© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:2107.09111 · Physical Review A

Bright-soliton frequency combs and dressed states in χ(2) microresonators

Danila N. Puzyrev, V. V. Pankratov, Alberto Villois, Dmitry V. Skryabin

Published Jul 19, 2021• 18 citations

Abstract

We present a theory of frequency comb generation in high-Q ring microresonators with quadratic nonlinearity and normal dispersion and demonstrate that the naturally large difference of the repetition rates at the fundamental and second-harmonic frequencies supports a family of bright soliton frequency combs provided the parametric gain is moderated by tuning the index-matching parameter to exceed the repetition rate difference by a significant factor. This factor equals the sideband number associated with the high-order phase-matched sum-frequency process. The theoretical framework, i.e., the dressed-resonator method, to study the frequency conversion and comb generation is formulated by including the sum-frequency nonlinearity into the definition of the resonator spectrum. The Rabi splitting of the dressed frequencies leads to four distinct parametric down conversion conditions (signal-idler-pump photon energy conservation laws). The parametric instability tongues associated with the generation of the sparse, i.e., Turing-pattern-like, frequency combs with varying repetition rates are analyzed in detail. The sum-frequency matched sideband exhibits optical Pockels nonlinearity and strongly modified dispersion, which limit the soliton bandwidth and also play a distinct role in Turing comb generation. Our methodology and data highlight the analogy between the driven multimode resonators and the photon-atom interaction.

DOI: 10.1103/physreva.104.013520

Related papers

Photon-photon polaritons in chi-2 microresonators

Dmitry V. Skryabin, V. V. Pankratov, Alberto Villois +1 more

We consider a high-Q microresonator with chi-2 nonlinearity under conditions when the coupling rate between the sidebands around the pump and its second harmonic exceeds the damping rates, implying the strong coupling regime (SC). Using the dressed-resonator methodology, which is similar to the well-known theory of the two-levels atoms dressed by the optical fields, we demonstrate that this regime leads to the dominance of the reversible energy transfer between the sidebands over the non-reversible sideband growth due to parametric gain. This observation has allowed us to introduce and apply the cross-area concept of the polariton quasi-particles in the context of chi-2 ring-microresonators, and to use it to predict the modified spectral response of the resonator to the weak probe field. This response reveals the splitting of the bare-resonator resonances, avoided crossings, and Rabi dynamics. Using polaritons as the basis has also allowed us to derive a discrete sequence of the parametric thresholds for generation of sidebands of different orders. These thresholds form spectacular patterns in the parameter space defined by the detunings of the fundamental and 2 nd harmonic fields, Figs (a) and (b).

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 21, 2021•1 citation

Autler-Townes Splitting and chi-2 Turing-Rolls in Microresonators

Dmitry V. Skryabin, Danila N. Puzyrev, V. V. Pankratov +1 more

We demonstrate that the generation of the sparse, i.e., Turing-pattern-like, frequency combs in chi-2 microresonators is explained by the four distinct signal-idler- pump photon energy conservation laws. The transformation of the usually unique three- photon energy conservation to the four conditions happens due to the effect analogous to the Autler-Townes splitting known in the strong photon-atom interaction.

Nonlinear Optics•Jan 1, 2021•0 citations

Autler-Townes Effect and chi-2 Turing-Rolls in Microresonators

Dmitry V. Skryabin, Danila N. Puzyrev, V. V. Pankratov +1 more

We demonstrate that the generation of the sparse, i.e., Turing-pattern-like, frequency combs in chi-2 microresonators is explained by the four distinct signal-idler-pump photon energy conservation laws. The transformation of the usually unique three-photon energy conservation to the four conditions happens due to the effect analogous to the Autler-Townes splitting known in the strong photon-atom interaction.

IEEE Photonics Conference•Oct 1, 2021•0 citations

Feshbach resonances in Kerr frequency combs

Andrey B. Matsko, Lute Maleki

We show that both the power and repetition rate of a frequency comb generated in a nonlinear ring resonator, pumped with continuous-wave (cw) coherent light, are modulated. The modulation is brought about by the interaction of the cw background with optical pulses excited in the resonator, and occurs in resonators with nonzero high-order chromatic dispersion and wavelength-dependent quality factor. The modulation frequency corresponds to the detuning of the pump frequency from the eigenfrequency of the pumped mode in the resonator.

arXiv:1410.8604•Physical Review A•Jan 22, 2015•16 citations

Toward quantum frequency combs: Boosting the generation of highly nonclassical light states by cavity-enhanced parametric down-conversion at high repetition rates

Alessandro Zavatta, Valentina Parigi, Marco Bellini

We demonstrate the generation of multiphoton quantum states of light by cavity-enhanced parametric down-conversion in the high-repetition-rate pulsed regime. An external enhancement cavity resonant with the spectral comb of modes of a mode-locked pump laser provides a coherent buildup of the pump intensity and greatly enhances the parametric gain without sacrificing its high repetition rate and comb structure. We probe the parametric gain enhancement by the conditional generation and tomographic analysis of two-photon Fock states. Besides its potential impact for efficiently generating highly nonclassical or entangled multiphoton states in many existing experimental setups, this scheme opens exciting perspectives toward the combination of quantum and comb technologies for enhanced measurements and advanced quantum computation protocols.

