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Development and characterization of a transportable aluminum ion quantum logic optical clock setup

Stephan Hannig

Published Jan 1, 2018• 0 citations
Publisher

Abstract

At the time of writing, state of the art stationary optical clocks reach 10 −18 sys- tematic fractional frequency uncertainty, which allows for the search of new physics beyond the standard model and lays the foundation for new applications such as chronometric leveling, where height differences relative to the geoid are derived from frequency comparisons among optical clocks. Transportable optical clocks allow for chronometric leveling between distant lo- cations which are not connected by a direct line of sight but via length stabilized optical fiber. Moreover, they facilitate frequency comparisons between distant sta- tionary clocks via subsequent side-by-side comparisons without the necessity of a long-range fiber connection. A transportable optical clock employing a single 40Ca+ ion has been reported and a neutral atom 87Sr lattice clock has been employed in a chronometric leveling campaign. However, these clocks report an estimated systematic fractional frequency uncertainty in the high 10^−17 range, which limits their height resolution to a level of approximately 1 m. 27Al+ has one of the smallest blackbody radiation shifts, small linear and quadratic Zeeman shifts and a negligible quadrupole shift, which makes it a candidate for a highly accurate optical clock. This thesis reports on the development, set-up, and characterization of a transportable 27Al+ clock setup with 40Ca+ as logic ion. The setup is simple, modular, compact, and mechanically stable. Ions of both species are generated via pulsed laser ablation and subsequent photoionization. They are confined in a multi-layer trap with segmented loading and experiment zones. Using a single 40Ca+ ion as probe, heating rates of below 10 quanta per second have been measured in all three directions for trap frequencies around 2π × 2 MHz, and pulsed sideband cooling to mean motional quantum numbers below 0.1 quanta was demonstrated. Imaging close to the diffraction limit with a signal to noise ratio of 800 for 300 ms exposure time on a sCMOS camera was achieved using a single NA = 0.51 biaspheric lens. Simultaneously, a state discrimination error below 10^−5 in 100 µs was obtained using a PMT. From the excess micromotion second order Doppler shift, secular motion second order Doppler shift, BBR shift, and background gas collision shift, a partial systematic fractional frequency uncertainty of 1.7 × 10^−18 was inferred, which is equivalent to a height resolution of ca. 2 cm. Moreover, a highly stable mechanical monolithic enhancement cavity for SHG has been developed and demonstrated to withstand accelerations of 3 g rms for 30 min. It has been operated for an uninterrupted period of 130 h without decay in output power in the mid-UV due to O2 -purging, its sealed design, and material selection, which solves the often observed crystal degradation in UV applications. The cavity has been employed in the 27Al+ logic laser system. In conclusion, it has been shown that an 27Al+ ion quantum logic optical clock operated in the present transportable setup could reach an estimated systematic fractional frequency uncertainty of 1.7 × 10^−18 , provided that all other shifts, such as the second order Zeeman shift, are negligible. This paves the way towards chronometric leveling with an unprecedented height resolution of about 2 cm.

