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Design and fabrication of ultrahigh Q chip-based silica WGM micro-resonators for single-atom cavity-QED

Tal Ohana, Gabriel Guendelman, Eran Mishuk, Nadav Kandel, Dror Garti, Doron Gurovich, Ora Bitton, Barak Dayan

Published Nov 4, 2024• 4 citations
Publisher

Abstract

Of the many applications of whispering-gallery-mode (WGM) micro-resonators, single-atom cavity quantum electrodynamics (cavity-QED) poses the most extreme demands on mode volume, dimensions, and quality factor ( Q ). Here we present the procedure for the fabrication of chip-based, small mode-volume, ultrahigh- Q silica WGM micro-resonators, designed for single-emitter cavity-QED. We demonstrate micro-resonators at varying geometries, from toroidal to micro-spheres, yielding ultrahigh-qualities as high as 1.7 × 10 8 at 780nm. We present a comprehensive theoretical model that allows tailoring the fabrication process to attain the desired micro-resonator geometry.

DOI
10.1364/oe.540508

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Sep 11, 2007•1 citation
Of the many applications of whispering-gallery-mode (WGM) micro-resonators, single-atom cavity quantum electrodynamics (cavity-QED) poses the most extreme demands on mode volume, dimensions, and quality factor ( Q ). Here we present the procedure for the fabrication of chip-based, small mode-volume, ultrahigh- Q silica WGM micro-resonators, designed for single-emitter cavity-QED. We demonstrate micro-resonators at varying geometries, from toroidal to micro-spheres, yielding ultrahigh-qualities as high as 1.7 × 10 8 at 780nm. We present a comprehensive theoretical model that allows tailoring the fabrication process to attain the desired micro-resonator geometry.
Of the many applications of whispering-gallery mode (WGM) microresonators, Single-atom cavity-QED poses the most extreme demands on mode-volume and quality factor. Here we present a model-based procedure for the fabrication of small mode-volume ultrahigh Q silica WGM microresonators of varying geometries, from toroidal to micro-spheres. We experimentally demonstrate WGM resonators with ultra-high qualities as high as 1.7×1081.7\times 10^81.7×108 at 780nm. We present a theoretical model that allows tailoring the recipe to attain the desired geometry of the fabricated WGM microresonators.
We investigate the suitability of toroidal microcavities for strong-coupling cavity quantum electrodynamics (QED). Numerical modeling of the optical modes demonstrate a significant reduction of the modal volume with respect to the whispering gallery modes of dielectric spheres, while retaining the high-quality factors representative of spherical cavities. The extra degree of freedom of toroid microcavities can be used to achieve improved cavity QED characteristics. Numerical results for atom-cavity coupling strength ggg, critical atom number N0{N}_{0}N0​, and critical photon number n0{n}_{0}n0​ for cesium are calculated and shown to exceed values currently possible using Fabry-Perot cavities. Modeling predicts coupling rates $g∕2\ensuremath{\pi}$ exceeding 700MHz700\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}700MHz and critical atom numbers approaching ${10}^{\ensuremath{-}7}$ in optimized structures. Furthermore, preliminary experimental measurements of toroidal cavities at a wavelength of 852nm852\phantom{\rule{0.3em}{0ex}}\mathrm{nm}852nm indicate that quality factors in excess of 108{10}^{8}108 can be obtained in a $50\text{\penalty1000-\hskip0pt}\ensuremath{\mu}\mathrm{m}$ principal diameter cavity, which would result in strong-coupling values of $\mathbf{(}g∕(2\ensuremath{\pi}),{n}_{0},{N}_{0}\mathbf{)}=(86\phantom{\rule{0.3em}{0ex}}\mathrm{MHz},4.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4},1.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3})$.
