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Physical Review A

Suppression of inhomogeneous broadening using the ac Stark shift

Deniz D. Yavuz, N. R. Brewer, Jared A. Miles, Zach J. Simmons

Published Dec 20, 2013• 12 citations
Publisher

Abstract

We analyze a general approach for suppressing inhomogeneous broadening of atomic transitions and thereby increasing the strength of the interaction between the atomic system and near-resonant light. The key idea is to compensate for the frequency shift due to the broadening process by using an intense laser to produce an equal and opposite Stark shift.

DOI
10.1103/physreva.88.063836

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We analyze a general approach for suppressing inhomogeneous broadening of atomic transitions and thereby increasing the strength of the interaction between the atomic system and near-resonant light. The key idea is to compensate for the frequency shift due to the broadening process by using an intense laser to produce an equal and opposite Stark shift.
A method for reducing the inhomogeneous broadening in the spectroscopic measurement of the hyperfine splitting of the ground state of optically trapped atoms is demonstrated. This reduction is achieved by the addition of a very weak light field (the "compensating beam"), whose frequency is tuned between the two hyperfine levels. The total shift is obtained by adding the shifts from the trap and the compensating beam, and a complete cancellation of the inhomogeneous broadening will occur for an intensity ratio of /spl sim/ (/spl Delta/HF/2/spl delta/)/sup 2/. With the suppression of inhomogeneous broadening, the atomic coherence time is next limited by the much smaller spontaneous scattering time. Finally, the introduction of the compensating beam provides with an experimental method to control the decoherence rate of the atomic ensemble, and thus to study the interesting interplay between dynamics and coherence in systems with a rich phase-space, for example in atom-optics billiards.
The dynamic Stark shift of an inhomogeneously broadened spectral transition has been studied. Our measurements show a shift in the observed 87 Rb ground-state hyperfine transition, which has a nonlinear dependence on light intensity when the conditions for inhomogeneous broadening are met. The nonlinearity is the result of light-intensity gradients in the signal volume, which produce an inhomogeneously broadened asymmetric microwave transition. We show that our measurements are in full agreement with the second-order perturbation-theory treatment of light-induced energy-level shifts when the effects of inhomogeneities are properly taken into consideration. The effects of inhomogeneous broadening must be carefully considered when one extracts oscillator strengths from light-shift data, or performs high-precision laser spectroscopy. Originator-supplied keywords include: AC stark effect, Atomic clocks, Atomic line shapes, Light shifts.
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 Q2{Q}^{2}Q2, where QQQ is the quality factor of the laser.
We propose a way to eliminate the inhomogeneous broadening for a ground-state hyperfine transition of an alkali metal atom in an optical trap by using a properly polarized trapping field. The ac Stark shift contribution from the vector polarizability has opposite sign for a pair of ground hyperfine levels. It can be used to eliminate the inhomogeneous broadening from the difference in the scalar polarizbilities due to the hyperfine splitting. The size of the vector term is determined by the polarization state of the trapping field, and by controlling the polarization tightly one can achieve a very narrow linewidth. We estimate required tolerance in the polarization control to achieve 1-Hz linewidth for a specific case of a cesium atom. This proposal has significant implications for an electric dipole moment measurement using cesium atoms and quantum information processing using an optical lattice.