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

Prospects for an active optical clock using forbidden transition in trapped ions

Georgy A. Kazakov, Thorsten Schumm

Published Jul 1, 2017• 1 citation
Publisher

Abstract

The concept of an active optical frequency standard was proposed about 10 years ago. The idea was to use optically trapped alkaline-earth atoms as a gain medium to built an extremely narrow-line laser, whose frequency would be robust against fluctuations of the cavity length. The main challenge in the realization of this concept is the short trap lifetime of the atoms. Recently we showed, that in such a laser, neutral atoms may be replaced by charged ions in a radio-frequency (RF) Paul trap with much longer lifetime. This idea rests on two pillars: the effect of synchronization of radiating dipoles with moderate inhomogeneous broadening, and the possibility to compensate (in leading orders) micromotion-induced shifts for some ion species in specially designed traps.

DOI
10.1109/fcs.2017.8088914

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The concept of an active optical frequency standard was proposed about 10 years ago. The idea was to use optically trapped alkaline-earth atoms as a gain medium to built an extremely narrow-line laser, whose frequency would be robust against fluctuations of the cavity length. The main challenge in the realization of this concept is the short trap lifetime of the atoms. Recently we showed, that in such a laser, neutral atoms may be replaced by charged ions in a radio-frequency (RF) Paul trap with much longer lifetime. This idea rests on two pillars: the effect of synchronization of radiating dipoles with moderate inhomogeneous broadening, and the possibility to compensate (in leading orders) micromotion-induced shifts for some ion species in specially designed traps.
We propose to build a bad-cavity laser using forbidden transitions in large ensembles of cold ions that form a Coulomb crystal in a linear Paul trap. This laser might realize an active optical frequency standard able to serve as a local oscillator in next-generation optical clock schemes. In passive optical clocks, large ensembles of ions appear less promising, as they suffer from inhomogeneous broadening due to quadrupole interactions and micromotion-related shifts. In bad-cavity lasers, however, the radiating dipoles can synchronize and generate stable and narrow-linewidth radiation. Furthermore, for specific ions, micromotion-induced shifts can be largely suppressed by operating the ion trap at a magic frequency. We discuss the output radiation properties and perform quantitative estimations for lasing on the ${}^{3}{D}_{2}\ensuremath{\rightarrow}{}^{1}{S}_{0}$ transition in 176Lu+^{176}\mathrm{Lu}{}^{+}176Lu+ ions in a spherically symmetric trap.
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 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.
Abstract The atomic clocks, whether operating at optical or microwave region, can be divided into two categories according to their working mode, namely the passive clocks and active clocks. The passive clocks, whose standard frequency is locked to an ultra-narrow atomic spectral line, such as laser cooled Cs beam or lattice trapped Sr atoms, depend on the spontaneous emission line. On the contrary, the active clocks, in which the atoms are used as the gain medium, are based on the stimulated emission radiation, their spectrum can be directly used as the frequency standard. Up to now, the active hydrogen maser has been the most stable microwave atomic clocks. Also, the Sr superradiant active atomic clock is prospects for a millihertz-linewidth laser. Moreover, the optical clocks are expected to surpass the performance of microwave clocks both in stability and uncertainty, since their higher working frequency. The active optical clock has the potential to improve the stability of the best clocks by 2 orders of magnitude. In this work, we introduce the development of active optical clocks, and their types is classified according to the energy-level structure of atoms for stimulated radiation.
We propose a scheme for an active ion optical clock with a detailed description of the pumping method, lasing states, output power, linewidth and light shift. Considering 171 Yb + ions in a Paul trap, we propose utilizing a Fabry—Perot resonator to realize the lasing of active optical frequency standards. The quantum-limited linewidth of an active 171 Yb + ion optical clock is narrower than 1 mHz. Based on the mechanism and the advantages of an active optical clock at the ion optical clock transition frequency, this new laser light source as a stable local oscillator will be beneficial to the single-ion optical clock, which currently is one of the most accurate clocks.
An optical clock or frequency standard based on the interrogation of an atomic transition in the optical domain, operates at ~1014Hz is capable of providing orders of magnitude better accuracy than the present primary standard of frequency or time operating in the microwave range. Optical transitions of an ions, confined within a radio frequency ion trap and laser cooled to ~mK temperature, provides better long term stability since they are free from Coulomb and intra-atomic interactions. Optical frequency standards have been realized with several ions, e.g.,199Hg+,171Yb+,115In+,88Sr+,40Ca+,27Al+and among those171Y+has multiple ultra-narrow optical transitions suitable for serving as frequency standards [1-2].