Summary form only given, as follows: The high Q whispering gallery modes of silica microspheres are promising for quantum optics and nonlinear optics experiments involving atoms and photons stored in very small volumes. We have developed the technology of these resonators, learning how to couple light in and out through optical fibers, how to obtain and measure record Q factors, and how to probe, by near-field optical microscopy, the electric field distribution immediately outside the sphere. Whispering gallery mode lasers have also been obtained with microspheres made of silica doped with neodymium ions. We describe these experiments and discuss projects involving the coupling of whispering gallery modes to single atoms or ions to perform cavity QED experiments in the optical domain.
The whispering gallery modes (WGMs) of quartz microspheres are investigated for the purpose of strong coupling between single photons and atoms in cavity quantum electrodynamics (cavity QED). Within our current understanding of the loss mechanisms of the WGMs, the saturation photon number n0{n}_{0}n0​ and critical atom number N0{N}_{0}N0​ cannot be minimized simultaneously, so that an ``optimal'' sphere size is taken to be the radius for which the geometric mean n0N0,\sqrt{{n}_{0}{N}_{0}},n0​N0​​, is minimized. While a general treatment is given for the dimensionless parameters used to characterize the atom-cavity system, detailed consideration is given to the D2{D}_{2}D2​ transition in atomic cesium at ${\ensuremath{\lambda}}_{0}=852\mathrm{nm}$ using fused-silica microspheres, for which the maximum coupling coefficient ${g}_{a}/(2\ensuremath{\pi})\ensuremath{\approx}750\mathrm{MHz}$ occurs for a sphere radius $a=3.63\ensuremath{\mu}\mathrm{m}$ corresponding to the minimum for ${n}_{0}\ensuremath{\approx}6.06\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}.$ By contrast, the minimum for ${N}_{0}\ensuremath{\approx}9.00\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ occurs for a sphere radius of $a=8.12\ensuremath{\mu}\mathrm{m},$ while the optimal sphere size for which n0N0\sqrt{{n}_{0}{N}_{0}}n0​N0​​ is minimized occurs at $a=7.83\ensuremath{\mu}\mathrm{m}.$ On an experimental front, we have fabricated fused-silica microspheres with radii $a\ensuremath{\sim}10\ensuremath{\mu}\mathrm{m}$ and consistently observed quality factors $Q>~0.8\ifmmode\times\else\texttimes\fi{}{10}^{7}.$ These results for the WGMs are compared with corresponding parameters achieved in Fabry-Perot cavities to demonstrate the significant potential of microspheres as a tool for cavity QED with strong coupling.
We have tuned the whispering-gallery modes of a fused-silica microresonator over nearly 1 nm at 800 nm, i.e., over half a free spectral range, or 10(6) linewidths of the resonator. This result has been achieved by use of a new method based on the stretching of a two-stem microsphere. We describe devices that will permit new cavity QED experiments with this high- Q optical resonator when it is desirable to optimize its coupling to emitters with given transition frequencies. The demonstrated tuning capability is compatible with both UHV and low-temperature operation, which should be useful for future experiments with laser-cooled atoms or single quantum dots.
We report the demonstration of strong coupling between single Cesium atoms and a high-Q chip-based microresonator. Our toroidal microresonators are compact, Si chip-based whispering gallery mode resonators that confine light to small volumes with extremely low losses, and are manufactured in large numbers by standard lithographic techniques. Combined with the capability to couple efficiently light to and from these microresonators by a tapered optical fiber, toroidal microresonators offer a promising avenue towards scalable quantum networks. Experimentally, laser cooled Cs atoms are dropped onto a toroidal microresonator while a probe beam is critically coupled to the cavity mode. When an atom interacts with the cavity, it modifies the resonance spectrum of the cavity, leading to rejection of some of the probe light from the cavity, and thus to an increase in the output power. By observing such transit events while systematically detuning the cavity from the atomic resonance, we determine the maximal accessible single-photon Rabi frequency of Ω0/2π ≈ (100 ± 24) MHz. This value puts our system in the regime of strong coupling, being significantly larger than the dissipation rates in our system.