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arXiv:2409.08230 · Physical Review A

Photon-pair generation via down-conversion in III-V semiconductor microrings: Modal dispersion and quasi-phase-matching

Samuel E. Fontaine, Colin Vendromin, Trevor J. Steiner, Amirali Atrli, Lillian Thiel, Joshua E. Castro, Galan Moody, John Edward Bowers, Marco Liscidini, John E. Sipe

Published Feb 10, 2025• 10 citations
arXivHTMLPDF

Abstract

We explore how III-V semiconductor microring resonators can efficiently generate photon pairs and squeezed vacuum states via spontaneous parametric down-conversion by utilizing their built-in quasi-phase-matching and modal dispersion. We present an analytic expression for the biphoton wave function of photon pairs generated by weak pump pulses and characterize the squeezed states that result under stronger pumping conditions. Our model includes loss and captures the statistics of the scattered photons. A detailed sample calculation shows that for low pump power conversion efficiencies of ${10}^{\ensuremath{-}5}$, corresponding to a rate of 39 MHz for a pump power of $1\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{W}$, are attainable for rudimentary structures such as a simple microring coupled to a waveguide, in both the continuous-wave and pulsed-excitation regimes. Our results suggest that high levels of squeezing and pump depletion are attainable, possibly leading to the deterministic generation of non-Gaussian states.

DOI
10.1103/physreva.111.023705

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We explore how III-V semiconductor microring resonators can efficiently generate photon pairs and squeezed vacuum states via spontaneous parametric down-conversion by utilizing their built-in quasi-phase-matching and modal dispersion. We present an analytic expression for the biphoton wave function of photon pairs generated by weak pump pulses and characterize the squeezed states that result under stronger pumping conditions. Our model includes loss and captures the statistics of the scattered photons. A detailed sample calculation shows that for low pump power conversion efficiencies of 10\ensuremath−5{10}^{\ensuremath{-}5}10\ensuremath−5, corresponding to a rate of 39 MHz for a pump power of 1\ensuremathμW1\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{W}1\ensuremathμW, are attainable for rudimentary structures such as a simple microring coupled to a waveguide, in both the continuous-wave and pulsed-excitation regimes. Our results suggest that high levels of squeezing and pump depletion are attainable, possibly leading to the deterministic generation of non-Gaussian states.
The intensity buildup of light inside a lossy microring resonator can be used to enhance the generation of squeezed states via spontaneous parametric downconversion (SPDC). In this work, we model the generation of squeezed light in a microring resonator that is pumped with a Gaussian pulse via a side-coupled channel waveguide. We theoretically determine the optimum pump pulse duration and ring-to-channel coupling constant to minimize the quadrature noise (maximize the squeezing) in the ring for a fixed input pump energy. We derive approximate analytic expressions for the optimal coupling and pump pulse duration as a function of scattering loss in the ring. These results will enable researchers to easily determine the optimal design of microring resonator systems for the generation of quadrature-squeezed states.
This thesis presents an analysis of photon pairs generated via either spontaneous parametric downconversion or spontaneous four-wave mixing in channel waveguides as well as in microring resonators side-coupled to channel waveguides. The state of photons exiting a particular device is calculated within a general Hamiltonian formalism that simplifies the link between quantum nonlinear optics experiments and classical nonlinear optics experiments. This state contains information regarding photon pair production efficiency as well as modal and spectral correlations between the two photons, characterized by a two-dimensional spectral distribution function called the biphoton wave function.\n\nIn the limit of a low probability of pair production, photon pair production fficiencies are cast into forms resembling corresponding well-known classical nonlinear optical frequency conversion efficiencies, making it easy to see what plays the role of a classical “seed” field in an un-seeded (quantum) process. This also allows photon pair production efficiencies to be calculated based on the results of classical nonlinear optical experiments. It is further calculated that, unless enerated photons are collected over a very narrow frequency range, their generation efficiency does not scale the same way with device length in a channel waveguide, or resonance quality factor in a microring resonator, as might be expected from the corresponding classical frequency conversion efficiency. Although calculations do not include self- or cross-phase modulation, nor two-photon absorption\nor free-carrier absorption, it is calculated that their neglect is justified in the low pair production probability limit. Linear (scattering) loss is also neglected, though partially addressed in the final chapter of this thesis.\n\nBiphoton wave functions are calculated explicitly, such that their shape and orientation, including approximate analytic expressions for their widths, can easily be determined. This further allows estimation of the suitability of their associated photon pairs for various quantum information processing applications. As an alternative to dispersion engineering a channel waveguide photon pair source, it is calculated that microring resonators can very naturally produce nearly spectrally uncorrelated photon pairs, which behave very much like idealized single-mode photons and are thus useful for applications involving the interference of photons from multiple sources.
We propose and design a high-brightness, ultracompact electrically pumped GaSb-based laser source of entangled photons generated by mode-matched intracavity parametric down-conversion of lasing modes. To describe the nonlinear mixing in highly dispersive and dissipative waveguides, we develop a nonperturbative quantum theory of parametric down-conversion of waveguide modes which takes into account the effects of modal dispersion, group and phase mismatch, propagation, dissipation, and coupling to noisy reservoirs. We extend our theory to the regime of quantized pump fields with an approach based on the propagation equation for the state vector which solves the nonperturbative boundary-value problem of the parametric decay of a quantized single-photon pump mode and can be generalized to include the effects of dissipation and noise. Our formalism is applicable to a wide variety of three-wave mixing propagation problems. It provides convenient analytic expressions for interpreting experimental results and predicting the performance of monolithic quantum photonic systems.
In this paper, a configuration consisting in a pump propagating in an orthogonal direction with respect to the surface of a nanowaveguide is studied. It is possible to show that the generation by spontaneous parametric down-conversion of a signal and an idler photons inside the nanowaveguide is strongly dependent on the waveguide thickness, because the high refractive index of the waveguide core creates also an optical cavity for the pump field. Furthermore, it was evaluated the best condition for photon-pair generation in case of a nanowaveguide in gallium indium phosphide, which has a −43m symmetry.For the same waveguide geometry, but orientation parallel to the [110] plane, it is possible to use spontaneous parametric down-conversion to generate counter-propagating photon-pair with the same polarization. When the efficiency of the generated photon-pairs in TM0 and TE0 modes is the same, then it is possible to obtain polarization entangled photons, by using this configuration. Furthermore, by adding a mirror at one of the end of the waveguide, the system can be used to produce a squeezed-state.
To achieve photon-pair generation scaling, we optimize the quality factor of microring resonators for efficient continuous-wave-pumped spontaneous four-wave mixing. Numerical studies indicate that a high intrinsic quality factor makes high pair rate and pair brightness possible, in which the maximums take place under overcoupling and critical-coupling conditions, respectively. We fabricate six all-pass-type microring resonator samples on a silicon-on-insulator chip involving gap width as the only degree of freedom. The signal count rate, pair brightness, and coincidence rate of all the samples are characterized, which are then compared with the modified simulations by taking the detector saturation and nonlinear loss into account. Being experimentally validated for the first time to the best of our knowledge, this work explicitly demonstrates that reducing the round-trip loss in a ring cavity and designing the corresponding optimized gap width are more effective to generate high-rate or high-brightness photon pairs than the conventional strategy of simply increasing the quality factor. (C) 2018 Chinese Laser Press