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Optics Letters

Optics Letters


  • Vol. 28, Iss. 1 — Jan. 1, 2003
  • pp: 46–48

Emission pattern of an atomic dipole in a high-finesse optical cavity

P. Maunz, T. Puppe, T. Fischer, P. W. H. Pinkse, and G. Rempe  »View Author Affiliations

Optics Letters, Vol. 28, Issue 1, pp. 46-48 (2003)

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An atom placed in a small high-finesse optical cavity will dominantly emit into modes sustained by the cavity. If the cavity supports many frequency-degenerate modes, the radiation pattern depends strongly on the position of the atom. These patterns can be used to detect the position of the atom with high sensitivity.

© 2003 Optical Society of America

OCIS Codes
(140.4780) Lasers and laser optics : Optical resonators
(230.5750) Optical devices : Resonators
(270.0270) Quantum optics : Quantum optics

P. Maunz, T. Puppe, T. Fischer, P. W. H. Pinkse, and G. Rempe, "Emission pattern of an atomic dipole in a high-finesse optical cavity," Opt. Lett. 28, 46-48 (2003)

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  9. The expression for ψeff can be derived by induction. We start by taking the first two basis modes ψ1, ψ2, with |ψ1(ra)| +|ψ2(ra) |>0. In the two-dimensional subspace spanned by {ψ1, ψ2 } a unitary transformation can be applied, forming the following two orthonormal superpositions: c1(r)=[ψ1*(ra1(r)+ψ2*(ra2(r)]/[ |ψ1(ra)|2+|ψ2(ra)|2]1/2 and χ~1(r)=[-ψ2(ra1(r)+ψ1(ra2 (r)]/[|ψ1 (ra)|2+|ψ2(ra)|2]1/2. It is easily verified that |c1(ra)| ≥(|ψ1(ra)|, |ψ2(ra)|) and χ~1(ra)=0. Hence, in this two-dimensional subspace, c1 is the mode with the largest value at ra and χ~1 does not couple to the atom. Now, basis mode y3 is combined with c1, and new superpositions c2 and χ~2 are constructed that, respectively, maximize and zero the mode value at ra in the subspace spanned by {c1, ψ3 }. This procedure is repeated for all ψi, so that the last constructed mode is the effective mode, ψeff=cN-1, given in Eq. 2, and the χχ~i form a noncoupling basis. By construction, ψeff is unique apart from a phase factor.
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  11. H. J. Carmichel, An Open Systems Approach to Quantum Optics (Springer-Verlag, Berlin, 1993).
  12. P. Horak and H. Ritsch, Phys. Rev. A 64, 033422 (2001).

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