Abstract

We show that a characteristic two-photon lineshape asymmetry arises in coherent population trapping (CPT) and three-photon (N) resonances, because both resonances are simultaneously induced by modulation sidebands in the interrogating laser light. The N resonance is a three-photon resonance in which a two-photon Raman excitation is combined with a resonant optical pumping field. This joint CPT and N resonance can be the dominant source of lineshape distortion, with direct relevance for the operation of miniaturized atomic frequency standards. We present the results of both an experimental study and theoretical treatment of the asymmetry of the joint CPT and N resonance under conditions typical to the operation of an N resonance clock.

© 2008 Optical Society of America

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  1. J. Kitching, S. Knappe, N. Vukičeviè, L. Hollberg, R. Wynands, and W. Weidmann, IEEE Trans. Instrum. Meas. 49, 1313 (2000).
    [CrossRef]
  2. M. Merimaa, T. Lindvall, I. Tittonen, and E. Ikonen, J. Opt. Soc. Am. B 20, 273 (2003).
    [CrossRef]
  3. L. A. Liew, S. Knappe, J. Moreland, H. Robinson, L. Hollberg, and J. Kitching, Appl. Phys. Lett. 84, 2694 (2004).
    [CrossRef]
  4. J. Vanier, Appl. Phys. B 81, 421 (2005).
    [CrossRef]
  5. J. Kitching, H. G. Robinson, L. Hollberg, S. Knappe, and R. Wynands, J. Opt. Soc. Am. B 18, 1676 (2001).
    [CrossRef]
  6. A. S. Zibrov, C. Y. Ye, Y. V. Rostovtsev, A. B. Matsko, and M. O. Scully, Phys. Rev. A 65, 043817 (2002).
    [CrossRef]
  7. E. Arimondo, Prog. Opt. XXXV, 257 (1996).
    [CrossRef]
  8. D. F. Phillips, I. Novikova, C. Y.-T. Wang, R. L. Walsworth, and M. Crescimanno, J. Opt. Soc. Am. B 22, 305 (2005).
    [CrossRef]
  9. I. Novikova, D. F. Phillips, A. S. Zibrov, R. L. Walsworth, A. V. Taichenachev, and V. I. Yudin, Opt. Lett. 31, 622 (2006).
    [CrossRef] [PubMed]
  10. S. Zibrov, I. Novikova, D. F. Phillips, A. V. Taichenachev, V. I. Yudin, R. L. Walsworth, and A. S. Zibrov, Phys. Rev. A 72, 011801 (2005).
    [CrossRef]
  11. I. Novikova, D. F. Phillips, A. S. Zibrov, R. L. Walsworth, A. V. Taichenachev, and V. I. Yudin, Opt. Lett. 31, 2353 (2006).
    [CrossRef] [PubMed]
  12. S. KnappeM. Stähler, C. Affolderbach, A. V. Taichenachev, V. I. Yudin, and R. Wynands, Appl. Phys. B 76, 57 (2003).
    [CrossRef]
  13. M. Stähler, R. Wynands, S. Knappe, J. Kitching, L. Hollberg, A. V. Taichenachev, and V. I. Yudin, Opt. Lett. 27, 1472 (2002).
    [CrossRef]

2006 (2)

2005 (3)

D. F. Phillips, I. Novikova, C. Y.-T. Wang, R. L. Walsworth, and M. Crescimanno, J. Opt. Soc. Am. B 22, 305 (2005).
[CrossRef]

J. Vanier, Appl. Phys. B 81, 421 (2005).
[CrossRef]

S. Zibrov, I. Novikova, D. F. Phillips, A. V. Taichenachev, V. I. Yudin, R. L. Walsworth, and A. S. Zibrov, Phys. Rev. A 72, 011801 (2005).
[CrossRef]

2004 (1)

L. A. Liew, S. Knappe, J. Moreland, H. Robinson, L. Hollberg, and J. Kitching, Appl. Phys. Lett. 84, 2694 (2004).
[CrossRef]

2003 (2)

