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arXiv:0904.0285

An Optical Clock Based on Coherent Population Trapping of Alkaline-earth Ions

Z. H. Lu, L. J. Wang

Published Apr 2, 2009• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.0904.0285

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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.
A sharp resonance line that appears in three-photon transitions between the 1S0 and 3P0 states of alkaline earth and Yb atoms is proposed as an optical frequency standard. This proposal permits the use of the even isotopes, in which the clock transition is narrower than in proposed clocks using the odd isotopes and the energy interval is not affected by external magnetic fields or the polarization of trapping light. With this method, the width and the rate of the clock transition can, in principle, be continuously adjusted from the MHz level to sub-mHz without loss of signal amplitude by varying the intensities of the three optical beams. Doppler and recoil effects can be eliminated by proper alignment of the three optical beams or by point confinement in a lattice trap. Light-shift effects on the clock accuracy can be limited to below a part in 10(18).
Direct Laser Cooling Al+{}^{+}+ Ion Optical Clocks
The Al ion optical clock is a very promising optical frequency standard candidate due to its extremely small black-body radiation shift. It has been successfully demonstrated with the indirect cooled, quantum-logic-based spectroscopy technique. Its accuracy is limited by second-order Doppler shift, and its stability is limited by the number of ions that can be probed in quantum logic processing. We propose a direct laser cooling scheme of Al ion optical clocks where both the stability and accuracy of the clocks are greatly improved. In the proposed scheme, two Al traps are utilized. The first trap is used to trap a large number of Al ions to improve the stability of the clock laser, while the second trap is used to trap a single Al ion to provide the ultimate accuracy. Both traps are cooled with a continuous wave 167 nm laser. The expected clock laser stability can reach . For the second trap, in addition to 167 nm laser Doppler cooling, a second stage pulsed 234 nm two-photon cooling laser is utilized to further improve the accuracy of the clock laser. The total systematic uncertainty can be reduced to about . The proposed Al ion optical clock has the potential to become the most accurate and stable optical clock .
We report an experimental observation of the weak 'SO-~PO transition in 171,173Ybl and new approaches for qubits and optical clocks with this single-photon resonance and a three-photon resonance in an even isotope, respectively. Introduction - Optical clocks show great promise as the next generation of precision frequency standards due to the high frequency and correspondingly high line-Q of weakly allowed atomic transitions. Thanks to femtosecond comb technology (l), clocks based on optical transitions in both single trapped ions and neutral atom clouds are poised to exceed the already stringent bounds on precision set by microwave frequency standards. A recent proposal combining the Lamb-Dicke confinement of single ion frequency standards with the high signal-tenoise of neutral atom cLouds, and exploiting a highly forbidden transition insensitive to external magnetic fields and trap light polarization has the potential to do even better (2). The scheme makes use of the 'SO-~P~ electric dipole transition in alkaline-earth atoms, weakly allowed in odd isotopes by the hyperfine interaction of the nuclear spin and completely forbidden by a single-photon process in even isotopes. Trapping the atoms in a Stark-free optical httice will allow a large ensemble of atoms to exhibit a spectrum free of Doppler and recoil shifts, leading to an estimated accuracy of a few parts in lo1* (3, 41. As an additional application, the long atomic coherence times in optical lattices also suggest using the 'SO-~PO pairs of states as an array of qubits for quantum information (5, 61. Yb and Sr are both strong candidates for an optical lattice clock as well as for creating useful qubits. Both atoms have experimentally accessible energy level transitions, allowing the atoms to be readily laser-cooled and trapped, and in the case of Yb, Eose-Einstein condensed. While the Sr clock transition has been studied extensively, both in and out of an optical lattice, the same transition in Yb has thus far remained unexplored experimentally. Here we report the direct excitation of the 578 nm 'SO-~P~ transition in odd isotope 171,173Yb. (We understand that a group at NIST has also observed this transition (7)). We also discuss the possible application of this type of transitions in making qubits for quantum computation and a clock scheme based on three-photon transition in an even isotope (8, 91. - The level structure of Yb and the experimental apparatus are diagrammed in Fig. 1. The experiment is performed on a sample of cold atoms collected in a magneto- optical trap (MOT). To excite the clock transition, we shut off the MOT beams and irradiate the cloud of atoms with a 578 nm probe. JVe t,hen turn the MOT beams back on, continuously monitoring 399 nm fluorescence from the atom cloud. As the probe laser frequency is scanned over the dock transition, there is an observable decrease in MOT fluorescence as atoms are excited into the metastable 3Po state and escape the trap. By chopping trap and probe beams out of phase, we avoid light shifts of the clock transition due to near-resonant 399 nm light while maintaining a steady-state MOT population. The MOT fluorescence reduction of 171Yb is shown in Fig. 2 (a). Since iodine lines have been well measured in Observation of the 1So-3P, Transition in 1713173Yb
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 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 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.