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arXiv:1709.01247 · New Journal of Physics

Atomic combination clocks

Nitzan Akerman, Roee Ozeri

Published Nov 29, 2018• 7 citations
arXivHTMLPDF

Abstract

Atomic clocks use atomic transitions as frequency references. The susceptibility of the atomic transition to external fields limits clock stability and introduces systematic frequency shifts. Here, we propose to realize an atomic clock that utilizes an entangled superposition of states of multiple atomic species, where the reference frequency is a sum of the individual transition frequencies. The superposition is selected such that the susceptibilities of the respective transitions, in individual species, partially cancel leading to improved stability and a reduction in the corresponding systematic shifts. We present and analyze two examples of such combinations. The first uses the optical quadrupole transitions in a Ca + – Yb + two-ion system. The second is a superposition of optical quadrupole transitions in one Sr + ion and three Hg + ions. These combinations have reduced susceptibility to external magnetic fields and blackbody radiation.

DOI
10.1088/1367-2630/aaf4cb

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Atomic clocks use atomic transitions as frequency references. The susceptibility of the atomic transition to external fields limits clock stability and introduces systematic frequency shifts. Here, we propose to realize an atomic clock that utilizes an entangled superposition of states of multiple atomic species, where the reference frequency is a sum of the individual transition frequencies. The superposition is selected such that the susceptibilities of the respective transitions, in individual species, partially cancel leading to improved stability and a reduction in the corresponding systematic shifts. We present and analyze two examples of such combinations. The first uses the optical quadrupole transitions in a Ca + – Yb + two-ion system. The second is a superposition of optical quadrupole transitions in one Sr + ion and three Hg + ions. These combinations have reduced susceptibility to external magnetic fields and blackbody radiation.
Abstract We develop a method of synthetic frequency generation to construct an atomic clock with blackbody radiation (BBR) shift uncertainties below 10−19 at environmental conditions with a very low level of temperature control. The proposed method can be implemented for atoms and ions, which have two different clock transitions with frequencies ν 1 and ν 2 allowing to form a synthetic reference frequency ν syn = (ν 1 − ɛν 2)/(1 − ɛ), which is absent in the spectrum of the involved atoms or ions. Calibration coefficient ɛ can be chosen such that the temperature dependence of the BBR shift for the synthetic frequency ν syn has a local extremum at an arbitrary operating temperature T 0. This leads to a weak sensitivity of BBR shift with respect to the temperature variations near operating temperature T 0. As a specific example, the Yb+ ion is studied in detail, where the utilized optical clock transitions are of electric quadrupole (S → D) and octupole (S → F) type. In this case, temperature variations of ±7 K lead to BBR shift uncertainties of less than 10−19, showing the possibility to construct ultra-precise combined atomic clocks (including portable ones) without the use of cryogenic techniques.
The optical clock is a fundamental applications of the coherence of ultracold atoms. Most of the implementations with trapped ions are based on the single-ion optical clock by Dehmelt [1], and some of them have successfully achieved inaccuracies in the 10-18level [2]. The idea has been extended to systems consisting of many neutral atoms by Katori with proper engineering on light shift associated with the optical lattice [3]. The enhanced stability is the great advantage obtained by multiple atoms. Extension of the single-ion system to multi-ion systems requires considerations on the inhomogeneous electric quadrupole shift originating from non-uniform electric field gradient at the location of each ion. A straightforward approach is to use ion species with null quadrupole moment such as In+, Al+[4]. We present another approach using ions with non-zero quadrupole moment. In the approach we use a planar surface trap to arrange the ions in an equally-spaced manner to vanish the inhomogeneous shift. We show that a clock with multiple Ca+ions can be operated even without a reference cavity for the clock laser, and that superradiant clock is expected when the ions are coupled to a cavity.
We develop a concept of atomic clocks where the blackbody radiation shift and its fluctuations can be suppressed by 1--3 orders of magnitude independent of the environmental temperature. The suppression is based on the fact that in a system with two accessible clock transitions (with frequencies ${\ensuremath{\nu}}_{1}$ and ${\ensuremath{\nu}}_{2}$) which are exposed to the same thermal environment, there exists a ``synthetic'' frequency ${\ensuremath{\nu}}_{\mathrm{syn}}$ $\ensuremath{\propto}$ (${\ensuremath{\nu}}_{1}\ensuremath{-}{\ensuremath{\epsilon}}_{12}{\ensuremath{\nu}}_{2}$) largely immune to the blackbody radiation shift. For example, in the case of 171Yb+^{171}\mathrm{Yb}^{+}171Yb+ it is possible to create a synthetic-frequency-based clock in which the fractional blackbody radiation shift can be suppressed to the level of ${10}^{\ensuremath{-}18}$ in a broad interval near room temperature ($300\ifmmode\pm\else\textpm\fi{}15\text{ }\text{ }\mathrm{K}$). We also propose a realization of our method with the use of an optical frequency comb generator stabilized to both frequencies ${\ensuremath{\nu}}_{1}$ and ${\ensuremath{\nu}}_{2}$, where the frequency ${\ensuremath{\nu}}_{\mathrm{syn}}$ is generated as one of the components of the comb spectrum.
In the mid-20th century, atoms were realized to be good candidates for time or frequency standards since transition energies or frequencies between two energy levels of some unperturbed atoms are more stable than those defined by the rotation of the earth or artefact-based clocks such as quartz crystal clocks. This motivated extensive research on realization and improvement of such kind of quantum-based time or frequency standards. The ultra-stable laser, referred to as a local oscillator in a clock, still drifts over time due to environmentally induced length fluctuations of the reference cavity. With the development of ion traps, ultra-narrow linewidth lasers and optical frequency combs, optical clocks based on single trapped ions as a new type of clocks have been realized in many laboratories. Ions can only stay in the trap within a certain region, which is called stability region. There is a variety of potential sources of systematic shifts associated with the clock transition in ion optical clocks.
An optical clock based upon a single mercury ion in a radio-frequency trap has the potential for both high stability and high accuracy. The systematic uncertainty of this frequency standard is limited by contributions due to two types of external fields. The clock has previously been operated with a magnetic bias field that destabilizes dark states that limit the rates of laser cooling and state detection. This bias field has previously resulted in a substantial second-order Zeeman shift. We now destabilize the dark states with a polarization-scrambling technique that allows us to operate with only a minimal magnetic field. The second uncertainty that we address here is the magnitude of the quadrupole shift due to the interaction of stray electric-field gradients with the quadrupole moment of the ion. We describe the steps that we are taking to evaluate this shift in the near future. 1
An ultra-stable optical clock based on coherent population trapping effect of alkaline-earth ions, such as Ca+^++, Sr+^++, Ba+^++, is analyzed here. The proposed transitions use the odd isotopes, so that the frequency shift is insensitive to the applied magnetic field. To enhance the signal, a large number of ions are trapped in a linear Paul trap, and laser cooled to crystallize such that the ions are in the Lamb-Dicke regime to avoid first order Doppler shift. Other relevant frequency shifts are also analyzed. Further techniques to improve the stability of the clock signal are discussed.