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arXiv:1704.08318 · Physical Review A

Prospects for a bad-cavity laser using a large ion crystal

Georgy A. Kazakov, Justin Bohnet, Thorsten Schumm

Published Aug 14, 2017• 15 citations
arXivHTMLPDF

Abstract

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 $^{176}\mathrm{Lu}{}^{+}$ ions in a spherically symmetric trap.

DOI
10.1103/physreva.96.023412

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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 3D2\ensuremath→1S0{}^{3}{D}_{2}\ensuremath{\rightarrow}{}^{1}{S}_{0}3D2​\ensuremath→1S0​ transition in 176Lu+^{176}\mathrm{Lu}{}^{+}176Lu+ ions in a spherically symmetric trap.
Here we study the possibilities of creating a bad cavity laser on forbidden transition in cold ions forming large Coulomb crystal in linear Paul trap. We consider micromotion-induced shifts and coupling strengths, and perform quantitative estimations of the attainable laser power for lasing on the 3D2→1S0{^3D_2} \rightarrow {^1S_0}3D2​→1S0​ transition in 176Lu+{\rm ^{176}Lu^+}176Lu+ ions in a spherical-symmetric trap.
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.
Superradiant lasers have emerged as a promising platform for optical frequency references due to their potential to achieve exceptionally narrow linewidths with reduced sensitivity to cavity noise. Trapped ion Coulomb crystals provide an attractive emitting medium due to their long coherence times, great environmental isolation and precise control over their motional dynamics. However, scaling trapped ion systems to the large ion numbers required for strong collective emission introduces new challenges, including crystal stability and position-dependent decoherence mechanisms. This work presents a numerical framework for modelling large Coulomb crystals confined within a linear Paul trap and assessing their suitability for superradiant lasing. A numerical simulation was developed to generate equilibrium crystal configurations, followed by a normal mode analysis to verify crystal’s dynamical stability and characterise the collective motional spectrum. The dependence of the crystal properties on the trapping parameters was examined, while the damping coefficient and integration timestep used in the numerical relaxation procedure were systematically optimised to obtain equilibrium configurations. The decoherence mechanisms expected to influence superradiant operation, including RF micromotion and electric quadrupole shifts, were also investigated as functions of ion number and trapping conditions. The simulations can produce accurate models of mechanically stable Coulomb crystals with up to 10,000 ions under appropriate relaxation conditions. They also show how the collective motional spectrum evolves across the trapping parameter space where they were also compared with the theoretical lasing threshold to assess the suitability of the trapping conditions for superradiant operation. Although the largest micromotion amplitudes increase with crystal size, a significant fraction of the ions remain confined close to the RF null, suggesting that large ion numbers may still be compatible with superradiant operation. The developed framework also provides a means of quantifying the quadrupole shift, indicating that the resulting frequency shifts are relatively small for the trapping parameters considered here, although further optimisation of the operating conditions is required to fully assess their influence on superradiant perfomance. Overall, the computational suite developed here establishes a versatile platform for studies of large Coulomb ion crystals and provides the tools to determine whether superradiant lasing thresholds can be reached with trapped ion crystals.
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.
We report on the design of a segmented linear Paul trap for optical clock applications using trapped ion Coulomb crystals. For an optical clock with an improved short-term stability and a fractional frequency uncertainty of 10−18, we propose 115In+ ions sympathetically cooled by 172Yb+. We discuss the systematic frequency shifts of such a frequency standard. In particular, we elaborate on high-precision calculations of the electric radiofrequency field of the ion trap using the finite element method. These calculations are used to find a scalable design with minimized excess micromotion of the ions at a level at which the corresponding second-order Doppler shift contributes less than 10−18 to the relative uncertainty of the frequency standard.
In this paper, we propose a scheme of active ion optical clock with detailed pumping method, lasing states, output power, linewidth and light shift. Using 171Yb+ ions in a Paul Trap we propose to utilize a Fabry-Perot resonator to realize lasing of active optical frequency standards. The quantum-limited linewidth of active 171Yb+ ion optical clock is narrower than 1 mHz. Based on the mechanism and advantages of active optical clock at 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 the most accurate clock.