S. KnappeM. Stähler, C. Affolderbach, A. V. Taichenachev, V. I. Yudin, and R. Wynands, Appl. Phys. B 76, 57 (2003).
[CrossRef]

M. Merimaa, T. Lindvall, I. Tittonen, and E. Ikonen, J. Opt. Soc. Am. B 20, 273 (2003).
[CrossRef]

2002 (2)

M. Stähler, R. Wynands, S. Knappe, J. Kitching, L. Hollberg, A. V. Taichenachev, and V. I. Yudin, Opt. Lett. 27, 1472 (2002).
[CrossRef]

A. S. Zibrov, C. Y. Ye, Y. V. Rostovtsev, A. B. Matsko, and M. O. Scully, Phys. Rev. A 65, 043817 (2002).
[CrossRef]

2001 (1)

2000 (1)

J. Kitching, S. Knappe, N. Vukičeviè, L. Hollberg, R. Wynands, and W. Weidmann, IEEE Trans. Instrum. Meas. 49, 1313 (2000).
[CrossRef]

1996 (1)

E. Arimondo, Prog. Opt. XXXV, 257 (1996).
[CrossRef]

Affolderbach, C.

S. KnappeM. Stähler, C. Affolderbach, A. V. Taichenachev, V. I. Yudin, and R. Wynands, Appl. Phys. B 76, 57 (2003).
[CrossRef]

Arimondo, E.

E. Arimondo, Prog. Opt. XXXV, 257 (1996).
[CrossRef]

Crescimanno, M.

Hollberg, L.

L. A. Liew, S. Knappe, J. Moreland, H. Robinson, L. Hollberg, and J. Kitching, Appl. Phys. Lett. 84, 2694 (2004).
[CrossRef]

M. Stähler, R. Wynands, S. Knappe, J. Kitching, L. Hollberg, A. V. Taichenachev, and V. I. Yudin, Opt. Lett. 27, 1472 (2002).
[CrossRef]

J. Kitching, H. G. Robinson, L. Hollberg, S. Knappe, and R. Wynands, J. Opt. Soc. Am. B 18, 1676 (2001).
[CrossRef]

J. Kitching, S. Knappe, N. Vukičeviè, L. Hollberg, R. Wynands, and W. Weidmann, IEEE Trans. Instrum. Meas. 49, 1313 (2000).
[CrossRef]

Ikonen, E.

Kitching, J.

L. A. Liew, S. Knappe, J. Moreland, H. Robinson, L. Hollberg, and J. Kitching, Appl. Phys. Lett. 84, 2694 (2004).
[CrossRef]

M. Stähler, R. Wynands, S. Knappe, J. Kitching, L. Hollberg, A. V. Taichenachev, and V. I. Yudin, Opt. Lett. 27, 1472 (2002).
[CrossRef]

J. Kitching, H. G. Robinson, L. Hollberg, S. Knappe, and R. Wynands, J. Opt. Soc. Am. B 18, 1676 (2001).
[CrossRef]

J. Kitching, S. Knappe, N. Vukičeviè, L. Hollberg, R. Wynands, and W. Weidmann, IEEE Trans. Instrum. Meas. 49, 1313 (2000).
[CrossRef]

Knappe, S.

L. A. Liew, S. Knappe, J. Moreland, H. Robinson, L. Hollberg, and J. Kitching, Appl. Phys. Lett. 84, 2694 (2004).
[CrossRef]

S. KnappeM. Stähler, C. Affolderbach, A. V. Taichenachev, V. I. Yudin, and R. Wynands, Appl. Phys. B 76, 57 (2003).
[CrossRef]

M. Stähler, R. Wynands, S. Knappe, J. Kitching, L. Hollberg, A. V. Taichenachev, and V. I. Yudin, Opt. Lett. 27, 1472 (2002).
[CrossRef]

J. Kitching, H. G. Robinson, L. Hollberg, S. Knappe, and R. Wynands, J. Opt. Soc. Am. B 18, 1676 (2001).
[CrossRef]

J. Kitching, S. Knappe, N. Vukičeviè, L. Hollberg, R. Wynands, and W. Weidmann, IEEE Trans. Instrum. Meas. 49, 1313 (2000).
[CrossRef]

Liew, L. A.

