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Physical Review A

Self-induced ac Stark shift in lasers

Lionel Gil, Gian Luca Lippi

Published Apr 29, 2011• 9 citations

Abstract

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.

DOI: 10.1103/physreva.83.043840

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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 have measured the ac Stark effect in a two-zone stimulated Raman interaction in a sodium atomic beam. In addition, we have derived simple theoretical expressions for the ac Stark shift, based on a closed three-level system, in the Λ configuration, and have achieved qualitative agreement with the data. In particular, the magnitude and sense of the ac Stark shifts are found to depend on laser intensities as well as on the initial populations of the two low-lying levels of the Λ configuration. Specifically, the observed ac Stark shifts are smaller for larger laser intensities and also for smaller initial population differences between the two low-lying levels. The ac Stark effect must be considered for many potential applications of the Raman effect, such as a Raman clock. In this connection, we have identified conditions for the reduction of the ac Stark shift in our sodium Raman clock.

In an optical Ramsey atomic interferometer using Ramsey separated oscillating fields method, AC Stark effect shows that an interference feature is superimposed on the AC Stark level shift dispersion line-shape. This phenomenon has never been observed before. In this report, an analytic expression of the AC Stark shift in optical Ramsey atomic interferometer has been derived, and the numerical result of this interesting feature has been analyzed. Finally, the condition to measure the Interference of AC Stark Effect has been discussed.

The energy shift of an atom due to its interaction with the oscillating electric field of an electromagnetic wave, or a laser light, is called the ac Stark shift. It has been studied both in the field of precision spectroscopy and atom optics. When the laser intensity is not constant spatially, its gradient gives rise to a dipole force. The force was used either to trap atoms in an optical trap or to reflect or guide atoms. We studied the ac Stark effect taking into account the fine structure of an alkali atom. We found that when the laser light is circularly polarized and properly detuned between the D1 and D2 transitions, the ac Stark shift can take the form of a pure Zeeman shift, hence the name analogous Zeeman shift.

The ac Stark shift of the resonance frequency of the nonlinear magneto-optic effect (NMOE) results in a fundamental broadening of this resonance which limits the precision of optical magnetometry based on NMOE. We have studied the dependence of the ac Stark shift versus frequency of the probing laser for the

{D}_{1}

and

{D}_{2}

lines of

{}^{87}\mathrm{Rb},

and have shown that there exists a frequency where the shifts from different hyperfine components of the upper level cancel each other. This holds promise for an in-principle increase in the sensitivity of optical magnetometers. The influence of buffer gas on Faraday rotation and ac Stark shifts is also considered.

This work presents a theoretical analysis of the Autler-Townes splitting pattern in the four-wave mixing signal generated in a three-level cascade Doppler-broadened system. We employ the density matrix formalism to write the Bloch equations and solve them numerically. The solutions allow us to compare the response of the upper level population and the generated signal coherence for homogeneously and nonhomogeneously broadened systems. Our results reveal an AC Stark shift in the nonlinear signal when the frequency of the strong or weak laser beam is scanned, in contrast to what is observed in the fluorescence. Furthermore, we present experimental data for the four-wave mixing signal in a hot rubidium vapor for the copropagating configuration of the laser beams that drive the $5S\ensuremath{\rightarrow}5P\ensuremath{\rightarrow}5D$ transition. The behavior of the AC Stark displacement and signal amplitude as a function of laser power indicates a good agreement between the model and the experimental results.