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

Progress towards a dual-isotope trapped mercury ion atomic clock: Further studies of background gas collision shifts

L. Yi, S. Taghavi-Larigani, Eric A. Burt, Robert L. Tjoelker

Published May 1, 2012• 7 citations
Publisher

Abstract

As part of an on-going effort to build a dual-isotope ion trap clock based on the199Hg+and201Hg+ground state hyperfine transitions, we continue to characterize the systematic sensitivities of the201Hg+29.9GHz clock transition. Here we present an extension to the previous201Hg+collision shift measurement for helium[1] to other background gases. We also measured the collision shifts in the199Hg+40.5GHz clock transition in the same physical system. We find that frequency sensitivities to collisions with background gas for the two isotopes agree within a factor of two. We will also discuss planned collision shift measurements with co-trapped199Hg+and201Hg+, as an important step towards a dual-isotope atomic clock.

DOI
10.1109/fcs.2012.6243693

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Summary form only given. As the performance of optical atomic clocks improves steadily, new sources of systematic errors need to be evaluated with increasingly higher accuracy. At present, the collisional frequency shift (CFS), due to interactions with background gas atoms in the environment of the clock ions, is in some cases the next-to-leading source of systematic uncertainty for trapped-ion optical clocks. Existing approaches towards evaluating the CFS have either assumed that only glancing-angle collisions are relevant, or assumed a worst-case scenario for the phase shift imparted to clock state superposition by a collision. The former approach, which was developed for laser-cooled cesium clocks, is not applicable to the deeply trapped atomic ions used in optical clocks, while the latter approach is likely to significantly overestimate the CFS. To address this problem we have developed a framework, based on a non-perturbative quantum channel description of the collision process. Our method leads to a convenient master equation and a compact expression for the CFS. In particular, this framework can be used to estimate the CFS in situations involving many partial waves and large collisional phase shifts, which is the case with thermal background gas atoms scattering off a clock ion. Our method lends itself to practical evaluations of the CFS, by using readily calculated molecular potential curves for the ion-background gas system to extract the collisional phase shifts which lead to the CFS. As an application of this method to a realistic and relevant situation, we have numerically estimated the frequency shift of the 674 nm clock transition in Sr+due to collisions with background helium gas. We find that the CFS is much smaller than the worst-case estimate. In this talk, we describe the theoretical background and motivate the steps that lead to our framework for calculating the CFS. Following this, we present our calculations for the Sr+-He system as an example of the general method, and discuss possible extensions and improvements that will allow us to evaluate the CFS for the Sr+clock at the National Research Council Canada.

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Amar C. Vutha, Tom Kirchner, P. Dubé

Collisions with background gas can perturb the transition frequency of trapped ions in an optical atomic clock. We develop a nonperturbative framework based on a quantum channel description of the scattering process and use it to derive a master equation which leads to a simple analytic expression for the collisional frequency shift. As a demonstration of our method, we calculate the frequency shift of the ${\mathrm{Sr}}^{+}$ optical atomic clock transition due to elastic collisions with helium.

