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Physical Review A

Quantum structure and dynamics for atom galleries

David W. Vernooy, Harry J. Kimble

Published Feb 1, 1997• 54 citations
Publisher

Abstract

The bound state structure and dynamics for an atom trap formed from the whispering gallery modes (WGMs) of a dielectric microsphere are investigated. The coupling of the quantized internal and external atomic degrees of freedom plays a fundamental role in the quantum dynamics of this atom gallery. The radiative processes for a cold atom near a microsphere are modified due to the special symmetry of the atom gallery, the WGM mode structure, and the finite extent of the center-of-mass (c.m.) wave packet. Finally, interesting implications of the quantized c.m. for atomic matter waves and cavity QED with a quantum field are mentioned.

DOI
10.1103/physreva.55.1239

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The bound state structure and dynamics for an atom trap formed from the whispering gallery modes (WGMs) of a dielectric microsphere are investigated. The coupling of the quantized internal and external atomic degrees of freedom plays a fundamental role in the quantum dynamics of this atom gallery. The radiative processes for a cold atom near a microsphere are modified due to the special symmetry of the atom gallery, the WGM mode structure, and the finite extent of the center-of-mass (c.m.) wave packet. Finally, interesting implications of the quantized c.m. for atomic matter waves and cavity QED with a quantum field are mentioned.
We report measurements of cavity-QED effects for the radiative coupling of atoms in a dilute vapor to the external evanescent field of a whispering-gallery mode (WGM) in a fused silica microsphere. The high QQQ $(5\ifmmode\times\else\texttimes\fi{}{10}^{7})$, small mode volume (10${}^{\ensuremath{-}8}$ cm3){}^{3})3), and unusual symmetry of the microcavity evanescent field enable velocity-selective interactions between fields with photon number of order unity in the WGM and ${N}_{T}\ensuremath{\sim}1$ atoms in the surrounding vapor.
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.
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.
The interaction is considered between a two-level atom and the continuum of electric field modes falling within the profile of one of the resonance modes of a dielectric microsphere (a whispering gallery mode). Subject to minimal assumptions, simple equations are obtained on first principles, which describe the spectral properties of the one-photon continuum and the relaxation processes occurring therein. If the initial state of the atom is excited, a doublet structure is formed in the emitted photon spectrum, provided that the interaction is strong enough. If it is the microsphere that is excited at the initial instant, the excited photon spectrum depends substantially on the excitation method used. When excitation is optimal, the atom is effectively excited, and a Rabi-doublet is then formed in the fluorescence spectrum. When the excitation conditions are other than optimal, the spectrum becomes of triplet character, and when the deviation from the optimal excitation conditions is strong enough, the atom practically fails to get excited, and the fluorescence spectrum is of singlet type. A considerable part of the results obtained is of a general nature and can easily be applied to other cases of strong interaction between atoms and resonators.