DOI
10.15488/3705

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At the time of writing, state of the art stationary optical clocks reach 10 −18 sys- tematic fractional frequency uncertainty, which allows for the search of new physics beyond the standard model and lays the foundation for new applications such as chronometric leveling, where height differences relative to the geoid are derived from frequency comparisons among optical clocks. Transportable optical clocks allow for chronometric leveling between distant lo- cations which are not connected by a direct line of sight but via length stabilized optical fiber. Moreover, they facilitate frequency comparisons between distant sta- tionary clocks via subsequent side-by-side comparisons without the necessity of a long-range fiber connection. A transportable optical clock employing a single 40Ca+ ion has been reported and a neutral atom 87Sr lattice clock has been employed in a chronometric leveling campaign. However, these clocks report an estimated systematic fractional frequency uncertainty in the high 10^−17 range, which limits their height resolution to a level of approximately 1 m. 27Al+ has one of the smallest blackbody radiation shifts, small linear and quadratic Zeeman shifts and a negligible quadrupole shift, which makes it a candidate for a highly accurate optical clock. This thesis reports on the development, set-up, and characterization of a transportable 27Al+ clock setup with 40Ca+ as logic ion. The setup is simple, modular, compact, and mechanically stable. Ions of both species are generated via pulsed laser ablation and subsequent photoionization. They are confined in a multi-layer trap with segmented loading and experiment zones. Using a single 40Ca+ ion as probe, heating rates of below 10 quanta per second have been measured in all three directions for trap frequencies around 2π × 2 MHz, and pulsed sideband cooling to mean motional quantum numbers below 0.1 quanta was demonstrated. Imaging close to the diffraction limit with a signal to noise ratio of 800 for 300 ms exposure time on a sCMOS camera was achieved using a single NA = 0.51 biaspheric lens. Simultaneously, a state discrimination error below 10^−5 in 100 µs was obtained using a PMT. From the excess micromotion second order Doppler shift, secular motion second order Doppler shift, BBR shift, and background gas collision shift, a partial systematic fractional frequency uncertainty of 1.7 × 10^−18 was inferred, which is equivalent to a height resolution of ca. 2 cm. Moreover, a highly stable mechanical monolithic enhancement cavity for SHG has been developed and demonstrated to withstand accelerations of 3 g rms for 30 min. It has been operated for an uninterrupted period of 130 h without decay in output power in the mid-UV due to O2 -purging, its sealed design, and material selection, which solves the often observed crystal degradation in UV applications. The cavity has been employed in the 27Al+ logic laser system. In conclusion, it has been shown that an 27Al+ ion quantum logic optical clock operated in the present transportable setup could reach an estimated systematic fractional frequency uncertainty of 1.7 × 10^−18 , provided that all other shifts, such as the second order Zeeman shift, are negligible. This paves the way towards chronometric leveling with an unprecedented height resolution of about 2 cm.
With the advent of optical clocks featuring fractional frequency uncertainties on the order of 10-17 and below, new applications such as chronometric leveling with few-centimeter height resolution emerge. We are developing a transportable optical clock based on a single trapped aluminum ion, which is interrogated via quantum logic spectroscopy. We employ singly charged calcium as the logic ion for sympathetic cooling, state preparation, and readout. Here, we present a simple and compact physics and laser package for manipulation of 40Ca+. Important features are a segmented multilayer trap with separate loading and probing zones, a compact titanium vacuum chamber, a near-diffraction-limited imaging system with high numerical aperture based on a single biaspheric lens, and an all-in-fiber 40Ca+ repump laser system. We present preliminary estimates of the trap-induced frequency shifts on 27Al+, derived from measurements with a single calcium ion. The micromotion-induced second-order Doppler shift for 27Al+ has been determined to be δνEMMν=-0.4-0.3 +0.4×10-18 and the black-body radiation shift is δνBBR/ν = (-4.0 ± 0.4) × 10-18. Moreover, heating rates of 30 (7) quanta per second at trap frequencies of ωrad,Ca+ ≈ 2π × 2.5 MHz (ωax,Ca+ ≈ 2π × 1.5 MHz) in radial (axial) direction have been measured, enabling interrogation times of a few hundreds of milliseconds.
With the advent of optical clocks featuring fractional frequency uncertainties on the order of 10−17 and below, new applications such as chronometric leveling with few-centimeter height resolution emerge. We are developing a transportable optical clock based on a single trapped aluminum ion, which is interrogated via quantum logic spectroscopy. We employ singly charged calcium as the logic ion for sympathetic cooling, state preparation, and readout. Here, we present a simple and compact physics and laser package for manipulation of 40Ca+. Important features are a segmented multilayer trap with separate loading and probing zones, a compact titanium vacuum chamber, a near-diffraction-limited imaging system with high numerical aperture based on a single biaspheric lens, and an all-in-fiber 40Ca+ repump laser system. We present preliminary estimates of the trap-induced frequency shifts on 27Al+, derived from measurements with a single calcium ion. The micromotion-induced second-order Doppler shift for 27Al+ has been determined to be δνEMMν=−0.4−0.3+0.4×10−18 and the black-body radiation shift is δνBBR/ν = (−4.0 ± 0.4) × 10−18. Moreover, heating rates of 30 (7) quanta per second at trap frequencies of ωrad,Ca+ ≈ 2π × 2.5 MHz (ωax,Ca+ ≈ 2π × 1.5 MHz) in radial (axial) direction have been measured, enabling interrogation times of a few hundreds of milliseconds.
