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Quantum Computing, Communication, and Simulation

A characterization of quantum Kerr optical frequency combs

Fengyu Liu, Yanne K. Chembo

Published Mar 8, 2023• 1 citation
Publisher

Abstract

Quantum Kerr optical frequency combs are generated by pumping a high-Q microresonator with a continuous wave resonant laser. Below threshold, two pump photons are symmetrically up- and down-converted as twin photons via spontaneous four-wave mixing, thereby generating up to a hundred paired channels. Furthermore, these chipscale, high-dimensional and room-temperature systems are expected to play a major role in quantum engineering. However, their theoretical description is still unclear. Here, we present an explicit description of this quantum system via a frequency-bin state and its density operator, and explore the properties of the eigenkets.

DOI
10.1117/12.2648052

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Quantum Kerr optical frequency combs are generated by pumping a high-Q microresonator with a continuous wave resonant laser. Below threshold, two pump photons are symmetrically up- and down-converted as twin photons via spontaneous four-wave mixing, thereby generating up to a hundred paired channels. Furthermore, these chipscale, high-dimensional and room-temperature systems are expected to play a major role in quantum engineering. However, their theoretical description is still unclear. Here, we present an explicit description of this quantum system via a frequency-bin state and its density operator, and explore the properties of the eigenkets.
Kerr optical frequency combs are generated by pumping a high-QQQintegrated microresonator with a resonant laser. Below threshold, the pump laser field mediates the phenomenon of spontaneous four-wave mixing, where two pump photons are symmetrically up- and down-converted as twin photons that can be entangled across up to tens of eigenmodes in the spectral domain. While these room-temperature integrated photonic circuits are expected to play a central role in quantum technology, their high dimensionality and dissipative nature are a challenge for their theoretical description, therefore hindering the understanding of their properties and potential of performance. In this article, we develop a framework that permits to obtain an explicit solution for the density operator of quantum microcombs below threshold. This self-consistent theoretical description allows for their complete characterization, as well as for the analytical determination of various performance metrics such as fidelity, purity, and entropy.
The dynamical behavior of Kerr optical frequency combs is very well understood today from the perspective of the semiclassical approximation. These combs are obtained by pumping an ultrahigh-QQQ whispering-gallery mode resonator with a continuous-wave laser. The long-lifetime photons are trapped within the toruslike eigenmodes of the resonator, where they interact nonlinearly via the Kerr effect. In this article, we use quantum Langevin equations to provide a theoretical understanding of the nonclassical behavior of these combs when pumped below and above threshold. In the configuration where the system is under threshold, the pump field is the unique oscillating mode inside the resonator, and it triggers the phenomenon of spontaneous four-wave mixing, where two photons from the pump are symmetrically up- and down-converted in the Fourier domain. This phenomenon, also referred to as parametric fluorescence, can only be understood and analyzed from a fully quantum perspective as a consequence of the coupling between the field of the central (pumped) mode and the vacuum fluctuations of the various side modes. We analytically calculate the power spectra of the spontaneous emission noise, and we show that these spectra can be either single- or double-peaked depending on the value of the laser frequency, chromatic dispersion, pump power, and spectral distance between the central mode and the side mode of interest. We also calculate as well the overall spontaneous noise power per side mode and propose simplified analytical expressions for some particular cases. In the configuration where the system is pumped above threshold, we investigate the phenomena of quantum correlations and multimode squeezed states of light that can occur in the Kerr frequency combs originating from stimulated four-wave mixing. We show that for all stationary spatiotemporal patterns, the side modes that are symmetrical relative to the pumped mode in the frequency domain display quantum correlations that can lead to squeezed states of light under some optimal conditions that are analytically determined. These quantum correlations can persist regardless the dynamical state of the system (rolls or solitons), regardless of the spectral extension of the comb (number side modes) and regardless of the dispersion regime (normal or anomalous). We also explicitly determine the phase quadratures leading to photon entanglement and analytically calculate their quantum-noise spectra. For both the below- and above-threshold cases, we study with particular emphasis the two principal architectures for Kerr comb generation, namely the add-through and add-drop configurations. It is found that regardless of the configuration, an essential parameter is the ratio between out-coupling and total losses, which plays a key role as it directly determines the efficiency of the detected fluorescence or squeezing spectra. We finally discuss the relevance of Kerr combs for quantum information systems at optical telecommunication wavelengths below and above threshold.
Kerr optical frequency combs are obtained by pumping an ultra-high Q whispering-gallery mode resonator with a continuous-wave laser. Here, we use quantum Langevin equations to investigate the non-classical behavior of these combs when pumped below and above threshold. Under threshold, we study the phenomenon of spontaneous four-wave mixing, while above threshold, we investigate the phenomenon of two-mode squeezing. For both the below- and above-threshold cases, we find that an essential parameter is the ratio between out-coupling and total losses, which directly determines the efficiency of the detected spontaneous noise or squeezing spectra.
The on-chip generation of optical quantum states will enable accessible advances for quantum technologies. We demonstrate that integrated quantum frequency combs (based on high-Q microring resonators made from a CMOS-compatible, high refractive-index doped-glass platform) can enable the generation of pure heralded single photons, cross-polarized photon pairs, as well as bi- and multi-photon entangled qubit states over a broad frequency comb covering the S, C, L telecommunications band, with photon frequencies corresponding to standard telecommunication channels spaced by 200 GHz. Exploiting a self-locked, intra-cavity excitation configuration, a highly-stable source of multiplexed heralded single photons is demonstrated, operating continuously for several weeks with less than 5% fluctuations. The photon bandwidth of 110 MHz is compatible with quantum memories, and high photon purity was confirmed through single-photon auto-correlation measurements. In turn, by simultaneously exciting two orthogonal polarization mode resonances, we demonstrate the first realization of type-II spontaneous FWM (in analogy to type-II spontaneous parametric down-conversion), allowing the direct generation of orthogonally-polarized photon pairs on a chip. By using a double-pulse excitation, we demonstrate the generation of time-bin entangled photon pairs. We measure qubit entanglement with visibilities above 90%, enabling the implementation of quantum information processing protocols. Finally, the excitation field and the generated photons are intrinsically bandwidth-matched due to the resonant characteristics of the ring cavity, enabling the multiplication of Bell states and the generation of a four-photon time-bin entangled state. We confirm the generation of this four-photon entangled state through four-photon quantum interference.
An optical frequency comb comprises a cluster of equally spaced, phase-locked spectral lines. Replacing these classical components with correlated quantum light gives rise to cluster quantum frequency combs, providing abundant quantum resources for measurement-based quantum computation, and multi-user quantum networks. We propose and generate cluster quantum microcombs within an on-chip optical microresonator driven by multi-frequency lasers. Through resonantly enhanced four-wave mixing processes, continuous-variable cluster states with 60 qumodes are deterministically created. The graph structures can be programmed into one- and two-dimensional lattices by adjusting the configurations of the pump lines, which are confirmed inseparable based on the measured covariance matrices. Our work demonstrates the largest-scale cluster states with unprecedented raw squeezing levels from a photonic chip, offering a compact and scalable platform for computational and communicational tasks with quantum advantages.