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Siberian Journal of Physics

Suppression of the Field Shift of Ramsey Resonance on Forbidden Transitions of Atoms and Ions

K. S. Tabatchikova, А. В. Тайченачев, Valeriy I. Yudin

Published Oct 1, 2012• 0 citations
Publisher

Abstract

We perform a theoretical analysis of the Ramsey scheme with pulses of different duration and with a phase step in the second pulse with account for the finite width of laser line. We define optimum features of pulses that correspond to maximum suppression of the field shift and maximum amplitude of resonance for both schemes. Ramsey scheme with a phase step in the second pulse provides effective suppression of the field shift and it is less sensitive to the Rabi frequency fluctuations in comparison with Ramsey scheme with pulses of different duration. First experiments on ytterbium single-ion optical clock (Germany, PTB) confirm theoretical predictions

DOI
10.54362/1818-7919-2012-7-3-6-14

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We perform a theoretical analysis of the Ramsey scheme with pulses of different duration and with a phase step in the second pulse with account for the finite width of laser line. We define optimum features of pulses that correspond to maximum suppression of the field shift and maximum amplitude of resonance for both schemes. Ramsey scheme with a phase step in the second pulse provides effective suppression of the field shift and it is less sensitive to the Rabi frequency fluctuations in comparison with Ramsey scheme with pulses of different duration. First experiments on ytterbium single-ion optical clock (Germany, PTB) confirm theoretical predictions
Ramsey schemes with pulses of different lengths and with a composite pulse have been analyzed taking into account a finite width of the laser line and spontaneous relaxation of atomic levels. The optimal parameters of pulses corresponding to the maximum suppression of the excitation-related shift and the maximum resonance amplitude have been found for both schemes. According to the numerical results, spontaneous relaxation of the atomic levels and a finite width of the laser line must be taken into account in the calculation of the optimal parameters of the excitation pulses. The Ramsey scheme with a composite pulse is less sensitive to fluctuations of the Rabi frequency than the scheme with pulses of different lengths.
We present nonstandard optical Ramsey schemes that use pulses individually tailored in duration, phase, and frequency to cancel spurious frequency shifts related to the excitation itself. In particular, the field shifts and their uncertainties can be radically suppressed (by two to four orders of magnitude) in comparison with the usual Ramsey method (using two equal pulses) as well as with single-pulse Rabi spectroscopy. Atom interferometers and optical clocks based on two-photon transitions, heavily forbidden transitions, or magnetically induced spectroscopy could significantly benefit from this method. In the latter case, these frequency shifts can be suppressed considerably below a fractional level of 101010${}^{\ensuremath{-}17}$. Moreover, our approach opens the door for high-precision optical clocks based on direct frequency comb spectroscopy.
We experimentally investigate a recently proposed optical excitation scheme V. I. Yudin et al. [Phys. Rev. A 82, 011804(R) (2010)] that is a generalization of Ramsey's method of separated oscillatory fields and consists of a sequence of three excitation pulses. The pulse sequence is tailored to produce a resonance signal that is immune to the light shift and other shifts of the transition frequency that are correlated with the interaction with the probe field. We investigate the scheme using a single trapped ^{171}Yb^{+} ion and excite the highly forbidden (2)S(1/2) - (2)F(7/2) electric-octupole transition under conditions where the light shift is much larger than the excitation linewidth, which is in the hertz range. The experiments demonstrate a suppression of the light shift by four orders of magnitude and an immunity against its fluctuations.
We present an interrogation scheme for the next generation of quantum clocks to suppress frequency shifts induced by laser probing fields that are themselves based on generalized hyper-Ramsey resonances. Sequences of composite laser pulses with a specific selection of phases, frequency detunings, and durations are combined to generate a very efficient and robust frequency locking signal with an almost perfect elimination of the light shift from off-resonant states and to decouple the unperturbed frequency measurement from the laser's intensity. The frequency lock point generated from synthesized error signals using either $\ensuremath{\pi}/4$ or $3\ensuremath{\pi}/4$ laser phase steps during the intermediate pulse is tightly protected against large laser-pulse area variations and errors in potentially applied frequency shift compensations. Quantum clocks based on weakly allowed or completely forbidden optical transitions in atoms, ions, molecules, and nuclei will benefit from these hyperstable laser frequency stabilization schemes to reach relative accuracies below the ${10}^{\ensuremath{-}18}$ level.
In this work, the peculiarities of Ramsey resonance and its sensitivity to the light shift from an optically dense medium of cold atoms are investigated. We considered different composite pulse protocols for clock spectroscopy such as hyper-Ramsey, modified and generalized hyper-Ramsey schemes. Shapes of resonances and error signals changes significantly due to the processes of absorption and dispersion in the atomic medium. The dependence of the position of the central fringe resonance with a residual uncompensated light shift of the atomic transition is theoretically studied when taking into account the attenuation of the radiation intensity in the medium. The change in pulses area of the hyper-Ramsey protocol allows us to suppress the sensitivity of the clock resonance position to the residual light shift for a certain length of the medium. It is shown that using a combination of generalized hyper- Ramsey error signals allows us to suppress the sensitivity to the light shift for any length of the medium. Also we analyzed the effect of spontaneous decay of high atomic state on the light shift sensitivity of the composite pulses schemes.