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Resonant nonlinear magneto-optical effects in atoms∗ - The Budker ...

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44<br />

x<br />

x<br />

x<br />

z<br />

z<br />

t ⩵ 3 Τ S<br />

<br />

8<br />

z<br />

t ⩵ 0<br />

y<br />

y<br />

t ⩵ 3 Τ S<br />

<br />

4<br />

y<br />

x<br />

x<br />

x<br />

z<br />

z<br />

z<br />

t ⩵ Τ S<br />

<br />

8<br />

y<br />

t ⩵ Τ S<br />

<br />

2<br />

y<br />

t ⩵ 7 Τ S<br />

<br />

8<br />

y<br />

x<br />

x<br />

x<br />

z<br />

z<br />

t ⩵ 5 Τ S<br />

<br />

8<br />

z<br />

t ⩵ Τ S<br />

<br />

4<br />

y<br />

y<br />

t ⩵ Τ S<br />

FIG. 22 A sequence of probability surfaces represent<strong>in</strong>g evolution<br />

of a state with F = 1. <strong>The</strong> state is <strong>in</strong>itially stretched<br />

along ŷ at t = 0 and an electric field is applied along ẑ, caus<strong>in</strong>g<br />

Stark beats with period τ S .<br />

Consider, for example, atoms prepared at t = 0 <strong>in</strong> the<br />

|F = 1, M = 1〉 (“stretched”) state with the quantization<br />

axis chosen along ŷ. An electric field E is applied along<br />

ẑ, caus<strong>in</strong>g evolution depicted <strong>in</strong> Fig. B.2. We see that<br />

the state orig<strong>in</strong>ally stretched along ŷ oscillates between<br />

this state and the one stretched along −ŷ. In between,<br />

the system evolves through states with no orientation,<br />

but which are aligned along the ẑ ± ˆx directions. S<strong>in</strong>ce<br />

the stretched states have orientation, this evolution is<br />

an example of orientation-to-alignment and alignmentto-orientation<br />

conversion (see, for example, discussion by<br />

Blum, 1996).<br />

APPENDIX C: Abbreviations<br />

AOC Alignment-to-orientation conversion<br />

BSR Bennett-structure-related<br />

DAVLL Dichroic atomic vapor laser lock<br />

EDM A permanent electric-dipole moment<br />

EIT Electromagnetically <strong>in</strong>duced transparency<br />

FS Forward scatter<strong>in</strong>g<br />

MOT Magneto-<strong>optical</strong> trap<br />

NMOE Nonl<strong>in</strong>ear <strong>magneto</strong>-<strong>optical</strong> <strong>effects</strong><br />

NMOR Nonl<strong>in</strong>ear <strong>magneto</strong>-<strong>optical</strong> rotation<br />

SR Self-rotation of light polarization<br />

y<br />

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