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arXiv:2408.10776 · Physical Review Applied

Simulating quantum light in lossy microring resonators driven by strong pulses

Youngbin Kim, Seongjin Jeon, Young-Ik Sohn

Published May 16, 2025• 5 citations
arXivHTMLPDF

Abstract

In this work, we present a quantum theory for pulsed photon pair generation in a single ring resonator. Our approach combines the Heisenberg picture input-output formalism with the Ikeda mapping from classical nonlinear optics. In doing so, we address the high-gain regime by incorporating nonperturbative effects, including self-phase modulation, cross-phase modulation, and time-ordering, which are roots for significantly different behaviors in the low-gain regime. We also account for optical losses by introducing an auxiliary waveguide, allowing for a more accurate representation of experimentally viable scenarios. Numerical simulations reveal that nonperturbative effects significantly distort transfer functions, making desirable operations challenging without careful optimization. We show that appropriate detuning of the pump frequency can mitigate these issues, leading to enhanced brightness and higher spectral purity in the high-gain regime. We further investigate the performance of a single ring resonator as a two-mode squeezer by analyzing various performance metrics under experimentally relevant optical loss conditions.

DOI
10.1103/physrevapplied.23.054045

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In this work, we present a quantum theory for pulsed photon pair generation in a single ring resonator. Our approach combines the Heisenberg picture input-output formalism with the Ikeda mapping from classical nonlinear optics. In doing so, we address the high-gain regime by incorporating nonperturbative effects, including self-phase modulation, cross-phase modulation, and time-ordering, which are roots for significantly different behaviors in the low-gain regime. We also account for optical losses by introducing an auxiliary waveguide, allowing for a more accurate representation of experimentally viable scenarios. Numerical simulations reveal that nonperturbative effects significantly distort transfer functions, making desirable operations challenging without careful optimization. We show that appropriate detuning of the pump frequency can mitigate these issues, leading to enhanced brightness and higher spectral purity in the high-gain regime. We further investigate the performance of a single ring resonator as a two-mode squeezer by analyzing various performance metrics under experimentally relevant optical loss conditions.
We present a detailed analysis of strongly driven spontaneous four-wave mixing in a lossy integrated microring resonator side coupled to a channel waveguide. A nonperturbative, analytic solution within the undepleted pump approximation is developed for a cw pump input of arbitrary intensity. In the strongly driven regime self- and cross-phase modulation, as well as multipair generation, lead to a rich variety of power-dependent effects; the results are markedly different than in the low-power limit. The photon-pair generation rate, single-photon spectrum, and joint spectral intensity (JSI) distribution are calculated. Splitting of the generated single-photon spectrum into a doublet structure associated with both pump detuning and cross-phase modulation is predicted, as well as substantial narrowing of the generated signal and idler bandwidths associated with the onset of optical parametric oscillation at intermediate powers. Both the correlated and the uncorrelated contributions to the JSI are calculated, and for sufficient powers the uncorrelated part of the JSI is found to form a quadruplet structure. The pump detuning is found to play a crucial role in all of these phenomena, and a critical detuning is identified which divides the system behavior into distinct regimes, as well as an optimal detuning strategy which preserves many of the low-power characteristics of the generated photons for arbitrary input power.
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.
We present a method for describing nonlinear electromagnetic interactions in integrated photonic devices utilizing an asymptotic-in (-out) field formalism. Our method expands upon previous continuous wave asymptotic treatments by describing the evolution nonperturbatively for an arbitrary pulsed input. This is presented in the context of a squeezing interaction within an integrated micro-ring resonator side coupled to an input-output waveguide, but is readily generalizable to other integrated structures, while including a variety of (nonsqueezing) third-order interactions. An example of a single-pump, nondegenerate squeezing interaction is studied, which is shown to match well with standard coupled-mode treatments for high-finesse resonators, as well as previous perturbative treatments dealing with the generation of pairs with low probability.
We develop a general Hamiltonian treatment of spontaneous four-wave mixing in a microring resonator side-coupled to a channel waveguide. The effect of scattering losses in the ring is included, as well as parasitic nonlinear effects including self- and cross-phase modulation. A procedure for computing the output of such a system for arbitrary parameters and pump states is presented. For the limit of weak pumping an expression for the joint spectral intensity of generated photon pairs, as well as the singles-to-coincidences ratio, is derived.
The intrinsic third-order nonlinearity in silicon has proven it to be quite useful in the field of quantum optics. Silicon is suitable for producing time-correlated photon pairs that are sources of heralded single-photon states for quantum integrated circuits. A quantum signal source in the form of single photons is an inherent requirement for the principles of quantum key distribution technology for secure communications. Here, we present numerical simulations of a silicon ring with a 6 μ m radius side-coupled with a bus waveguide as the source for the generation of single photons. The photon pairs are generated by exploring the process of degenerate spontaneous four-wave mixing (SFWM). The free spectral range (FSR) of the ring is quite large, simplifying the extraction of the signal/idler pairs. The phase-matching condition is considered by studying relevant parameters like the dispersion and nonlinearity. We optimize the ring for a high quality factor by varying the gap between the bus and the ring waveguide. This is the smallest ring studied for photon pair generation with a quality factor in the order of 10 5 . The width of the waveguides is chosen such that the phase-matching condition is satisfied, allowing for the propagation of fundamental modes only. The bus waveguide is pumped at one of the ring resonances with the minimum dispersion (1543.5 nm in our case) to satisfy the principle of energy conservation. The photon pair generation rate achieved is comparable to the state of the art. The photon pair sources exploiting nonlinear frequency conversion/generation processes is a promising alternative to atom-like single-photon emitters in the field of integrated photonics. Such miniaturized structures will benefit future on-chip architectures where multiple single-photon source devices are required on the same chip.
Squeezed states, with their noise reduction below the standard quantum limit, are promising quantum states of light exploited for enhancing sensitivity in quantum sensing or as carriers of information in continuous variable quantum computing and communication. To make use of their quantum advantage, the main common challenge in generating these states is achieving high levels of squeezing in low loss setups.Over the years, several bulk optical nonlinear crystals and cavities have been employed for the generation of different types of high-quality squeezed states. However, recent progress in fabricating ultra-low loss integrated waveguides has shifted the interest of the community towards the integration of squeezing sources to gain advantages in terms of compactness, scalability, and reproducibility.The aim of this thesis is to investigate the main characteristics, limits, and requirements for the generation of vacuum and bright squeezed states by second- and third-order nonlinear devices, with more emphasis on integrated cavities. In particular, we demonstrate high on-chip intensity difference squeezing between bright mode pairs created in an engineered SiN microring resonator. In addition, we propose the use of the Ikeda map, a semi-classical simulation tool, for the investigation of two-mode quadrature squeezing generation in microresonators, discussing its competitiveness against standard quantum models. These results contribute to the optimization of engineered integrated devices with the aim of attaining high levels of squeezing sufficient to bring real advantages in classical and quantum applications.