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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 22, Iss. 1 — Jan. 1, 2005
  • pp: 29–36

Velocity distribution of laser-induced atomic polarization moments in antirelaxation-coated cell and magneto-optic rotation

A. I. Okunevich  »View Author Affiliations

JOSA B, Vol. 22, Issue 1, pp. 29-36 (2005)

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It is shown with the use of the solution of the Boltzmann equation for laser pumping in a cell with antirelaxation coating that the velocity distribution of atomic polarization moments (PMs) is essentially dependent on the value of the magnetic field H. The z-velocity distribution of PMs in a low field, H approximately 10^−4 A/m, is a Maxwellian one with a small admixture of an almost monokinetic one. At larger field the same distribution remains for longitudinal alignment, but for transverse alignment the Maxwellian part of the distribution disappears (at H approximately 1 A/m). It appears that the radial velocity distribution is also dependent on the field H. A calculation accounting for wall Maxwellization in low field gives for the pumping power needed to saturate the magneto-optic rotation a value similar to the experimentally determined value. It is shown that the known semiphenomenological theory neglecting the Maxwellization gives an acceptable description of magneto-optic rotation only for high (approximately 1 A/m) magnetic field.

© 2005 Optical Society of America

OCIS Codes
(020.0020) Atomic and molecular physics : Atomic and molecular physics
(020.1670) Atomic and molecular physics : Coherent optical effects
(020.2070) Atomic and molecular physics : Effects of collisions

A. I. Okunevich, "Velocity distribution of laser-induced atomic polarization moments in antirelaxation-coated cell and magneto-optic rotation," J. Opt. Soc. Am. B 22, 29-36 (2005)

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  1. C. G. Aminoff, "Velocity-selective optical pumping and collision effects," Ann. Phys. (Paris) 10, 995-1006 (1985).
  2. E. B. Alexandrov, M. V. Balabas, A. S. Pazgalev, A. K. Vershovskii, and N. N. Yakobson, "Double-resonance atomic magnetometers: from gas discharge to laser pumping," Laser Phys. 6, 244-251 (1996).
  3. D. Budker, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and M. Zolotarev, "Sensitive magnetometry based on nonlinear magneto-optical rotation," Phys. Rev. A 62, 043403/1-7 (2000).
  4. D. Budker, W. Gawlik, D. F. Kimball, V. V. Yashchuk, and A. Weis, "Resonant nonlinear magneto-optical effects in atoms," Rev. Mod. Phys. 74, 1153-1201 (2002).
  5. S. Nakayama, "Optical pumping theory in polarization spectroscopy of Na," J. Phys. Soc. Jpn. 50, 609-614 (1981).
  6. S. I. Kanorsky, A. Weis, J. Wurster, and T. W. Hansch, "Quantative investigation of the resonant nonlinear Faraday effect under conditions of optical hyperfine pumping," Phys. Rev. A 47, 1220-1226 (1993).
  7. A. I. Okunevich, "Laser pumping and magneto-optical rotation of polarization plane of the light in the cell with antirelaxation coating of the walls. I. Raising and solving the problem. II. Calculation for the atoms with Lambda scheme of the levels," Opt. Spectrosc. 97, 890-904 (2004).
  8. As in the preceding work,7 we will consider the density matrix defined in the representation of polarization moments [M. I. Dyakonov, "Theory of resonance scattering of light in gas in magnetic field," Zh. Eksp. Teor. Fiz. 47, 2213-2221 (1964) [Sov. Phys. JETP 20 , 1484-1492 (1964)]. In this representation the density matrix is given by the set of components phiQK with 0< or =K< or =2j,−K< or =Q< or =K. We will call "truncated" the density matrix defined as a set of components phiQK with nonzero ranks K . PM with zero rank will be defined by the relation phi00 ≡Spphi=nF(v ), where n is the concentration of atoms.
  9. Ref. 7 consists of two parts; the references to the formulas in these parts will be given with the addition of "I-" and "II-", respectively, before the formula number.
  10. The orientation is absent because its arising at the transverse pumping (E ,H ) considered is the effect of the second order in light intensity.11
  11. D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, "Nonlinear magneto-optical rotation via alignment-to-orientation conversion," Phys. Rev. Lett. 85, 2088-2091 (2000).
  12. In the case of the uncoated cell at H=1A/m we obtained for the quantities v~rho f01 ,v~rho Re f22 , and v~rho Im f22 exactly the same curves as in Fig. 4 b. For the quantity v~rho f02 we obtained the curve similar to the curve for the quantity v~rho f01 in Fig. 4 a.
  13. D. Budker, V. Yashchuk, and M. Zolotarev, "Nonlinear magneto-optic effects with ultranarrow widths," Phys. Rev. Lett. 81, 5788-5791 (1998).
  14. V. V. Yashchuk, E. Mikhailov, I. Novikova, and D. Budker, "Nonlinear magneto-optical rotation with separated light fields in 85Rb vapor contained in an anti-relaxation-coated cell," Technical Report LBNL-44762 (Lawrence Berkeley National Laboratory, 1999).

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