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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Photon-photon polaritons in chi-2 microresonators

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

Published Jun 21, 2021• 1 citation
Publisher

Abstract

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).

DOI
10.1109/cleo/europe-eqec52157.2021.9541787

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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 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.
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 have investigated resonant two-photon absorption and second harmonic generation in a microcavity geometry. In a single beam arrangement, the transmission depends on the intensity according to a simple two-level picture with an intensity-dependent coupling; at resonance, in particular, the system exhibits a two-photon Rabi splitting. In a pump and probe arrangement, the presence of the strong incident pump beam substantially modifies the absorption spectrum of the weak probe beam: for moderate pump intensities the behaviour can be interpreted as a two-photon version of the well-known optical Stark effect. At higher intensities, more complicated hyper-Raman processes take place, which give also rise to gain in well-determined spectral regions. Finally, we have shown how the non-linear coupling coefficient appearing in the model Hamiltonian is related to the material constants and geometrical parameters of a specific microcavity configuration.
After reviewing the important roles of excitons in nonlinear optical responses, we demonstrate mutual and quantum-mechanical control of radiation field and excitons on the same footing in a microcavity. First we introduce dressed excitons as bosons interacting coherently and reversibly with a radiation mode in the microcavity. Although the vacuum Rabi splitting of the dressed exciton is the same as that of dressed atom, the emission spectrum under strong pumping shows quartet structure different from the triplet of dressed atom. Secondly, the population dynamics of dressed excitons, i.e., one-dimensional polaritons in the mesoscopic system is solved and the dominant distribution on a single mode is demonstrated above the critical pumping.
Optical microcavities and metallic nanostructures have been shown to significantly modulate the dynamics and spectroscopic response of molecular systems. We present a study of the nonlinear optics of a model consisting of NNN anharmonic multilevel systems (e.g., Morse oscillators) undergoing collective strong coupling with a resonant infrared microcavity. We find that, under experimentally accessible conditions, molecular systems in microcavities may have nonlinear phenomena significantly intensified due to the high quality of polariton resonances and the enhanced microcavity electromagnetic energy density relative to free space. Particularly large enhancement of multiphoton absorption happens when multipolariton states are resonant with bare molecule multiphoton transitions. In particular, our model predicts two-photon absorption cross-section enhancements by several orders of magnitude relative to free space when the Rabi splitting ${\mathrm{\ensuremath{\Omega}}}_{R}$ is approximately equal to the molecular anharmonic shift $2\mathrm{\ensuremath{\Delta}}$. Our results provide rough upper bounds to resonant nonlinear-response enhancement factors as relaxation to dark states is treated phenomenologically. Notably, ensembles of two-level systems undergoing strong coupling with a cavity (described by the Tavis-Cummings model) show no such optical nonlinearity enhancements, highlighting the rich phenomenology afforded by multilevel anharmonic systems. Similar conclusions are expected to hold for excitonic systems that share features with our model (e.g., molecular dyes with accessible ${S}_{0}\ensuremath{\rightarrow}{S}_{1}\ensuremath{\rightarrow}{S}_{2}$ transitions) and strongly interact with a UV-visible cavity.
Resonance interaction between a molecular transition and a confined electromagnetic field can reach the coupling regime where coherent exchange of energy between light and matter becomes reversible. In this case, two new hybrid states separated in energy are formed instead of independent eigenstates, which is known as Rabi splitting. This modification of the energy spectra of the system offers new possibilities for controlled impact on various fundamental properties of coupled matter (such as the rate of chemical reactions and the conductivity of organic semiconductors). To date, the strong coupling regime has been demonstrated in many configurations under different ambient conditions. However, there is still no comprehensive approach to determining parameters for achieving the strong coupling regime for a wide range of practical applications. In this review, a detailed analysis of various systems and corresponding conditions for reaching strong coupling is carried out and their advantages and disadvantages, as well as the prospects for application, are considered. The review also summarizes recent experiments in which the strong coupling regime has led to new interesting results, such as the possibility of collective strong coupling between X-rays and matter excitation in a periodic array of Fe isotopes, which extends the applications of quantum optics; a strong amplification of the Raman scattering signal from a coupled system, which can be used in surface-enhanced and tip-enhanced Raman spectroscopy; and more efficient second-harmonic generation from the low polaritonic state, which is promising for nonlinear optics. The results reviewed demonstrate great potential for further practical applications of strong coupling in the fields of photonics (low-threshold lasers), quantum communications (switches), and biophysics (molecular fingerprinting).