric process also determines the OAM content of the down-converted photons, and here its influence is also revealed.
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 calculate the anticipated correlation between measurements of the orbital angular momentum of the signal and idler beams for parametric down-conversion. These calculations apply to the experiments where the orbital angular momentum state is measured by the use of computer-generated holograms. Displacement of these holograms with respect to the beam axis allows the measurement of superpositions of Laguerre—Gaussian modes. The correlations between such superposition modes of the signal and idler beams show their entanglement and could be used for Bell-type tests of nonlocality.