arXiv:1705.10019•Physical Review A•Aug 11, 2017•25 citations
As part of an on-going effort to build a dual-isotope ion trap clock based on the199Hg+and201Hg+ground state hyperfine transitions, we continue to characterize the systematic sensitivities of the201Hg+29.9GHz clock transition. Here we present an extension to the previous201Hg+collision shift measurement for helium[1] to other background gases. We also measured the collision shifts in the199Hg+40.5GHz clock transition in the same physical system. We find that frequency sensitivities to collisions with background gas for the two isotopes agree within a factor of two. We will also discuss planned collision shift measurements with co-trapped199Hg+and201Hg+, as an important step towards a dual-isotope atomic clock.
There are two stable odd isotopes of mercury with singly ionized hyperfine structure suitable for a microwave clock:199Hg+and201Hg+. Virtually all trapped mercury ion clocks to date have used the 199 isotope. We have begun to investigate the viability of a trapped ion clock based on201Hg+. We have measured the unperturbed frequency of the2S1/2F = 1, mF= 0 to2S1/2F = 2, mF=0 clock transition to be 29.9543658211(2) GHz. In this paper we describe initial measurements with201Hg+and new applications to clocks and fundamental physics.
We report measured buffer gas collision shifts of the 40.507347996xx GHz mercury ion clock transition using inert helium, neon, and argon gases and getterable molecular hydrogen and nitrogen gases. The frequency shift due to methane was also examined. At low partial pressures methane gas did not impact the trapped ion number but was observed to strongly relax the population difference in the two hyperfine clock states thereby reducing the clock resonance signal. A similar population relaxation was also observed for other molecular buffer gases (N/sub 2/, H/sub 2/) but at much reduced rate.
The influences of different buffer gas, neon and helium, on199Hg+clock transition are compared in trapped199Hg+linear trap. By the technique of time domain’s Ramsey separated oscillatory fields, the buffer gas pressure frequency shifts of199Hg+clock transition are measured to be(d f /dPNe)(1/ f) = 1.8 × 10-8Torr-1for neon and(d f /dPHe)(1/ f) = 9.1 × 10-8Torr-1for helium. Meanwhile, the line-width of199Hg+clock transition spectrum with the buffer gas neon is narrower than that with helium at the same pressure. These experimental results show that neon is a more suitable buffer gas than helium in199Hg+ions microwave frequency standards because of the199Hg+clock transition is less sensitive to neon variations and the better cooling effect of neon. The optimum operating pressure for neon is found to be about 1.0 × 10-5Torr in our linear ion trap system.
Trapped mercury ion is a promising candidate for portable and operational atomic clocks. It operates at the 40.5GHz ground state hyperfine transition of 199Hg ions. Mercury ions are confined in a linear RF trap, buffer-gas cooled, with a long ion storage lifetime in an ultra-high vacuum enclosure without an active pump. The clock transition is optically-pumped and detected with a Hg discharge lamp without need of a laser light source. This approach has proven to provide simplicity in design and implementation and robustness in operation. In this paper, we report our recently effort on developing a micro and low-power mercury trapped ion clock in the DARPA ACES program. In a 5 mm x 10 mm linear trap (0.25 cc), we have achieved the clock fractional frequency stability of .7 × 10-12τ-1/2and reached down to 7 × 10-14after 1000 seconds of averaging. We will discuss the clock performance under different conditions and implications toward a micro mercury trapped ion clock with low power and high stability.
Summary form only given. As the performance of optical atomic clocks improves steadily, new sources of systematic errors need to be evaluated with increasingly higher accuracy. At present, the collisional frequency shift (CFS), due to interactions with background gas atoms in the environment of the clock ions, is in some cases the next-to-leading source of systematic uncertainty for trapped-ion optical clocks. Existing approaches towards evaluating the CFS have either assumed that only glancing-angle collisions are relevant, or assumed a worst-case scenario for the phase shift imparted to clock state superposition by a collision. The former approach, which was developed for laser-cooled cesium clocks, is not applicable to the deeply trapped atomic ions used in optical clocks, while the latter approach is likely to significantly overestimate the CFS. To address this problem we have developed a framework, based on a non-perturbative quantum channel description of the collision process. Our method leads to a convenient master equation and a compact expression for the CFS. In particular, this framework can be used to estimate the CFS in situations involving many partial waves and large collisional phase shifts, which is the case with thermal background gas atoms scattering off a clock ion. Our method lends itself to practical evaluations of the CFS, by using readily calculated molecular potential curves for the ion-background gas system to extract the collisional phase shifts which lead to the CFS. As an application of this method to a realistic and relevant situation, we have numerically estimated the frequency shift of the 674 nm clock transition in Sr+due to collisions with background helium gas. We find that the CFS is much smaller than the worst-case estimate. In this talk, we describe the theoretical background and motivate the steps that lead to our framework for calculating the CFS. Following this, we present our calculations for the Sr+-He system as an example of the general method, and discuss possible extensions and improvements that will allow us to evaluate the CFS for the Sr+clock at the National Research Council Canada.
Collisions with background gas can perturb the transition frequency of trapped ions in an optical atomic clock. We develop a nonperturbative framework based on a quantum channel description of the scattering process and use it to derive a master equation which leads to a simple analytic expression for the collisional frequency shift. As a demonstration of our method, we calculate the frequency shift of the Sr+{\mathrm{Sr}}^{+}Sr+ optical atomic clock transition due to elastic collisions with helium.