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arXiv:0711.2025 · Physical Review A

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

Jan Peřina

Published Jan 8, 2008• 21 citations
arXivHTMLPDF

Abstract

A nonlinear planar waveguide pumped by a beam orthogonal to its surface may serve as a versatile source of photon pairs. By changing the pump-pulse duration, pump-beam transverse width, and angular decomposition of the pump-beam frequency characteristics of a photon pair, including the spectral widths of signal and idler fields, the pair time duration as well as the degree of entanglement of the two fields, can be changed significantly. Using the measured spectral widths of the down-converted fields and the width of a coincidence-count dip in a Hong-Ou-Mandel interferometer, the entropy of entanglement can be determined.

DOI
10.1103/physreva.77.013803

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A nonlinear planar waveguide pumped by a beam orthogonal to its surface may serve as a versatile source of photon pairs. By changing the pump-pulse duration, pump-beam transverse width, and angular decomposition of the pump-beam frequency characteristics of a photon pair, including the spectral widths of signal and idler fields, the pair time duration as well as the degree of entanglement of the two fields, can be changed significantly. Using the measured spectral widths of the down-converted fields and the width of a coincidence-count dip in a Hong-Ou-Mandel interferometer, the entropy of entanglement can be determined.
We have developed a rigorous quantum model of spontaneous parametric down-conversion in a nonlinear 1D photonic-band-gap structure based upon expansion of the field into monochromatic plane waves. The model provides a two-photon amplitude of a created photon pair. The spectra of the signal and idler fields, their intensity profiles in the time domain, as well as the coincidence-count interference pattern in a Hong-Ou-Mandel interferometer are determined both for cw and pulsed pumping regimes in terms of the two-photon amplitude. A broad range of parameters characterizing the emitted down-converted fields can be used. As an example, a structure composed of 49 layers of GaN∕AlN\mathrm{Ga}\mathrm{N}∕\mathrm{Al}\mathrm{N}GaN∕AlN is analyzed as a suitable source of photon pairs having high efficiency.
We experimentally demonstrate an integrated semiconductor source of counterpropagating twin photons in the telecom range. A pump beam impinging on top of an AlGaAs waveguide generates parametrically two counterpropagating, orthogonally polarized signal/idler guided modes. A 2 mm long waveguide emits at room temperature one average photon pair per pump pulse, with a spectral linewidth of 0.15 nm. The twin character of the emitted photons is ascertained through a time-correlation measurement. This work opens a route towards new guided-wave semiconductor quantum devices.
The conditions required for spontaneous parametric down-conversion in a waveguide with periodic nonlinearity in the presence of an unguided pump field are established. Control of the periodic nonlinearity and the physical properties of the waveguide permits the quasiphase matching equations that describe counterpropagating guided signal and idler beams to be satisfied. We compare the tuning curves and spectral properties of such counterpropagating beams to those for copropagating beams under typical experimental conditions. We find that the counterpropagating beams exhibit a narrow bandwidth, permitting the generation of quantum states that possess discrete-frequency entanglement. Such states may be useful for experiments in quantum optics and technologies that benefit from frequency entanglement.
We have designed and fabricated a set of AlGaAs multilayer waveguides, which can serve as a source of entangled photons at 1.55μm through parametric fluorescence. In our scheme two counterpropagating, orthogonally polarized signal/idler modes are nonlinearly generated by a pump wave impinging on the upper surface of the waveguide. To check the compliance with design specifications on phase-matching wavelength and parametric gain, we have systematically measured effective indices and surface-emitting second-harmonic generation, respectively. This characterization allowed us to single out a nominal sample with optimum performances, which we numerically modeled for counterpropagating parametric fluorescence. We predict a pair generation efficiency ηPF=4×10−13 (signal photons per pump photon). For a 1W (peak), 100ns pump pulse at normal incidence, this corresponds to about 14 photons per dark count with state-of-the-art avalanche photodiodes.
Abstract Frequency entangled biphoton sources have played an important role in quantum information. There are two key characteristics which determine the extent of their applications: the spectral indistinguishability and the degree of frequency entanglement. Previously, the spectral indistinguishability of the biphoton state is measured by the Hong–Ou–Mandel (HOM) interference visibility, whereas the degree of frequency entanglement is normally characterized with independent spectral measurements. However, these two quantum features have not been successfully measured with a single experimental setup. In this paper, we deduce the temporal distribution of a short-pulse pumped type-II spontaneous parametric down converted (SPDC) biphoton source and its relevant temporal entanglement parameter R t for operationally quantifying the degree of frequency entanglement. Furthermore, we theoretically and experimentally demonstrate, due to the inherent group delay, the difference between the signal and idler photons at the exit of the type-II nonlinear crystal, resulting in a HOM-shape dip at both sides of the center fringed envelope of the MZ interferometric coincidence diagram. By measuring the HOM-shape dip depth, the separation between the two sideband dips as well as the MZ fringed envelope width, both the spectral indistinguishability and the temporal entanglement parameter can thus be simultaneously quantified. This implementation provides us a unified and convenient method to characterize the frequency entanglement of the short-pulse pumped biphotons.