arXiv:0803.1712•Physical Review A•Sep 9, 2008•26 citations

Hook-and-Loop laser fastening of an optical frequency comb to a strongly driven two-level quantum system

Gilbert Reinisch

In order to control the state of a two-level quantum system (e.g. the spin state of an ion qubit), optical frequency combs perform a two-photon stimulated Raman process through stimulated absorption from one comb tooth and stimulated emission into another comb tooth. If the two-level energy gap is an integer multiple of the repetition rate of the laser, resonant Rabi oscillations are excited. When these latter have a frequency close to the qubit’s transition one, a strongly anharmonic phase-locked cycle may exist on the Bloch sphere, which generates a sub-harmonic series of very narrow, equally spaced, spectral lines. If the repetition rate of an optical frequency comb is appropriately tuned to these latter (up to the average carrier envelope frequency), a highly resonant dynamical regime of the two-level system should be reached where the Raman stimulated absorption and emission processes would occur for any pair of adjacent comb teeth.

Results in Physics•Jan 6, 2022•1 citation

We present a theory of frequency comb generation in high-Q ring microresonators with quadratic nonlinearity and normal dispersion and demonstrate that the naturally large difference of the repetition rates at the fundamental and second-harmonic frequencies supports a family of bright soliton frequency combs provided the parametric gain is moderated by tuning the index-matching parameter to exceed the repetition rate difference by a significant factor. This factor equals the sideband number associated with the high-order phase-matched sum-frequency process. The theoretical framework, i.e., the dressed-resonator method, to study the frequency conversion and comb generation is formulated by including the sum-frequency nonlinearity into the definition of the resonator spectrum. The Rabi splitting of the dressed frequencies leads to four distinct parametric down conversion conditions (signal-idler-pump photon energy conservation laws). The parametric instability tongues associated with the generation of the sparse, i.e., Turing-pattern-like, frequency combs with varying repetition rates are analyzed in detail. The sum-frequency matched sideband exhibits optical Pockels nonlinearity and strongly modified dispersion, which limit the soliton bandwidth and also play a distinct role in Turing comb generation. Our methodology and data highlight the analogy between the driven multimode resonators and the photon-atom interaction.

We consider a high-Q microresonator with chi-2 nonlinearity under conditions when the coupling rate between the sidebands around the pump and its second harmonic exceeds the damping rates, implying the strong coupling regime (SC). Using the dressed-resonator methodology, which is similar to the well-known theory of the two-levels atoms dressed by the optical fields, we demonstrate that this regime leads to the dominance of the reversible energy transfer between the sidebands over the non-reversible sideband growth due to parametric gain. This observation has allowed us to introduce and apply the cross-area concept of the polariton quasi-particles in the context of chi-2 ring-microresonators, and to use it to predict the modified spectral response of the resonator to the weak probe field. This response reveals the splitting of the bare-resonator resonances, avoided crossings, and Rabi dynamics. Using polaritons as the basis has also allowed us to derive a discrete sequence of the parametric thresholds for generation of sidebands of different orders. These thresholds form spectacular patterns in the parameter space defined by the detunings of the fundamental and 2 nd harmonic fields, Figs (a) and (b).

We show that both the power and repetition rate of a frequency comb generated in a nonlinear ring resonator, pumped with continuous-wave (cw) coherent light, are modulated. The modulation is brought about by the interaction of the cw background with optical pulses excited in the resonator, and occurs in resonators with nonzero high-order chromatic dispersion and wavelength-dependent quality factor. The modulation frequency corresponds to the detuning of the pump frequency from the eigenfrequency of the pumped mode in the resonator.

We demonstrate the generation of multiphoton quantum states of light by cavity-enhanced parametric down-conversion in the high-repetition-rate pulsed regime. An external enhancement cavity resonant with the spectral comb of modes of a mode-locked pump laser provides a coherent buildup of the pump intensity and greatly enhances the parametric gain without sacrificing its high repetition rate and comb structure. We probe the parametric gain enhancement by the conditional generation and tomographic analysis of two-photon Fock states. Besides its potential impact for efficiently generating highly nonclassical or entangled multiphoton states in many existing experimental setups, this scheme opens exciting perspectives toward the combination of quantum and comb technologies for enhanced measurements and advanced quantum computation protocols.

In order to control the state of a two-level quantum system (e.g. the spin state of an ion qubit), optical frequency combs perform a two-photon stimulated Raman process through stimulated absorption from one comb tooth and stimulated emission into another comb tooth. If the two-level energy gap is an integer multiple of the repetition rate of the laser, resonant Rabi oscillations are excited. When these latter have a frequency close to the qubit’s transition one, a strongly anharmonic phase-locked cycle may exist on the Bloch sphere, which generates a sub-harmonic series of very narrow, equally spaced, spectral lines. If the repetition rate of an optical frequency comb is appropriately tuned to these latter (up to the average carrier envelope frequency), a highly resonant dynamical regime of the two-level system should be reached where the Raman stimulated absorption and emission processes would occur for any pair of adjacent comb teeth.