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

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

http://dx.doi.org/10.1364/JOSAB.22.000029

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### Abstract

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

**Citation**

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)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-22-1-29

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### References

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- 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.
- 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.
- 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
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- 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.
- D. Budker, V. Yashchuk, and M. Zolotarev, "Nonlinear magneto-optic effects with ultranarrow widths," Phys. Rev. Lett. 81, 5788-5791 (1998).
- 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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