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).

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).

[CrossRef]

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).

[CrossRef]

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).

[CrossRef]
[PubMed]

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

[CrossRef]

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).

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).

[CrossRef]
[PubMed]

C. G. Aminoff, "Velocity-selective optical pumping and collision effects," Ann. Phys. (Paris) 10, 995-1006 (1985).

S. Nakayama, "Optical pumping theory in polarization spectroscopy of Na," J. Phys. Soc. Jpn. 50, 609-614 (1981).

[CrossRef]

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.

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).

C. G. Aminoff, "Velocity-selective optical pumping and collision effects," Ann. Phys. (Paris) 10, 995-1006 (1985).

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).

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).

[CrossRef]

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).

[CrossRef]
[PubMed]

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).

[CrossRef]

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

[CrossRef]

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.

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).

[CrossRef]

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).

[CrossRef]
[PubMed]

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).

[CrossRef]
[PubMed]

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).

[CrossRef]

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).

[CrossRef]
[PubMed]

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).

[CrossRef]

S. Nakayama, "Optical pumping theory in polarization spectroscopy of Na," J. Phys. Soc. Jpn. 50, 609-614 (1981).

[CrossRef]

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).

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).

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).

[CrossRef]
[PubMed]

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).

[CrossRef]

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).

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).

[CrossRef]

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).

[CrossRef]
[PubMed]

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).

[CrossRef]
[PubMed]

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).

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

[CrossRef]

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).

[CrossRef]

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).

[CrossRef]
[PubMed]

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).

[CrossRef]

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).

[CrossRef]

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

[CrossRef]

C. G. Aminoff, "Velocity-selective optical pumping and collision effects," Ann. Phys. (Paris) 10, 995-1006 (1985).

S. Nakayama, "Optical pumping theory in polarization spectroscopy of Na," J. Phys. Soc. Jpn. 50, 609-614 (1981).

[CrossRef]

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).

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).

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).

[CrossRef]

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).

[CrossRef]
[PubMed]

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).

[CrossRef]
[PubMed]

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

[CrossRef]

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).

[CrossRef]

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

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).

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.