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arXiv:1401.3497 · Physical Review A

Theoretical and experimental investigation of the light shift in Ramsey coherent population trapping

Yuichiro Yano, Wujie Gao, Shigeyoshi Goka, Masatoshi Kajita

Published Jul 21, 2014• 42 citations
arXivHTMLPDF

Abstract

The ac Stark shift (or light shift) of the $6{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}(F=3\ensuremath{\leftrightarrow}4)$ transition in ${}^{133}$Cs, as observed through coherent population trapping under pulsed excitation, is measured using a ${}^{133}$Cs gas cell and the $D$${}_{1}$-line vertical-cavity surface-emitting laser. This light shift can be calculated using density-matrix analysis. We derive an expression for this shift as a function of light intensity, showing that it varies linearly with respect to light intensity only with intensities higher than 1.0 mW/cm${}^{2}$. For pulsed excitation of high laser intensity, the variation in light shift is 20 times lower than that when using a continuous wave. The differences between the results of theory and experiment are discussed, taking into account the difference in conditions assumed; the results from theoretical analysis, taking the attenuation of the first-order sideband into account, approximately agree with the experimental results. The light shift is reduced by shortening the observation times.

DOI
10.1103/physreva.90.013826

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The ac Stark shift (or light shift) of the 62S1/2(F=3\ensuremath↔4)6{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}(F=3\ensuremath{\leftrightarrow}4)62S1/2​(F=3\ensuremath↔4) transition in 133{}^{133}133Cs, as observed through coherent population trapping under pulsed excitation, is measured using a 133{}^{133}133Cs gas cell and the D$${}_{1}-line vertical-cavity surface-emitting laser. This light shift can be calculated using density-matrix analysis. We derive an expression for this shift as a function of light intensity, showing that it varies linearly with respect to light intensity only with intensities higher than 1.0 mW/cm2{}^{2}2. For pulsed excitation of high laser intensity, the variation in light shift is 20 times lower than that when using a continuous wave. The differences between the results of theory and experiment are discussed, taking into account the difference in conditions assumed; the results from theoretical analysis, taking the attenuation of the first-order sideband into account, approximately agree with the experimental results. The light shift is reduced by shortening the observation times.
This paper presents a theoretical and experimental investigation on the light shift (AC Stark shift) of the 62S1/2(F = 3 ↔ 4) transition in133Cs, as observed through coherent population trapping (CPT) under a pulsed excitation. The calculated results are good agreement in the experimental results on various parameters and show that the light shift under pulsed excitation is 20∼30 times less than that under continuous excitation. In addition, this paper also presents a two-step pulse method for suppressing the light shift.
The off-resonant ac Stark shift for coherent population trapping (CPT) resonances probed with Ramsey spectroscopy is investigated experimentally and theoretically. Measurements with laser-cooled 87Rb^{87}\mathrm{Rb}87Rb atoms show excellent quantitative agreement with a simple theory. The shift depends on the relative intensity of the two CPT light fields, but depends only weakly on the total intensity. Since the origin of the shift is through couplings of the interrogation light to off-resonant excited-state hyperfine levels, the size and sign of the shift depend on the specific interrogation scheme. The theory also shows that for several commonly used interrogation schemes it is possible to minimize the off-resonant light shift or its dependence on the CPT intensity ratio by properly selecting the system parameters.
We have measured the spectral position of the absorption minimum in a coherent population trapping resonance in thermal cesium vapor as a function of light intensity. The dependence of position on intensity is found to be almost linear. We have furthermore studied the dependence of this light shift on neon bufier gas pressure and flnd a strong reduction for higher pressures. So the addition of a bufier gas not only reduces the linewidth of the resonance but also a very important systematic efiect for precision measurements. An atomic three-level system with two low-lying and long-lived levels (a so-called ⁄ system) can exhibit a two-photon resonance when the difierence frequency of two driving flelds matches the splitting of the two lower levels (flg. 1), !2 i !1 = !12 (1). The resonance is called \dark since one-photon absorption and resonance ∞uorescence are strongly reduced because of the trapping of the atomic population in a coherent superposition state of the two lower levels that is no longer coupled to the light flelds (coherent population trapping, CPT) (2). The two-photon resonance can be very narrow (3, 4), with linewidths rivaling those of the microwave-driven magnetic dipole transition between the two lower atomic states. The use of dark resonances for the construction of atomic radio frequency standards (5) or applications for precision measurements, for instance in magnetometry (6), has been suggested, and flrst steps in this direction have been taken (7). It is an essential requirement for such precision applications to understand the in∞uence of experimental conditions on the position and shape of the resonance under investigation. Because of the flnite dephasing rate between the two lower states the position of the absorption minimum at the dark resonance can depend on intensity (8,1), and in experiments a shift of the center of the resonance (light shift, AC Stark shift) is readily observed (9), as was discussed, for instance, for an atomic beam (5) or in connection with a CPT maser (10). In this letter we report measurements of the light shift of the two-photon resonance that couples two hyperflne ground-state levels of the cesium atoms in a thermal vapor both with and without an additional bufier gas.
This study aimed to detect the light shift by utilizing various atomic resonances observed under pulsed excitation with drive current modulation (DCM). Light shift degrades the performance of atomic clocks, and several studies have attempted to mitigate or correct it. Pulsed excitation with DCM facilitates the observation of various Ramsey-coherent population trapping (CPT) resonances owing to wavelength variation. Further, in the Ramsey-CPT sequence, a semi-continuous wave CPT resonance (SCW-CPT resonance), which is a continuous wave CPT resonance from pulsed lasers, is also observed. As these atomic resonances exhibit different frequency sensitivities to laser intensity, the frequency shifts differ based on the changes in laser intensity. This facilitates the detection of the light shift. By simultaneously measuring the resonance frequencies of two Ramsey-CPT resonances and the SCW-CPT resonance while varying the laser intensity to induce light shifts, we measured the resulting frequency changes. Each resonance exhibited a different frequency shift in response to the light shift. Therefore, this study conformed the feasibility of detecting and estimating the light shift in an operational atomic clock.
We present a comparative study of the light-shifts (ac Stark shift) in a Rb vapour cell using two possible schemes for Rb atomic clocks: double resonance (DR) and coherent population trapping (CPT). For both schemes, the same wall-coated cell in a compact atomic resonator was used. The light-shift resulting from a monochromatic (DR) or a non-monochromatic (CPT) optical excitation was measured as a function of the laser intensity and the laser frequency and compared with existing theoretical results.
This paper presents a theoretical study of the light-induced shift of the coherent population trapping resonance. An analytical model is proposed that describes the interaction of two radiation components with an atomic system using a ΛΛΛ scheme and takes into account an additional level of excited state. Both weak and strong coupling regimes with off-resonant transitions are considered. It is shown that, in addition to the conventional dynamic Stark shift, an extra shift arises due to the distortion of the resonance line shape when bichromatic laser radiation interacts with off-resonant atomic transitions. An analytical expression for this additional shift is derived in the weak-coupling limit, and its significant impact on the resonance shape and sensitivity to the intensities of the laser field components is demonstrated. It is found that under strong coupling conditions, the additional shift can deviate substantially from a linear dependence on light intensity, suggesting new opportunities for controlling light shifts in precision atomic devices such as quantum frequency standards.