Compact Optical Atomic Clock Based on a Two-Photon Transition in Rubidium

Kyle W. Martin, Gretchen Phelps, Nathan D. Lemke, Matthew S. Bigelow, Benjamin Stuhl, Michael Wojcik, Michael Holt, Ian Coddington, Michael W. Bishop, and John H. Burke

Phys. Rev. Applied 9, 014019 – Published 18 January 2018

Abstract

Extralaboratory atomic clocks are necessary for a wide array of applications (e.g., satellite-based navigation and communication). Building upon existing vapor-cell and laser technologies, we describe an optical atomic clock, designed around a simple and manufacturable architecture, that utilizes the 778-nm two-photon transition in rubidium and yields fractional-frequency instabilities of $4 \times 10^{- 13} / \sqrt{τ (s)}$ for $τ$ from 1 to 10 000 s. We present a complete stability budget for this system and explore the required conditions under which a fractional-frequency instability of $1 \times 10^{- 15}$ can be maintained on long time scales. We provide a precise characterization of the leading sensitivities to external processes, including magnetic fields and fluctuations of the vapor-cell temperature and 778-nm laser power. The system is constructed primarily from commercially available components, an attractive feature from the standpoint of the commercialization and deployment of optical frequency standards.

Received 20 September 2017
Revised 28 November 2017

DOI:https://doi.org/10.1103/PhysRevApplied.9.014019

Physics Subject Headings (PhySH)

Atomic, optical & lattice clocks Metrology Optoelectronics Photonics Time & frequency standards

Fabry-Pérot interferometry

Atomic, Molecular & Optical

Authors & Affiliations

Kyle W. Martin¹, Gretchen Phelps², Nathan D. Lemke², Matthew S. Bigelow¹, Benjamin Stuhl³, Michael Wojcik³, Michael Holt³, Ian Coddington⁴, Michael W. Bishop², and John H. Burke²

¹Applied Technology Associates d/b/a ATA, 1300 Britt Street, Southeast Albuquerque, New Mexico 87123, USA
²Air Force Research Laboratory, Space Vehicles Directorate, Kirtland Air Force Base, New Mexico 87117, USA
³Space Dynamics Laboratory, 1695 North Research Park Way, North Logan, Utah 84341, USA
⁴National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA

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Vol. 9, Iss. 1 — January 2018

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Images

Figure 1
(a) Partial energy-level diagram of Rb. The virtual state associated with two-photon excitation at 778 nm is shown by the dashed line. The cascade decay path $5 D_{5 / 2} \to 6 P_{3 / 2} \to 5 S_{1 / 2}$ results in the emission of a 420-nm photon, which we use to observe the two-photon resonance. (b) Two-photon excitation spectrum of ${}^{87}{Rb}$ ( $F = 2$ ). The frequency axis is presented as the 778-nm laser detuning from the $F = 2 \to F^{'} = 4$ transition, which has the largest Clebsch-Gordan coefficient. Included is a fit using a sum of four Lorentzian peaks of equal width and with relative peak heights and detunings constrained by the values presented in Ref. [26]. The fitting procedure results in a full-width-at-half-maximum linewidth of 609 kHz, which exceeds the natural linewidth by a factor of 1.8, which, we expect, is due to line broadening from helium collisions [33].
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Figure 2
An optical and simplified electrical schematic of the Rb two-photon frequency standard described in the text. EOM, electro-optic modulator; PMT, photomultiplier tube; VOA, variable optical attenuator; ISO, optical isolator; EDFA, erbium-doped fiber amplifier; SHG, second-harmonic generator; RAM, residual amplitude modulation; PID, proportional-integral-differential lock mechanism.
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Figure 3
(a) Experimentally measured 778-nm ac Stark shift for a ( $0.66 \pm 0.05$ )-mm beam. The fitting routine employs orthogonal distance regression (ODR) to account for error bars in both coordinates, yielding a reduced $χ^{2}$ of 1.57. (b) Experimentally measured dependence of the clock frequency on vapor-cell temperature, again fit with ODR to yield a reduced $χ^{2}$ value of 0.908.
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Figure 4
Magnetic-field splitting for the $5 D_{5 / 2}$ states of ${}^{87}{Rb}$ , which is determined by numerical diagonalization of the total Hamiltonian, as described in the text.
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Figure 5
The measured fractional-frequency instability for typical operating conditions (the black circles) plotted as a total Allan deviation along with a $1 / \sqrt{τ}$ white-noise line (the black solid line). Also shown are the measured instability when the frequency standard is operated with a larger signal-to-noise ratio (the gray circles) and the expected intermodulation limit (the red line), as described in Sec. 3a.
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Figure 6
The fractional-frequency instability plotted as a total Allan deviation for ${}^{87}{Rb}$ with $1 / \sqrt{τ}$ white noise (black), as well as anticipated limits on the clock stability arising from cell temperature fluctuations (blue) and laser power fluctuations (red). We believe the instability limit arising from laser power fluctuations is an overestimate due to temperature-dependent effects in the witness photodiode, as described in the text.
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Physical Review Applied