Autobalanced Ramsey Spectroscopy

Christian Sanner, Nils Huntemann, Richard Lange, Christian Tamm, and Ekkehard Peik

Phys. Rev. Lett. 120, 053602 – Published 30 January 2018

Abstract

We devise a perturbation-immune version of Ramsey’s method of separated oscillatory fields. Spectroscopy of an atomic clock transition without compromising the clock’s accuracy is accomplished by actively balancing the spectroscopic responses from phase-congruent Ramsey probe cycles of unequal durations. Our simple and universal approach eliminates a wide variety of interrogation-induced line shifts often encountered in high precision spectroscopy, among them, in particular, light shifts, phase chirps, and transient Zeeman shifts. We experimentally demonstrate autobalanced Ramsey spectroscopy on the light shift prone ${}^{171}{Yb}^{+}$ electric octupole optical clock transition and show that interrogation defects are not turned into clock errors. This opens up frequency accuracy perspectives below the $10^{- 18}$ level for the ${Yb}^{+}$ system and for other types of optical clocks.

Received 7 July 2017
Revised 22 November 2017

DOI:https://doi.org/10.1103/PhysRevLett.120.053602

Physics Subject Headings (PhySH)

Atomic, optical & lattice clocks

Precision measurements Spectroscopy

Atomic, Molecular & Optical

Authors & Affiliations

Christian Sanner, Nils Huntemann, Richard Lange, Christian Tamm, and Ekkehard Peik

Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany

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Issue

Vol. 120, Iss. 5 — 2 February 2018

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Images

Figure 1
Ramsey interrogation with shift-inducing drive pulses. The drive pulse frequency $ω_{LO drive}$ in (a) is assumed to be slightly higher than the light-shifted transition frequency $ω_{e g}^{'}$ . This corresponds to an increasing LO phase deviation during the drive period compared to an oscillator that evolves precisely with $ω_{e g}^{'}$ and $ω_{e g}$ . Over the following dark Ramsey time interval of variable duration $T$ , the acquired phase difference between the LO field and atomic oscillator will remain unchanged (aside from the $ϕ^{\pm}$ modulation) if the LO phase advances with the unperturbed transition frequency $ω_{LO} = ω_{e g}$ (solid curve). In this case, the phase-to-population conversion performed by the second drive pulse will produce identical outcomes after short and long Ramsey times. Otherwise, for nonzero Ramsey detuning (dashed curve), a $T$ -dependent relative phase is accumulated resulting in differing populations. (b) An auto-balancing control scheme comprises two servo loops acting in parallel on alternately operated short and long Ramsey sequences. Servo 1 equalizes the phase modulated excited state populations $p_{short}^{+}$ and $p_{short}^{-}$ ; i.e., it nulls ${\tilde{p}}_{short}$ by adjusting $ϕ^{c}$ in both the short and long sequences. Servo 2 nulls ${\tilde{p}}_{long}$ via $ω_{LO}$ , also addressing both sequences. The two example plots, displaying LO frequency versus time, represent distorted but isomorphic sequences that only differ in their dark times. (c) One complete probe cycle for a balanced acquisition consists of four Ramsey pulse pairs combining two dark times with two phase hopping directions.
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Figure 2
Simulated Ramsey lock fringes $\tilde{p} (δ)$ (top row) and rectified feedback responses $R (δ) = | \tilde{p} P_{0} |$ for a resonant Gaussian sampling frequency distribution $P_{0} (δ)$ (bottom row). $R (δ)$ is calculated for fringes obtained with nonzero detunings $δ^{'}$ between the drive frequency and the interaction-shifted atomic resonance (dotted red graphs in top row). In agreement with experimental conditions, no coupling is assumed between $δ^{'}$ and the dark time detuning $δ$ . All curves are calculated assuming $Ω_{0} τ = π / 2$ , $Ω_{0} T_{long} = 2 π$ , and $T_{short} / T_{long} = 0.02$ . (a) A fringe generated via the standard Ramsey protocol is horizontally shifted by approximately $δ = - 2 δ^{'} / (Ω_{0} T)$ for small drive detunings $δ^{'}$ . Accordingly, an engaged feedback loop will pull the frequency distribution toward lower frequencies. (b) Passive balancing, i.e., subtracting from ${\tilde{p}}_{long}$ the corresponding response ${\tilde{p}}_{short}$ of an isomorphic short Ramsey sequence, displaces the fringe laterally so that its zero crossing is kept at the origin. However, for $δ^{'} \neq 0$ any finite-width sampling distribution will experience a skewed response that pushes the center frequency away from the $δ = 0$ lock point. (c) Autobalanced generation of the frequency discriminant relies on a servo-controlled common-mode correction at the phase level instead of applying direct population corrections. This ensures antisymmetric frequency feedback for any drive detuning. At large detunings $δ^{'} > Ω_{0}$ , the fringe loses contrast but maintains all symmetry properties.
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Figure 3
Clock shifts on the ${}^{171}{Yb}^{+}$ $E 3$ transition frequency as obtained through autobalanced Ramsey spectroscopy when operated with intentionally detuned drive pulses. (a) For isomorphic short and long interrogation sequences, the autobalanced clock is fully immune against drive frequency deviations and the measured data points ( $1 σ$ error bars shown) line up on the zero clock shift axis. The magenta curve illustrates the $δ^{'}$ -to- $δ$ error propagation expected with the original hyper-Ramsey protocol. (b) Even without heating compensation, the coupling between the clock shift and drive detuning is strongly suppressed. Within statistical uncertainty, the measured clock deviations reproduce the numerically simulated dependance (blue curve).
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Figure 4
Defective drive sequences and resulting clock shifts for the case of standard Ramsey spectroscopy (light blue data points with vertical arrows indicating the theoretically expected shift values) and for autobalanced Ramsey spectroscopy (dark blue data points). The applied intensity defect (a), phase excursion (b), and phase lag (c) lead to large clock offsets that are eliminated in the autobalanced Ramsey mode. Both phase deviation plots display $ϕ^{-}$ (red) and $ϕ^{+}$ (green) traces simultaneously.
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