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Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)

The Optical Stark Shift on a Two-Photon Transition in Rubidium

Kyle W. Martin, N. Lemke, Gretchen R. Phelps, John H. Burke, Benjamin Stuhl

Published May 1, 2018• 1 citation
Publisher

Abstract

An atomic clock designed around the 778 nm two-photon transition in rubidium vapor has become an appealing option for future portable optical clocks. However, two-photon transitions are known to suffer from large AC Stark shifts. We present an analysis of the AC Stark shift in the$5\mathrm{S}_{1/2}\rightarrow 5\mathrm{D}_{5/2}$two photon transition of Rb, along with an improved determination of the blackbody radiation Stark shift.

DOI
10.1109/fcs.2018.8597481

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Physical Review A•Feb 29, 2016•25 citations
An atomic clock designed around the 778 nm two-photon transition in rubidium vapor has become an appealing option for future portable optical clocks. However, two-photon transitions are known to suffer from large AC Stark shifts. We present an analysis of the AC Stark shift in the5S1/2→5D5/25\mathrm{S}_{1/2}\rightarrow 5\mathrm{D}_{5/2}5S1/2​→5D5/2​two photon transition of Rb, along with an improved determination of the blackbody radiation Stark shift.
The $5{S}_{1/2}\ensuremath{\rightarrow}5{D}_{5/2}$ two-photon transition in Rb is of interest for the development of a compact optical atomic clock. Here we present a rigorous calculation of the 778.1-nm ac Stark shift $[2.30(4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}{(\mathrm{mW}/{\mathrm{mm}}^{2})}^{\ensuremath{-}1}]$ that is in good agreement with our measured value of $2.5(2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}{(\mathrm{mW}/{\mathrm{mm}}^{2})}^{\ensuremath{-}1}$. We include a calculation of the temperature-dependent blackbody radiation (BBR) shift, and we predict that the clock could be operated either with zero net BBR shift [T=495.9(27)[T=495.9(27)[T=495.9(27) K] or with zero first-order sensitivity [T=368.1(14)[T=368.1(14)[T=368.1(14) K]. Also described is the calculation of the dc Stark shift of $5.5(1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}/(\mathrm{V}/{\mathrm{cm}}^{2}$) as well as clock sensitivities to optical alignment variations in both a cat's eye and a flat mirror retroreflector. Finally, we characterize these Stark effects, discussing mitigation techniques necessary to reduce final clock instabilities.
Two-photon vapor cell-based optical clocks are strong candidates for next-generation portable atomic standards, offering simplicity, compactness, and high performance. Their narrow clock transitions with counter-propagating beams enable first-order Doppler-free operation. However, systematic perturbations such as the AC Stark shift, temperature-induced shift, and drifts resulting from the laser system pose challenges cause instabilities to medium- to long-term performance. This paper provides a comprehensive overview of Rb two-photon vapor cell optical standards, focusing on the long-term performance-limiting effects and potential mitigation strategies, aiming for clock stabilities better than 1 × 10−15 over the averaging time of a day and beyond.
The two-photon transition in rubidium is an attractive candidate for use in the next generation of field-deployable atomic clocks and frequency references. However, this transition is known to suffer from a large AC Stark shift, through which fluctuations in the intensity of the interrogation laser cause fluctuations of the clock frequency, often limiting long-term stability. We implement an interrogation protocol known as the auto-compensated shift (ACS) in a two-photon rubidium optical frequency reference, reducing its sensitivity to optical intensity fluctuations by a factor of 1000. ACS alleviates the tradeoff between short-term and long-term stability imposed by the light shift and enables us to simultaneously achieve a fractional instability of 3 x 10^-14 at an integration time of 1 s and 2 x 10^-14 at an integration time of 10,000 s. We also examine a stability limit imposed on clocks using ACS by frequency noise on the laser.
Abstract We analyze an optical atomic clock using two-photon 5 S 1 / 2 → 4 D J transitions in rubidium. Four one- and two-color excitation schemes to probe the 4 D 3 / 2 and 4 D 5 / 2 fine-structure states are considered in detail. We compare key characteristics of Rb 4 D J and 5 D 5 / 2 two-photon clocks. The 4 D J clock features a high signal-to-noise ratio due to two-photon decay at favorable wavelengths, low dc electric and magnetic susceptibilities, and minimal black-body shifts. Ac Stark shifts from the clock interrogation lasers are compensated by two-color Rabi-frequency matching. We identify a ‘magic’ wavelength near 1060 nm, which allows for in-trap, Doppler-free clock-transition interrogation with lattice-trapped cold atoms. From our analysis of clock statistics and systematics, we project a quantum-noise-limited relative clock stability at the 10 − 13 / τ ( s ) -level, with integration time τ in seconds, and a relative accuracy of ∼ 10 − 13 . We describe a potential architecture for implementing the proposed clock using a single telecom clock laser at 1550 nm, which is conducive to optical communication and long-distance clock comparisons. Our work could be of interest in efforts to realize small and portable Rb clocks and in high-precision measurements of atomic properties of Rb 4 D J -states.
The ac Stark shift (also known as the ``light shift'') is one of the most important physical processes that arises in precision spectroscopy, affecting the basic understanding of field-matter interactions, measurements of fundamental constants, and even the atomic clocks onboard GPS satellites. Although the theory of the ac Stark shift was fully developed by the 1960s and 1970s, precision tests of theory have, for the most part, been few. Taking advantage of recent developments in atomic clock technology, specifically the pulsed approach to atomic signal generation, which allows frequency measurements with a resolution of $\ensuremath{\sim}{10}^{\ensuremath{-}15}$, we demonstrate a methodology for measuring the ac Stark shift. Here, we report results from a precision examination of the ac Stark shift in a vapor phase system, examining the resonant frequency of the 87Rb^{87}\text{Rb}87Rb 0-0 hyperfine transition for a perturbing laser tuned over a broad optical frequency range (18 GHz) around the D1{D}_{1}D1​ absorption resonance. Over the full frequency range the agreement between semiclassical theory and experiment is very good (better than $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$), and in our experiments we test both the frequency dependence of the scalar and tensor components of the light shift.