L. A. Liew, S. Knappe, J. Moreland, H. Robinson, L. Hollberg, and J. Kitching, Appl. Phys. Lett. 84, 2694 (2004).
[CrossRef]

Lindvall, T.

Matsko, A. B.

A. S. Zibrov, C. Y. Ye, Y. V. Rostovtsev, A. B. Matsko, and M. O. Scully, Phys. Rev. A 65, 043817 (2002).
[CrossRef]

Merimaa, M.

Moreland, J.

L. A. Liew, S. Knappe, J. Moreland, H. Robinson, L. Hollberg, and J. Kitching, Appl. Phys. Lett. 84, 2694 (2004).
[CrossRef]

Novikova, I.

Phillips, D. F.

Robinson, H.

L. A. Liew, S. Knappe, J. Moreland, H. Robinson, L. Hollberg, and J. Kitching, Appl. Phys. Lett. 84, 2694 (2004).
[CrossRef]

Robinson, H. G.

Rostovtsev, Y. V.

A. S. Zibrov, C. Y. Ye, Y. V. Rostovtsev, A. B. Matsko, and M. O. Scully, Phys. Rev. A 65, 043817 (2002).
[CrossRef]

Scully, M. O.

A. S. Zibrov, C. Y. Ye, Y. V. Rostovtsev, A. B. Matsko, and M. O. Scully, Phys. Rev. A 65, 043817 (2002).
[CrossRef]

Stähler, M.

S. KnappeM. Stähler, C. Affolderbach, A. V. Taichenachev, V. I. Yudin, and R. Wynands, Appl. Phys. B 76, 57 (2003).
[CrossRef]

M. Stähler, R. Wynands, S. Knappe, J. Kitching, L. Hollberg, A. V. Taichenachev, and V. I. Yudin, Opt. Lett. 27, 1472 (2002).
[CrossRef]

Taichenachev, A. V.

Tittonen, I.

Vanier, J.

J. Vanier, Appl. Phys. B 81, 421 (2005).
[CrossRef]

Vukiceviè, N.

J. Kitching, S. Knappe, N. Vukičeviè, L. Hollberg, R. Wynands, and W. Weidmann, IEEE Trans. Instrum. Meas. 49, 1313 (2000).
[CrossRef]

Walsworth, R. L.

Wang, C. Y.-T.

Weidmann, W.

J. Kitching, S. Knappe, N. Vukičeviè, L. Hollberg, R. Wynands, and W. Weidmann, IEEE Trans. Instrum. Meas. 49, 1313 (2000).
[CrossRef]

Wynands, R.

S. KnappeM. Stähler, C. Affolderbach, A. V. Taichenachev, V. I. Yudin, and R. Wynands, Appl. Phys. B 76, 57 (2003).
[CrossRef]

M. Stähler, R. Wynands, S. Knappe, J. Kitching, L. Hollberg, A. V. Taichenachev, and V. I. Yudin, Opt. Lett. 27, 1472 (2002).
[CrossRef]

J. Kitching, H. G. Robinson, L. Hollberg, S. Knappe, and R. Wynands, J. Opt. Soc. Am. B 18, 1676 (2001).
[CrossRef]

J. Kitching, S. Knappe, N. Vukičeviè, L. Hollberg, R. Wynands, and W. Weidmann, IEEE Trans. Instrum. Meas. 49, 1313 (2000).
[CrossRef]

Ye, C. Y.

A. S. Zibrov, C. Y. Ye, Y. V. Rostovtsev, A. B. Matsko, and M. O. Scully, Phys. Rev. A 65, 043817 (2002).
[CrossRef]

Yudin, V. I.

Zibrov, A. S.

