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arXiv:1606.01582 · Physical Review A

Quantum frequency conversion and strong coupling of photonic modes using four-wave mixing in integrated microresonators

Z. Vernon, Marco Liscidini, John E. Sipe

Published Aug 2, 2016• 23 citations
arXivHTMLPDF

Abstract

Single-photon-level quantum frequency conversion has recently been demonstrated using silicon nitride microring resonators. The resonance enhancement offered by such systems enables high-efficiency translation of quantum states of light across wide frequency ranges at subwatt pump powers. We present a detailed theoretical analysis of the conversion dynamics in these systems and show that they are capable of converting single- and multiphoton quantum states. Analytic formulas for the conversion efficiency, spectral conversion probability density, and pump-power requirements are derived which are in good agreement with previous theoretical and experimental results. We show that with only modest improvement to the state of the art, efficiencies exceeding 95% are achievable using less than 100 mW of pump power. At the critical driving strength that yields maximum conversion efficiency, the spectral conversion probability density is shown to exhibit a flat-topped peak, indicating a range of insensitivity to the spectrum of a single-photon input. Two alternate theoretical approaches are presented to study the conversion dynamics: a dressed-mode approach that yields a better intuitive picture of the conversion process, and a study of the temporal dynamics of the participating modes in the resonator, which uncovers a regime of Rabi-like coherent oscillations of single photons between two different frequency modes. This oscillatory regime arises from the strong coupling of distinct frequency modes mediated by coherent pumps.

DOI
10.1103/physreva.94.023810

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Single-photon-level quantum frequency conversion has recently been demonstrated using silicon nitride microring resonators. The resonance enhancement offered by such systems enables high-efficiency translation of quantum states of light across wide frequency ranges at subwatt pump powers. We present a detailed theoretical analysis of the conversion dynamics in these systems and show that they are capable of converting single- and multiphoton quantum states. Analytic formulas for the conversion efficiency, spectral conversion probability density, and pump-power requirements are derived which are in good agreement with previous theoretical and experimental results. We show that with only modest improvement to the state of the art, efficiencies exceeding 95% are achievable using less than 100 mW of pump power. At the critical driving strength that yields maximum conversion efficiency, the spectral conversion probability density is shown to exhibit a flat-topped peak, indicating a range of insensitivity to the spectrum of a single-photon input. Two alternate theoretical approaches are presented to study the conversion dynamics: a dressed-mode approach that yields a better intuitive picture of the conversion process, and a study of the temporal dynamics of the participating modes in the resonator, which uncovers a regime of Rabi-like coherent oscillations of single photons between two different frequency modes. This oscillatory regime arises from the strong coupling of distinct frequency modes mediated by coherent pumps.
In this thesis I study in detail the quantum dynamics of several nonlinear optical processes in microresonator systems. A Heisenberg-picture input-output formalism is developed from first principles that includes the effects of scattering losses and independent quality factors and coupling ratios for different resonances. The task of calculating the device output is then reduced to solving a set of driven, damped, ordinary differential equations for the resonator mode operators alone. This theoretical framework is used to study photon pair generation via spontaneous four-wave mixing in the weakly pumped regime, on which the effects of scattering losses are appraised. A more strongly driven regime is studied for continuous wave pumps, demonstrating when self- and cross-phase modulation and multi-photon pair generation become important, and their effects on the spectral and power scaling properties of the system are examined; A detuning strategy is presented that compensates for some of these effects. The results of the weak-pump regime are applied to study microresonator-based her- alded single photon sources. The impact of scattering losses is studied, revealing that typical systems suffer from low heralding efficiency due to these losses. A technique to improve heralding efficiency is presented through over-coupling the resonator-channel system, and a resultant trade-off between heralding rate and heralding efficiency is un- covered. Limitations to the spectral purity of the heralded single photon output for conventional microresonator systems are also analysed, and a more sophisticated cou- pling scheme presented to overcome the upper bound for spectral purity of 93% that exists in typical systems, permitting the generation of single photons with spectral pu- rity arbitrarily close to 100% without spectral filtering or sophisticated phase-matching techniques. The theory of quantum frequency conversion in microresonators using four-wave mix- ing is then developed in detail, and the spectral conversion probability and conversion efficiency studied. Efficiencies exceeding 90% using less than 100 mW of pump power are predicted to be achievable with current technology. A dressed mode picture is developed to better understand the conversion dynamics. Rabi-like spectral splitting and temporal oscillations of the intraresonator mean photon number are predicted, exhibiting a novel regime of strongly coupled photonic modes.
Microring resonators are attractive for low-power frequency conversion via Bragg-scattering four-wave-mixing due to their comb-like resonance spectrum, which allows resonant enhancement of all four waves while maintaining energy and momentum conservation. However, the symmetry of such mode structures limits the conversion efficiency to 50% due to the equal probability of up- and down-conversion. Here, we demonstrate how two coupled microrings enable highly directional conversion between the spectral modes of one of the rings. An extinction between up- and down-conversion of more than 40 dB is experimentally observed. Based on this method, we propose a design for on-chip multiplexed single-photon sources that probabilistically generate photon pairs across many frequency modes of a ring resonator and subsequently convert them to a single frequency—thereby enabling quasi-deterministic photon emission. Our numerical analysis shows that once a photon is generated, it can be converted and emitted into a wave packet having a 90% overlap with a Gaussian with 99% efficiency for a ratio between intrinsic and coupling quality factors of 400.
The conversion and interaction between quantum signals at the single-photon level are essential for scalable quantum photonic information technology. Using a fully optimized periodically poled lithium niobate microring, we demonstrate ultraefficient sum-frequency generation on a chip. The external quantum efficiency reaches $(65\ifmmode\pm\else\textpm\fi{}3)\mathrm{%}$ with only $(104\ifmmode\pm\else\textpm\fi{}4)$-$\ensuremath{\mu}\mathrm{W}$ pump power. At peak conversion, $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$-noise photon is created during the cavity lifetime, which meets the requirement of quantum applications using single-photon pulses. Using a pump and signal in single-photon coherent states, we directly measure the conversion probability produced by a single pump photon to be ${10}^{\ensuremath{-}5}$, which is a significant improvement from the state of the art, and the photon-photon coupling strength to be 9.1 MHz. Our results mark steady progress toward quantum nonlinear optics at the ultimate single-photon limit, with potential applications in highly integrated photonics and quantum optical computing.
Photonic chips with silicon nitride (Si3N4\mathrm{Si_3N_4}Si3​N4​) microring resonators are well established as heralded single-photon sources, but their operation as frequency-degenerate twin-photon sources has not previously been demonstrated. Here, we realise a twin-photon source at telecommunication wavelengths in a Si3N4\mathrm{Si_3N_4}Si3​N4​ ring microresonator via an inverse four-wave mixing (FWM) process, in which two photons from spectrally distinct pumps are converted into a pair of identical twin photons. The measurements show a maximum coincidence-to-accidental ratio (CAR) of 5.4±0.65.4\pm0.65.4±0.6. In addition, the microresonator functions as a heralded single-photon source through pump-degenerate spontaneous four-wave mixing (SFWM), exhibiting a spectral purity of P=0.67±0.05P=0.67\pm0.05P=0.67±0.05 and a heralded anti-bunching of gh(2)(0)=0.0042±0.0015g^{(2)}_h(0)=0.0042\pm0.0015gh(2)​(0)=0.0042±0.0015. Together, these results demonstrate both photon-generation schemes on a single integrated Si3N4\mathrm{Si_3N_4}Si3​N4​ platform, highlighting its potential for scalable, tailored quantum light generation.