The advancement of optical atomic clocks in the past two decades has motivated many potential applications in navigation, communication, and science. Accurate optical clocks that outperform the current cesium time standard also trigger a discussion about a possible redefinition of the SI second. The 27Al+ quantum logic clocks developed at the National Institute of Standards and Technology (NIST) were the first to achieve the clock fractional frequency uncertainty below 10-17 in 2010. To date, a few research groups around the world have demonstrated optical clocks based on various atomic transitions with fractional frequency uncertainty in the 10-18 range. The accuracy of the previous 27Al+ clocks was limited by the second order Doppler (time dilation) shift and the blackbody shift. Since 2010, the third 27Al+ optical clock is being developed at NIST to achieve a higher accuracy. The frequency uncertainties dominant in the previous clocks are controlled and reduced in the current optical clock. The new design of the ion trap system has reduced significantly both the blackbody radiation shift uncertainty and the time dilation shift uncertainty due to micromotion, while the time dilation shift uncertainty due to the secular motion has been reduced by more than an order of magnitude by operating the optical clock near the three dimensional zero-point energy. Despite those previously dominant uncertainties, several other systematic effects are being evaluated and some other efforts are being made to achieve a total uncertainty towards 1.0 x 10-18. In this thesis, I will document the detail of the construction and evaluation of the current 27Al+ optical clock developed at NIST.
We describe an optical atomic clock based on quantum-logic spectroscopy of the ^{1}S_{0}↔^{3}P_{0} transition in ^{27}Al^{+} with a systematic uncertainty of 9.4×10^{-19} and a frequency stability of 1.2×10^{-15}/sqrt[τ]. A ^{25}Mg^{+} ion is simultaneously trapped with the ^{27}Al^{+} ion and used for sympathetic cooling and state readout. Improvements in a new trap have led to reduced secular motion heating, compared to previous ^{27}Al^{+} clocks, enabling clock operation with ion secular motion near the three-dimensional ground state. Operating the clock with a lower trap drive frequency has reduced excess micromotion compared to previous ^{27}Al^{+} clocks. Both of these improvements have led to a reduced time-dilation shift uncertainty. Other systematic uncertainties including those due to blackbody radiation and the second-order Zeeman effect have also been reduced.
The invention of the atomic clock has enabled applications like the global navigation satellite system, are important for telecommunication and are used for the definition of the SI second. Nowadays, optical clocks allow for measurement of height differences on the centimeter scale and can be employed for tests of the standard model of particle physics. Among the various implementations of optical clocks, this thesis focuses on an Al⁺ clock. For this work an optical resonator is examined, which enables the simultaneous frequency stabilization of two laser on the same mirror pair through the use of a dual-wavelength coating. Various contributions on the frequency stability are characterized and correlations are investigated. This cavity enables high fidelities in coherent manipulation of trapped ions, as required to operate the Al⁺ clock. This thesis partly builds upon the findings presented in Ref. Kramer, 2023. The setup and the systematic shifts are revisited and a detailed evaluation of the shifts is conducted, resulting in a total fractional frequency uncertainty of 1.6×10⁻¹⁸. The biggest contribution is from an ac-Stark shift induced by cooling during the clock interrogation, resulting in a shift of −9.3(1.1) × 10⁻¹⁸. The cooling reduces the second order Doppler shift to −1.6(0.2)×10⁻¹⁸. Additionally, a position dependent micromotion of the ion was investigated, which contributes an uncertainty of 0.38 × 10⁻¹⁸. Moreover, the first-order Doppler shift, servo error, ac-Stark shift of the clock laser and the phase chirp are determined for the first time, showing uncertainties below 10⁻¹⁸. The first frequency comparison between the Al⁺ clock and the ¹¹⁵In⁺, ¹⁷¹Yb⁺ and ⁸⁷Sr clocks at PTB are demonstrated. Measurements against Sr reveal a stability of the Al+ clock of 5.9 × 10⁻¹⁶ at 1s , which is one of the best single ion clock stabilities to date. All measured frequency ratios fall within the 10⁻¹⁸ uncertainty regime. The ratio between Sr/Al⁺ exhibits a significant deviation of more than 8.6𝜎 from published measurement data, underscoring the importance of inter-institutional frequency ratio measurements to verify the uncertainty budgets and reproducibility of optical clocks.
For the past 15 years, tremendous progress within the fields of laser stabilization, optical frequency combs and atom cooling and trapping have allowed the realization of optical atomic clocks with unrivaled performances. These instruments can perform frequency comparisons with fractional uncertainties well below 10-17, finding applications in fundamental physics tests, relativistic geodesy and time and frequency metrology. Even though most optical clocks are currently laboratory setups, several proposals for using these clocks for field measurements or within an optical clock network have been published, and most of time and frequency metrology institutes have started to develop transportable optical clocks. For the purpose of this special issue, we chose to focus on trapped-ion optical clocks. Even though their short-term fractional frequency stability is impaired by a lower signal-to-noise ratio, they offer a high potential for compactness: trapped ions demand low optical powers and simple loading schemes, and can be trapped in small vacuum chambers. We review recent advances on the clock key components, including ion trap and ultra-stable optical cavity, as well as existing projects and experiments which draw the picture of what future transportable, single-ion optical clocks may resemble.