1. Influence of spontaneous emission on the linear and nonlinear
resonances of alkali atoms confined in an Extremely Thin Cell
T. Vartanyan1 , V. Polischuk1, A.Sargsyan2, A. Krasteva3, St. Cartaleva3, G. Todorov3
1St.Petersburg ITMO University, Kronverkskiy pr. 49, St.Petersburg , Russian Federation
2Institute for Physical Research, National Academy of Sciences of Armenia, Ashtarak-2, Armenia
3Institute of Electronics, Bulgarian Academy of Sciences, boul. Tzarigradsko shosse 72, 1784 Sofia, Bulgaria
Abstract
Theory: basic equations
Energy level diagram for D2 line of 133Cs
The sub-Doppler spectroscopy of alkali atom vapour was strongly advanced by the invention of the Extremely Thin Cells (ETC) [1]. Using the conventional spectroscopic methods of registration, a number of peculiarities in the absorption, reflection and fluorescence spectra were observed in these cells, which are not present in commonly used (cm-size) cells. The main reason for the formation of the sub-Doppler structures in the spectra is the strong spatial anisotropy in the ETC environment. Collisions with the cell walls induce loss of atomic phase memory and excitation quenching. Hence, the atoms departing from the cell walls undergo a transient regime of excitation before they acquire the steady state polarization that corresponds to their velocity as well as to the laser field intensity and detuning. Nonlinear resonances in absorption and fluorescence are also influenced by velocity selective optical pumping [2].The present work gives a description of the interaction of resonant laser fields with alkali atoms in an ETC with the full account of the hyperfine sublevel degeneracy using iteration procedure over the laser field
The problem of determination of the nonlinear atomic polarization was solved for arbitrary values of the total angular momenta of the resonance levels for excitation with linearly polarized laser light. Using the previously developed methodology [3-6], the equations of motion for the statistical operatorу in the irreducible tensor operator (ITO) representation were solved, taking into account the transient processes in the atomic collisions with the cell walls. Analytical solutions are obtained for the spatial part of the tensor components, , which characterize the population and longitudinal alignment of the upper , and lower resonance levels and the optical coherence , with accuracy up to the third-order terms with respect to the laser field. Taking into account the spontaneous transfer from the excited level, it was possible to relate the sign reversal of the nonlinear resonance at the closed transition with a corresponding reversal of the sign of the lower level alignment. In contrast to other works, here the resonance level decay constants and the optical coherences are assumed to be different. The numerical calculation results show excellent agreement with experimental data obtained for the D2 lines of 133Cs confined in an ETC.
Absorption
Fluorescence
0.01 < Gf < 0.04
Longitudinal alignment of the ground state -Theoretical results
Longitudinal alignment resonance for Fj = 4 → Ff = 3 hyperfine transition.
Longitudinal alignment resonance for Fj = 4 → Ff = 4 and
Fj = 4 → Ff = 5 hyperfine transition.
Dependence of the sing reversal resonance on the
Comparison with the experiment
Sign reversal of Fj = 4 → Ff = 3, 4, 5 hyperfine transition in absorption spectra for l = 6λ.
Fluorescence spectra of the sets of Fj = 3 → Ff = 2, 3, 4 and
Fj = 4 → Ff = 3, 4, 5 hyperfine transitions at l = (3/2)λ.
Absorption spectra of the sets of Fj = 3 → Ff = 2, 3, 4 for l = λ and l = 3λ/2 and Fj = 4 → Ff = 3, 4, 5 hyperfine transitions
for l = λ/2 and l = 3λ/2.
Conclusions
The developed theoretical analysis demonstrates good sensitivity to the transient processes that have very different characteristic times for the absorption and the fluorescence. The time of the transient process also depends on the longitudinal dimension of the ETC. Indeed, the proposed approach reproduces in a quantitative way the multicomponent absorption and fluorescence spectra that are very different in ETCs. This was not the case in the previous works where only individual hyperfine transitions were concerned theoretically and a qualitative agreement between the theory and experiment was achieved.
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Acknowledgements This work was supported by the Russian–Armenian bilateral project RFBR , 15 RF-024; and by the Russian Ministry of Education and Science 2014/190, 074-U01. G.Т. thanks also Dr D. Slavov for the assistance in the numerical calculations. AK acknowledges the project DFNP-188/ under scientific program “Assistance for young scientists”, BAS.