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arXiv:quant-ph/0501002 · Physical Review A

Tunable whispering-gallery-mode resonators for cavity quantum electrodynamics

Yann Louyer, Dieter Meschede, Arno Rauschenbeutel

Published Sep 15, 2005• 178 citations
arXivHTMLPDF

Abstract

We theoretically study the properties of highly prolate-shaped dielectric microresonators. Such resonators sustain whispering-gallery modes that exhibit two spatially well-separated regions with enhanced field strength. The field per photon on the resonator surface is significantly higher than, e.g., for equatorial whispering-gallery modes in microsphere resonators with a comparable mode volume. At the same time, the frequency spacing of these modes is much more favorable, so that a tuning range of several free spectral ranges should be attainable. We discuss the possible application of such resonators for cavity quantum electrodynamics experiments with neutral atoms and reveal distinct advantages with respect to existing concepts.

DOI
10.1103/physreva.72.031801

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We theoretically study the properties of highly prolate-shaped dielectric microresonators. Such resonators sustain whispering-gallery modes that exhibit two spatially well-separated regions with enhanced field strength. The field per photon on the resonator surface is significantly higher than, e.g., for equatorial whispering-gallery modes in microsphere resonators with a comparable mode volume. At the same time, the frequency spacing of these modes is much more favorable, so that a tuning range of several free spectral ranges should be attainable. We discuss the possible application of such resonators for cavity quantum electrodynamics experiments with neutral atoms and reveal distinct advantages with respect to existing concepts.
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 have tuned the whispering gallery modes of a fused silica micro-resonator over nearly 1 nm at 800 nm, i.e. over half of a free spectral range or the equivalent of 10 6 linewidths of the resonator. This has been achieved by a new method based on the stretching of a two-stem microsphere. The devices described below will permit new cavity-QED experiments with this ultra high finesse optical resonator when it is desirable to optimize its coupling to emitters with given transition frequencies. The tuning capability demonstrated is compatible with both UHV and low temperature operation, which should be useful for future experiments with laser cooled atoms or single quantum dots. A general overview of the current state of the art in microspheres is given as well as a more general introduction.
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 external fields of optical whispering gallery modes may be used to confine atoms in stable orbits around a dielectric microsphere. As an example, a toroidal dipole-force trap (atom gallery) for three-level atoms is investigated, and the possibility of achieving an atomic (matter-wave) resonator is discussed. The extremely small electromagnetic mode volumes and high Q's of the whispering gallery modes should permit a circulating photon to be repeatedly absorbed and reemitted by a trapped whispering atom.
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 $\mathbf{(}g∕(2\ensuremath{\pi}),{n}_{0},{N}_{0}\mathbf{)}=(86\phantom{\rule{0.3em}{0ex}}\mathrm{MHz},4.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4},1.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3})$.