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OSA Advanced Photonics Congress

Revealing Arnold’s Tongues in Photon-pair Generation and Quantum Frequency Conversion

Philip B. Main, Peter J. Mosley, Andrey V. Gorbach

Published Jan 1, 2020• 0 citations
Publisher

Abstract

We show that the widely-accepted theory of photon-pair generation via spontaneous down-conversion (SPDC) in nonlinear optical crystals and waveguides is incomplete, as it fails to account for the important physical phenomenon of parametric resonances.
DOI
10.1364/iprsn.2020.jm2e.1

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The existing widely-accepted theory of photon-pair generation via spontaneous down-conversion (SPDC) in nonlinear optical crystals and waveguides is incomplete, as it fails to account for the important physical phenomenon of parametric resonances. We demonstrate that exponential gain of classical fields in the regime of parametric resonance corresponds to resonant delocalization in the Glauber-Fock model of quantum SPDC. We propose a quantitative measure of localisation of Floquet eigen-modes as an analogue of classical gain to identify regimes of resonant delocalization. Using this method, we are able to reconstruct the classical "Arnold tongues" map of domains of instabilities for SPDC. We also predict novel regimes of resonant delocalization in the two-level model describing quantum frequency conversion processes.
Abstract The existing widely-accepted theory of photon-pair generation via spontaneous down-conversion (SPDC) in nonlinear optical crystals and waveguides is incomplete, as it fails to account for the important physical phenomenon of parametric resonances. We demonstrate that exponential gain of classical fields in the regime of parametric resonance corresponds to resonant delocalisation in the Glauber–Fock model of quantum SPDC. We propose a quantitative measure of localisation of Floquet eigen-modes as an analogue of classical gain to identify regimes of resonant delocalisation. Using this method, we are able to reconstruct the classical ‘Arnold tongues’ map of domains of instabilities for SPDC. We also predict novel regimes of resonant delocalisation in the two-level model describing quantum frequency conversion processes.
Integrated optical circuits enable stable and scalable realization of quantum logic devices, which can form a basis for the mass production of photonic chips for quantum communications and computations. An important challenge is the integration of single-photon sources, which should provide on-chip generation and preparation of quantum photon states. Spontaneous parametric down-conversion (SPDC) provides an attractive solution for experimental generation of correlated and entangled photon pairs [1,2]. However, internal losses in the waveguides may still be present, affecting nontrivially the emerging photon state [3].
A theory is presented for the quantum state of photon pairs generated from spontaneous parametric down-conversion nonlinear process. In this theory, the influence of the final sizes of nonlinear optical crystals on optical eigenmodes is explicitly taken into consideration. It was found that these photon pairs are not in entangled quantum states. Polarization correlations between the signal beam and the idler beam are explained. It is also shown that the two photons generated from SPDC are not spatially separated, therefore the polarization correlation between the signal and idler beams is not an evidence for quantum non-locality.
Spontaneous parametric down-conversion (SPDC) in a nonlinear crystal has been a workhorse for the generation of entangled and correlated single-photon pairs used for quantum communications applications for nearly three decades. However, as a naturally broadband process, the ability of SPDC to interface with the very narrow energy transitions in atomic ensembles for implementing quantum memories, which are needed for quantum repeaters to extend the reach of quantum communications, was initially limited. To overcome this limitation, the process was enhanced by placing the nonlinear crystal inside a resonating cavity. This modified process has some important advantages, including narrowing the spectral linewidth of generated photons into brighter resonant modes of the cavity, and the ability to lock the desired mode of the cavity to the targeted transition frequency of the atomic ensemble. This paper presents an overview of the principle of cavity-enhanced SPDC, a review of works to date using this technique, and an example of one of these implementations.
Generation of entangled photon pairs at telecom wavelength has been garnering a growing interest in the context of quantum communications and quantum computing. Several generation techniques have been proposed, including spontaneous Four-Wave Mixing in resonators or Spontaneous Parametric Down Conversion (SPDC) in Periodically Polled Lithium Niobate (PPLN) waveguides. Large photon pair efficiencies have been demonstrated in particular in PPLN on insulator [3]. However, polarization entangled photon pair generation (Type II phase matching configuration) suffers from a less favourable non-linear coefficient and optical mode birefringence in PPLN.