I. Novikova, D. F. Phillips, A. S. Zibrov, R. L. Walsworth, A. V. Taichenachev, and V. I. Yudin, Opt. Lett. 31, 622 (2006).
[CrossRef] [PubMed]

I. Novikova, D. F. Phillips, A. S. Zibrov, R. L. Walsworth, A. V. Taichenachev, and V. I. Yudin, Opt. Lett. 31, 2353 (2006).
[CrossRef] [PubMed]

S. Zibrov, I. Novikova, D. F. Phillips, A. V. Taichenachev, V. I. Yudin, R. L. Walsworth, and A. S. Zibrov, Phys. Rev. A 72, 011801 (2005).
[CrossRef]

A. S. Zibrov, C. Y. Ye, Y. V. Rostovtsev, A. B. Matsko, and M. O. Scully, Phys. Rev. A 65, 043817 (2002).
[CrossRef]

Zibrov, S.

S. Zibrov, I. Novikova, D. F. Phillips, A. V. Taichenachev, V. I. Yudin, R. L. Walsworth, and A. S. Zibrov, Phys. Rev. A 72, 011801 (2005).
[CrossRef]

Appl. Phys. B (2)

J. Vanier, Appl. Phys. B 81, 421 (2005).
[CrossRef]

S. KnappeM. Stähler, C. Affolderbach, A. V. Taichenachev, V. I. Yudin, and R. Wynands, Appl. Phys. B 76, 57 (2003).
[CrossRef]

Appl. Phys. Lett. (1)

L. A. Liew, S. Knappe, J. Moreland, H. Robinson, L. Hollberg, and J. Kitching, Appl. Phys. Lett. 84, 2694 (2004).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

J. Kitching, S. Knappe, N. Vukičeviè, L. Hollberg, R. Wynands, and W. Weidmann, IEEE Trans. Instrum. Meas. 49, 1313 (2000).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Lett. (3)

Phys. Rev. A (2)

A. S. Zibrov, C. Y. Ye, Y. V. Rostovtsev, A. B. Matsko, and M. O. Scully, Phys. Rev. A 65, 043817 (2002).
[CrossRef]

S. Zibrov, I. Novikova, D. F. Phillips, A. V. Taichenachev, V. I. Yudin, R. L. Walsworth, and A. S. Zibrov, Phys. Rev. A 72, 011801 (2005).
[CrossRef]

Prog. Opt. (1)

E. Arimondo, Prog. Opt. XXXV, 257 (1996).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

(a) Simplified level diagram with applied fields Ω 0 (carrier) and Ω 1 , Ω 2 (sidebands). (b) Example experimental N+CPT joint resonance, illustrating the typical asymmetry of the transmitted probe field Ω 1 lineshape in the presence of the Ω 2 sideband. The x axis is the two-photon detuning. The laser power is 0.088 mW , and the one-photon detuning is 350 MHz .

Fig. 2
Fig. 2

Numerical calculations of the probe field Ω 1 transmission intensity for (top) CPT, (bottom) N , and (middle) joint N+CPT resonances, vertically offset for clarity. All parameters are for the Rb 87 atom with Rabi frequencies typical of experiments and a 100 MHz one-photon detuning (causing the background to not be level). The x axis is two-photon detuning.

Fig. 3
Fig. 3

Lineshape asymmetry B A for N+CPT resonances on the D 1 transition of Rb 87 with and largely without (85% reduced intensity) the + 2 sideband. Numerical calculations based on our model are the lines; the “+” and “x” are the associated fitted B A from experimental data.

Fig. 4
Fig. 4

Comparison of N+CPT lineshape asymmetry for D 1 and D 2 transitions: (a) Numerical calculations and (b) experiment (data from [11]). Note that the experimental regime of [11] is different from that of the experiment of Fig. 3 and is at higher light power than our model can pertubatively accomodate.

Equations (2)

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( Γ i ( δ + Ω 1 2 Ω 0 2 4 ( h Δ ) ) ) ρ a b = i Ω 1 2 ρ c b + i Ω 2 2 ρ a c + Ω 1 Ω 0 4 ( h Δ ) ( ρ b b ρ a a ) ,
I ( δ ) = C + D δ + A Γ + B ( δ δ 0 ) ( δ δ 0 ) 2 + Γ 2 .

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