Lifetime-Limited Interrogation of Two Independent $^{27}{\mathrm{Al}}^{+}$ Clocks Using Correlation Spectroscopy

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Lifetime-Limited Interrogation of Two Independent ${}^{27}{Al}^{+}$ Clocks Using Correlation Spectroscopy

Ethan R. Clements, May E. Kim, Kaifeng Cui, Aaron M. Hankin, Samuel M. Brewer, Jose Valencia, Jwo-Sy Chen, Chin-Wen Chou, David R. Leibrandt, and David B. Hume

Phys. Rev. Lett. 125, 243602 – Published 9 December 2020

Abstract

Laser decoherence limits the stability of optical clocks by broadening the observable resonance linewidths and adding noise during the dead time between clock probes. Correlation spectroscopy avoids these limitations by measuring correlated atomic transitions between two ensembles, which provides a frequency difference measurement independent of laser noise. Here, we apply this technique to perform stability measurements between two independent clocks based on the ${{}^{1}S}_{0} \leftrightarrow {{}^{3}P}_{0}$ transition in ${}^{27}{Al}^{+}$ . By stabilizing the dominant sources of differential phase noise between the two clocks, we observe coherence between them during synchronous Ramsey interrogations as long as 8 s at a frequency of $1.12 \times 10^{15} Hz$ . The observed contrast in the correlation spectroscopy signal is consistent with the 20.6 s ${}^{3}{P_{0}}$ state lifetime and represents a measurement instability of $(1.8 \pm 0.5) \times 10^{- 16} / \sqrt{τ / s}$ for averaging periods longer than the probe duration when dead time is negligible.

Received 9 July 2020
Revised 13 October 2020
Accepted 30 October 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.243602

Physics Subject Headings (PhySH)

Atomic, optical & lattice clocks Laser spectroscopy Optical coherence Quantum correlations in quantum information Quantum measurements Quantum metrology

Atomic, Molecular & OpticalQuantum Information, Science & Technology

Authors & Affiliations

Ethan R. Clements ^1,2,*, May E. Kim¹, Kaifeng Cui ^1,3, Aaron M. Hankin^1,2,†, Samuel M. Brewer^1,‡, Jose Valencia^1,2, Jwo-Sy Chen^1,2,§, Chin-Wen Chou¹, David R. Leibrandt ^1,2, and David B. Hume^1,∥

¹National Institute of Standards and Technology, Boulder, Colorado 80305, USA
²Department of Physics, University of Colorado, Boulder, Colorado 80305, USA
³HEP Division, Argonne National Laboratory, Lemont, Illinois 60439, USA

^*ethan.clements@nist.gov
^†Present address: Honeywell Quantum Solutions, Broomfield, Colorado 80021, USA.
^‡Present address: Colorado State University, Fort Collins, Colorado 80523, USA.
^§Present address: IonQ Inc., College Park, Maryland 20740, USA.
^∥david.hume@nist.gov

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Vol. 125, Iss. 24 — 11 December 2020

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Figure 1
Schematic of the correlation spectroscopy experiment, including the laser path-length stabilization and active magnetic field stabilization setups. Here $f_{B eat} = 2 (f_{1} - f_{2})$ is phase locked to a maser-referenced 10 MHz signal, and the relative phase is corrected by modulating the path 2 AOM, denoted by $f_{2} + δ f$ . The magnetic field is stabilized using measurements from single-axis flux gate sensors (shown as yellow circles) oriented along the quantization axis $B_{q}$ . In the ${}^{25}{Mg}^{+} / {}^{27}{Al}^{+}$ clock, two pairs of coils are used, while in the ${}^{40}{Ca}^{+} / {}^{27}{Al}^{+}$ system there is only one. Boxes labeled $\times 2$ denote frequency doubling of the input light where the final light sent to the atomic clocks is at 267.4 nm.
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Figure 2
Parity fringes obtained for Ramsey probe durations between 0.5 and 8 s (upper right labels). Here, the transition used for correlation spectroscopy is the $| {{}^{1}S}_{0}, m_{F} = 3 / 2 ⟩ \leftrightarrow | {{}^{3}P}_{0}, m_{F} = 1 / 2 ⟩$ transition. Experimental data (dots) are shown with error bars dominated by quantum projection noise. Fits to these parity fringes (lines) and their $1 σ$ confidence intervals (shaded region) are determined by resampling the data using nonparametric bootstrapping methods. The maximum obtainable parity amplitude (gray dashed lines) due to the finite lifetime of the two ${}^{27}{Al}^{+}$ ions is calculated using Eq. (3).
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Figure 3
(a) Contrast as a function of the probe duration. The measured contrast (solid points) and associated uncertainty come from fits to the parity fringes. For comparison, a fit to the laser-coherence-limited Ramsey spectroscopy contrast [15] (red line) and the calculated upper bound on the correlation spectroscopy contrast set by the lifetime limit (black line) are plotted. A fit to the experimental points using the model function $A \exp^{- T_{R} / t_{d}}$ is determined, where $A$ is the contrast and $t_{d}$ is the decay time. Fitting with this function gives $A = 0.4 \pm 0.04$ and $t_{d} = 19 \pm 11 s$ for $| {{}^{1}S}_{0}, m_{F} = 3 / 2 ⟩ \leftrightarrow | {{}^{3}P}_{0}, m_{F} = 1 / 2 ⟩$ and $A = 0.4 \pm 0.06$ and $t_{d} = 4 \pm 2 s$ for $| {{}^{1}S}_{0}, m_{F} = 5 / 2 ⟩ \leftrightarrow | {{}^{3}P}_{0}, m_{F} = 5 / 2 ⟩$ . (b) Comparison of the instability calculations and measurements as a function of probe duration. The instability $σ_{upper}$ , calculated using Eq. (6), is shown with green dots. This can be compared with the instability $σ_{est}$ determined with Eq. (5) shown with blue dots. A lower bound on the instability is given by the lifetime limit [black line, Eq. (4)], which assumes a randomized laser phase at all probe durations. Also included is an estimate of the instability at the laser-noise limit both from the analytical estimate [red line, Eq. (1)] and a numerical simulation (red points) assuming a flicker-frequency noise floor at $4.4 \times 10^{- 16} \sqrt{τ / s}$ . Numerical simulations stop at a probe duration of $\approx 200 ms$ due to fringe hops occurring in our numerical simulation. For all theoretical estimates, we assume a dead time of only 0.1 s (the average single-cycle dead time of our clocks), which has negligible impact at longer probe durations. The inset displays the Allan deviation of the frequency ratio measurement at a Ramsey probe duration of 8 s (details and data for other probe durations are given in Supplemental Material [15]).
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Physical Review Letters

Lifetime-Limited Interrogation of Two Independent Al+27 Clocks Using Correlation Spectroscopy

Ethan R. Clements, May E. Kim, Kaifeng Cui, Aaron M. Hankin, Samuel M. Brewer, Jose Valencia, Jwo-Sy Chen, Chin-Wen Chou, David R. Leibrandt, and David B. Hume

Phys. Rev. Lett. 125, 243602 – Published 9 December 2020

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Lifetime-Limited Interrogation of Two Independent ${}^{27}{Al}^{+}$ Clocks Using Correlation Spectroscopy