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Nonlinear Optics

Coincidence Dips and Revivals from a Type-II Optical Parametric Amplifier

Jeffrey H. Shapiro

Published Jan 1, 2002• 7 citations

Abstract

Parametric downconversion sources are intrinsically broadband; THz bandwidths are typical. Our recent proposal for long-distance qubit teleportation [1], however, requires a high-brightness narrowband source of polarization entanglement, to match the MHz linewidth of its trapped-atom quantum memory [2]. We have shown theoretically [3] that the polarization-combined outputs from a pair of coherently-pumped, doubly-resonant, optical parametric amplifiers (OPAs) will fulfill this need. That analysis employed a lumped-element model for the OPA behavior in the vicinity of the double resonance, and was sufficiently generic to include both type-I and type-II phase matching. In the present paper, we report a traveling-wave treatment of the type-II phase matched, doubly-resonant OPA. When restricted to frequencies close to the double resonance, the new analysis reproduces the lumped-element results. Without this restriction, however, a new quantum interference effect emerges: coincidence-counting dips and revivals in a Hong-Ou-Mandel interferometer [4].

DOI: 10.1364/nlo.2002.fc7

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Parametric downconversion sources are intrinsically broadband; THz bandwidths are typical. Our recent proposal for long-distance qubit teleportation [1], however, requires a high-brightness narrowband source of polarization entanglement, to match the MHz linewidth of its trapped-atom quantum memory [2]. We have shown theoretically [3] that the polarization-combined outputs from a pair of coherently-pumped, doubly-resonant, optical parametric amplifiers (OPAs) will fulfill this need. That analysis employed a lumped-element model for the OPA behavior in the vicinity of the double resonance, and was sufficiently generic to include both type-I and type-II phase matching. In the present paper, we report a traveling-wave treatment of the type-II phase matched, doubly-resonant OPA. When restricted to frequencies close to the double resonance, the new analysis reproduces the lumped-element results. Without this restriction, however, a new quantum interference effect emerges: coincidence-counting dips and revivals in a Hong-Ou-Mandel interferometer [4].

A 532 nm pumped type-II phase-matched, doubly resonant KTP optical parametric amplifier (OPA) was operated near frequency degeneracy to yield an inferred downconverted photon pair production rate of 1.7×10 6 s -1 at a pump power of 100 µW. The OPA output consisted of three components: narrowband doubly resonant mode pairs; narrowband singly resonant mode pairs for which either the signal or idler was resonant with the cavity and broadband nonresonant mode pairs. Under frequency-degenerate operation, the broadband nonresonant mode pairs were polarization triplet states. We observed quantum interference between the orthogonally polarized photons of the triplet states when they were analysed with a polarizer set at 45° relative to the OPA's output polarizations, leading to reduced coincidence counts.

The signals and idlers from a pair of matched, doubly resonant optical parametric amplifiers (OPAs) can be combined to yield polarization-entangled vector signal and idler beams. Within any coincidence interval much longer than the OPA cavity lifetime, every signal photon of polarization is accompanied by an idler photon of the conjugate polarization ´, and vice versa. For periodically poled lithium tantalate OPAs, the pair production rate is estimated to be approximately 1.5 × 10 6 s -1 , within a 30 MHz bandwidth at a 795 nm centre wavelength and a 70 ns duration coincidence interval, using only 0.7 mW of pump power per OPA.

Summary form only given. A type-II phase-marched parametric downconverter can be used to produce polarization-entangled photon pairs. We propose a production scheme for polarization-entangled photon pairs by using a pair of optical parametric amplifiers (OPAs) whose narrowband generation rate is high enough to make it a practical source for a trapped-atom quantum memory. For a type-II system using periodically-poled potassium titanyl phosphate (PPKTP) (KTiOPO/sub 4/) optical parametric amplifiers OPAs.

In this theoretical study, we demonstrate that entangled states are able to significantly extend the functionality of Hong-Ou-Mandel (HOM) interferometers. By generating a coherent superposition of parametric-down-conversion photons and spatial entanglement in the input channel, the coincidence probability measured at the output changes from a typical HOM-type dip (photon bunching) into much richer patterns, including an antibunching peak and rapid oscillation fringes with twice the optical frequency. The considered system should be realizable on a single chip using current waveguide technology in the

{\mathrm{LiNbO}}_{3}

platform.

We study the Hong-Ou-Mandel interferometer in the regime of spontaneous parametric down-conversion with high pump beam power at the crystal. In this regime one and two photons from a pump pulsed laser beam generate one and two pairs of photons, respectively. These photons are then directed to the beam splitter of the interferometer and detected at its exit in coincidence. An interesting phenomenon is observed: The reduction of the visibility of the Hong-Ou-Mandel coincidence peak (or dip) with the increase of pump power. We study the relation between the visibility of the fourth-order interference pattern and the power of the pumping laser beam for type I and type II phase-matching crystals. Our theoretical calculations are in good agreement with the experimental results.

The nondegenerate optical parametric amplifier (OPA) has many uses for investigating quantum fluctuations of light. Among them are EPR-type quadrature-phase correlations,1 QND measurement,2 and phase-sensitive quantum amplification.3 To study these problems, a reliable high-gain low-loss optical parametric amplifier (OPA) is crucial. Although OPAs operated at 1064 nm with KTP crystals pumped by a frequency doubled YAG laser exist,1 their performance is compromised because of problems with beam walk-off and polarization mixing for pairs of critically phase-matched KTP crystals. To avoid such problems, we have constructed a different nondegenerate OPA, which is operated at 1080 nm and consists of a single KTP crystal with type II noncritical phase matching. The pump beam at 540 nm for the amplifier is obtained from intracavity frequency doubling of a single-mode Nd: YAP laser with a similar KTP crystal as in the OPA.