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arXiv:1506.06934 · Physical Review A

Suppression of the ac-Stark-shift scattering rate due to non-Markovian behavior

Muzaffar Qadir Lone, Tim Byrnes

Published Jul 7, 2015• 15 citations
arXivHTMLPDF

Abstract

The ac Stark shift in the presence of spontaneous decay is typically considered to induce an effective dephasing with a scattering rate equal to ${\mathrm{\ensuremath{\Gamma}}}_{s}{|\mathrm{\ensuremath{\Omega}}|}^{2}/{\mathrm{\ensuremath{\Delta}}}^{2}$, where ${\mathrm{\ensuremath{\Gamma}}}_{s}$ is the spontaneous decay rate, $\mathrm{\ensuremath{\Omega}}$ is the laser transition coupling, and $\mathrm{\ensuremath{\Delta}}$ is the detuning. We show that under realistic circumstances this dephasing rate may be strongly modified due to non-Markovian behavior. The non-Markovian behavior arises due to an effective modification of the light-atom coupling in the presence of the ac-Stark-shift laser. An analytical formula for the non-Markovian ac-Stark-shift-induced dephasing is derived. We obtain that for narrow laser linewidths the effective dephasing rate is suppressed by a factor of ${Q}^{2}$, where $Q$ is the quality factor of the laser.

DOI
10.1103/physreva.92.011401

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The ac Stark shift in the presence of spontaneous decay is typically considered to induce an effective dephasing with a scattering rate equal to \ensuremathΓs∣\ensuremathΩ∣2/\ensuremathΔ2{\mathrm{\ensuremath{\Gamma}}}_{s}{|\mathrm{\ensuremath{\Omega}}|}^{2}/{\mathrm{\ensuremath{\Delta}}}^{2}\ensuremathΓs​∣\ensuremathΩ∣2/\ensuremathΔ2, where \ensuremathΓs{\mathrm{\ensuremath{\Gamma}}}_{s}\ensuremathΓs​ is the spontaneous decay rate, \ensuremathΩ\mathrm{\ensuremath{\Omega}}\ensuremathΩ is the laser transition coupling, and \ensuremathΔ\mathrm{\ensuremath{\Delta}}\ensuremathΔ is the detuning. We show that under realistic circumstances this dephasing rate may be strongly modified due to non-Markovian behavior. The non-Markovian behavior arises due to an effective modification of the light-atom coupling in the presence of the ac-Stark-shift laser. An analytical formula for the non-Markovian ac-Stark-shift-induced dephasing is derived. We obtain that for narrow laser linewidths the effective dephasing rate is suppressed by a factor of Q2{Q}^{2}Q2, where QQQ is the quality factor of the laser.
The ac Stark effect is a well-known, well-established effect associated with the displacement of the atomic energy levels in the presence of an electromagnetic (e.m.) field. As the origin of the e.m. field is irrelevant, a self-induced ac Stark effect should be present in a laser. However, not only has this effect never been reported but it is not included in any laser model. Here, we show that a self-induced ac Stark shift does exist in the theoretical description of a two-level laser, provided that the reduced equations are derived not from the rotating-wave approximation, but from the full density matrix formulation. Interesting fundamental consequences are discussed and quantitative estimates of the self-induced frequency shift resulting from the laser field's ac Stark shift are obtained for a variety of lasers. We find that the effect is generally small but (at least in some cases) measurable and that the transfer of laser amplitude noise into frequency noise may play a role in future, ultrahigh-precision metrological applications.
We report on an experimental and theoretical study of the dynamic (ac) Stark effect on a forbidden transition. A general framework for parametrizing and describing off-resonant ac-Stark shifts is presented. A model is developed to calculate spectral line shapes resulting from resonant excitation of atoms in an intense standing light wave in the presence of off-resonant ac-Stark shifts. The model is used in the analysis and interpretation of a measurement of the ac-Stark shifts of the static-electric-field-induced $6{s}^{2}\phantom{\rule{0.2em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}5d6s^{3}D_{1}$ transition at 408nm408\phantom{\rule{0.3em}{0ex}}\mathrm{nm}408nm in atomic Yb. The results are in agreement with estimates of the ac-Stark shift of the transition under the assumption that the shift is dominated by that of the 6s21S06{s}^{2}\phantom{\rule{0.2em}{0ex}}^{1}S_{0}6s21S0​ ground state. A detailed description of the experiment and analysis is presented. A biproduct of this work is an independent determination (from the saturation behavior of the 408-nm transition) of the Stark transition polarizability, which is found to be in agreement with our earlier measurement. This work is part of the ongoing effort aimed at a precision measurement of atomic parity-violation effects in Yb.
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We demonstrate that the differential ac-Stark shift of a Zeeman-sensitive ground hyperfine transition in an optical trap can be eliminated by using properly polarized trapping light. We use the vector polarizability of an alkali-metal atom to produce a polarization-dependent ac-Stark shift that resembles a Zeeman shift. We study a transition from the $|2{S}_{1/2},F=2,{m}_{F}=\ensuremath{-}2⟩$ to the $|2{S}_{1/2},F=1,{m}_{F}=\ensuremath{-}1⟩$ state of 7Li^{7}\mathrm{Li}7Li to observe $0.59\ifmmode\pm\else\textpm\fi{}0.02\text{ }\text{ }\mathrm{Hz}$ linewidth with interrogation time of 2 s and $0.82\ifmmode\pm\else\textpm\fi{}0.06\text{ }\text{ }\mathrm{s}$ coherence time of a superposition state. Implications of the narrow linewidth and the long coherence time for precision spectroscopy and quantum information processing using atoms in an optical lattice are discussed.
We have investigated the ac Stark shift of a two-photon transition induced by a model stochastic field by using a Monte Carlo technique. The model field has a stochastic single mode, which can possess both colored amplitude and colored frequency fluctuations. The stochastic field’s modification of the ac Stark shift is quantified by a parameter M, which is the ratio of the Stark shift in the model stochastic field to the Stark shift that would be obtained in a phase-diffusion field of equivalent linewidth (i.e., a field with frequency fluctuations but no amplitude fluctuations). In the regime of weak fields, below saturation of the bound-bound transition, we find that M is greater than unity: the Stark shift is enhanced by the stochastic field. Moreover, in this regime M is an increasing function of the field’s degree of photon bunching. In strong fields, where the bound–bound transition is nearly saturated, the enhancement of the Stark shift is diminished, so much so that in extremely strong fields M is actually less than unity. Our calculations indicate that the ac Stark shift’s modification occurs through two distinct processes, depending on the strength of the field. In weak fields enhancement of a multiphoton transition’s Stark shift is influenced primarily by the intrinsic correlation between ac-Stark-shift fluctuations and Rabi-frequency fluctuations. In strong fields the fluctuating Stark shifts give rise to an asymmetric resonance line shape in a fashion analogous to inhomogeneous broadening. The line shape’s peak position then has a sublinear dependence on the stochastic field’s intensity, and this yields a diminished value of M.