Abstract

We present the theory of optical excitation of a two-level quantum system, using an interaction Hamiltonian that permits both adiabatic following and diabatic following.

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References

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  1. K.-A. Suominen, "Time Dependent Two-State Models and Wave Packet Dynamics," Univ. of Helsinki Report Series in Theoretical Physics HU-TFT-IR-92-1 (1992).
  2. L.D. Landau, "Zur Theorie der Energieubertragung.II," Phys. Z. Sowjet Union 2, 46-51 (1932).
  3. C. Zener, "Non-Adiabatic Crossing of Energy Levels," Proc. Roy. Soc. Lond. A 137, 696-702 (1932).
  4. N. F. Ramsey, Molecular Beams (Oxford Univ. Press, England, 1956).
  5. C. E. Carroll and F. T. Hioe, "Analytic solutions for three-state systems with overlapping pulses," Phys. Rev. A 42, 1522-1531 (1990).
    [CrossRef] [PubMed]
  6. L. Allen and J.H . Eberly, Optical Resonance and Two-Level Atoms (Dover Publications, Inc., New York, 1987), Sec. 2.4.
  7. P. Guttinger, "Das Verhalten von Atomen im magnetischen Drehfeld," Zeits. f. Phys. 73, 169-184 (1931).
    [CrossRef]

Other

K.-A. Suominen, "Time Dependent Two-State Models and Wave Packet Dynamics," Univ. of Helsinki Report Series in Theoretical Physics HU-TFT-IR-92-1 (1992).

L.D. Landau, "Zur Theorie der Energieubertragung.II," Phys. Z. Sowjet Union 2, 46-51 (1932).

C. Zener, "Non-Adiabatic Crossing of Energy Levels," Proc. Roy. Soc. Lond. A 137, 696-702 (1932).

N. F. Ramsey, Molecular Beams (Oxford Univ. Press, England, 1956).

C. E. Carroll and F. T. Hioe, "Analytic solutions for three-state systems with overlapping pulses," Phys. Rev. A 42, 1522-1531 (1990).
[CrossRef] [PubMed]

L. Allen and J.H . Eberly, Optical Resonance and Two-Level Atoms (Dover Publications, Inc., New York, 1987), Sec. 2.4.

P. Guttinger, "Das Verhalten von Atomen im magnetischen Drehfeld," Zeits. f. Phys. 73, 169-184 (1931).
[CrossRef]

Supplementary Material (2)

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Figures (3)

Figure 1.
Figure 1.

A plot of Pesc , given in (1), as a function of the rapidity parameter x, which is defined in (19). An expanded view of the approach to the singular oscillations near the adiabatic limit is given in the left graph.

Figure 2.
Figure 2.

A frame from a movie (352KB) showing adiabatic following of the Bloch vector as it precesses rapidly about Ω, which is rotating slowly with the relative rotation rate 1/40.

Figure 3.
Figure 3.

A frame from a movie (570KB) showing diabatic following of the Bloch vector as it achieves inversion and then full 2π rotation as a consequence of successive “kicks” by Ω.

Equations (35)

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P esc = x 2 1 + x 2 sin 2 ( π 2 1 + x 2 x 2 ) .
d S dt = Ω × S
Ω { r , 0 , Δ } ,
r = 2 ħ and Δ = ω 0 ω L .
d Ω dt = A × Ω ,
S = ± ( Ω ( t ) A ) T ad ,
( A 2 + Ω 2 ) T ad 2 = 1 ,
r = ± Ω sin At , Δ = ± Ω cos At ,
A = 2 ̂ A = { 0 , A , 0 } .
Ω ( t ) = A ̂ ( A ̂ · Ω 0 ) + ( A ̂ × Ω 0 ) sin At
A ̂ × ( A ̂ × Ω 0 ) cos At ,
Ω = 1 ̂ Ω sin At 3 ̂ Ω cos At
= Ω { sin At , 0 , cos At }
Ω Ω ̂ ( t )
Ω ̂ = { sin At , 0 , cos At } ,
A ̂ = { 0,1,0 } ,
A ̂ × Ω ̂ = { cos At , 0 , sin At } .
S ( t ) = α ( t ) A ̂ + β ( t ) Ω ̂ ( t )
+ γ ( t ) A ̂ × Ω ̂ ( t )
d 2 γ d t 2 + 1 T ad 2 γ = 0 .
α ( t ) = ΩA T ad 2 ( cos ( t T ad ) 1 ) ,
β ( t ) = 1 + A 2 T ad 2 ( cos ( t T ad ) 1 ) ,
γ ( t ) = A T ad sin ( t T ad ) .
S = A ̂ Ω A T ad 2 ( cos t T ad 1 ) + Ω ̂ ( 1 + A 2 T ad 2 ( cos t T ad 1 ) )
( A ̂ × Ω ̂ ) A T ad sin t T ad ,
S = 1 ̂ { A T ad sin t T ad cos At ( 1 + A 2 T ad 2 ( cos t T ad 1 ) ) sin At }
+ 2 ̂ { ΩA T ad 2 ( cos t T ad 1 ) }
+ 3 ̂ { A T ad sin t T ad sin At ( 1 + A 2 T ad 2 ( cos t T ad 1 ) ) cos At } .
x A Ω 1 ( highly adiabatic )
x 1 ( very nonadiabatic ) .
S 3 ( π ) = 1 ( A T ad ) 2 ( 1 cos π A T ad ) .
P esc 1 2 ( 1 cos π ) 1 , ( x , zero transfer ) ,
1 2 x 2 ( 1 cos ( π x ) ) 0 , ( x 0 , complete transfer ) ,
S = 1 ̂ sin ( t T ad At ) + 2 ̂ Ω T ad ( cos t T ad 1 ) 3 ̂ cos ( t T ad At ) .
( 1 T ad A ) ( A 2 + Ω 2 A ) Ω 2 2 A Ω A .

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