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Journal of the Optical Society of America B

Optical-clock local-oscillator stabilization scheme

V. Letchumanan, Patrick Robert Gill, Alastair G. Sinclair, Erling Riis

Published Apr 1, 2006• 8 citations
Publisher

Abstract

Stabilization of a laser to an optical-clock transition has been demonstrated using Ramsey's phase-modulation technique. The technique was implemented using a 674 nm laser and a component of the 5 s 2S1/2 → 4d 2D5/2 optical clock transition in a single 88Sr+ ion. The lock performance observed was consistent with the short-term stability of the local oscillator. Compared with existing frequency-modulation stabilization schemes, this technique offers advantages for use in single-ion optical clocks through its possible increased resolution and the ability to conveniently compensate known systematic shifts.

DOI
10.1364/josab.23.000714

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Coherent optical spectroscopy has been performed on the narrow $5s\phantom{\rule{0.3em}{0ex}}^{2}S_{1∕2}--4d\phantom{\rule{0.3em}{0ex}}^{2}D_{5∕2}$ quadrupole transition in a single Doppler-cooled and trapped $^{88}\mathrm{Sr}^{+}$ ion. High-contrast optical Ramsey spectra have been observed with fringe visibilities up to $\ensuremath{\sim}90%$. The visibility decreased as the free precession period was increased, and was limited by the interrogation laser's coherence. The effect of varying the relative phase of the second Ramsey pulse was investigated. By measuring the difference in excitation probability on reversing a $90\ifmmode^\circ\else\textdegree\fi{}$ relative phase shift between the two Ramsey pulses, we have demonstrated Ramsey's anti-symmetric line shape in the optical domain. A significant advantage of this line shape is the zero crossing at line center and the independence of this center frequency on drifts in signal amplitude. This optical Ramsey line shape is suitable for stabilizing a local oscillator to an atomic reference transition in an optical frequency standard. All observed optical Ramsey signals are well described by a model using the optical Bloch equations.

Physical Review A•Sep 30, 2004•33 citations
Stabilization of a laser to an optical-clock transition has been demonstrated using Ramsey's phase-modulation technique. The technique was implemented using a 674 nm laser and a component of the 5 s 2S1/2 → 4d 2D5/2 optical clock transition in a single 88Sr+ ion. The lock performance observed was consistent with the short-term stability of the local oscillator. Compared with existing frequency-modulation stabilization schemes, this technique offers advantages for use in single-ion optical clocks through its possible increased resolution and the ability to conveniently compensate known systematic shifts.
A simultaneous observation of the optical-clock ${}^{2}{S}_{1/2}{\ensuremath{-}}^{2}{D}_{5/2}$ transition at 674 nm, in two separately trapped single 88Sr+{}^{88}{\mathrm{Sr}}^{+}88Sr+ ions, is reported. Two nominally identical miniature rf Paul traps were used together with a 674-nm sideband-injection-locked extended-cavity diode laser. This ``slave'' laser was optically phase locked about 650 MHz away from a ``master'' diode laser, which was itself locked to a high-finesse, ultra-low-expansion (ULE) cavity. The ULE cavity was temperature-stabilized and suspended in an evacuated enclosure, and provided an ``optical flywheel'' reference standard with a relative drift rate of better than 1 part in 1011{10}^{11}1011 per hour. The difference between center frequencies of the single 88Sr+{}^{88}{\mathrm{Sr}}^{+}88Sr+-ion 674-nm (445-THz) transition multiplet in two traps was 120(90) Hz (one standard uncertainty). Thus the two trap center frequencies agree to 3 parts in 1013.{10}^{13}.1013.
The frequency of the 5s 2S(1/2)-4d 2D(5/2) electric quadrupole clock transition in a single, trapped, laser-cooled 88Sr+ ion has been measured by using an optical frequency comb referenced to a cesium fountain primary frequency standard. The frequency of the transition is measured as 444,779,044,095,484.6 (1.5) hertz, with a fractional uncertainty within a factor of 3 of that of the cesium standard. Improvements required to obtain a cesium-limited frequency measurement are described and are expected to lead to a 88Sr+ optical clock with stability and reproducibility exceeding that of the primary cesium 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.
Coherent optical spectroscopy has been performed on the narrow 5s2S1∕2−−4d2D5∕25s\phantom{\rule{0.3em}{0ex}}^{2}S_{1∕2}--4d\phantom{\rule{0.3em}{0ex}}^{2}D_{5∕2}5s2S1∕2​−−4d2D5∕2​ quadrupole transition in a single Doppler-cooled and trapped 88Sr+^{88}\mathrm{Sr}^{+}88Sr+ ion. High-contrast optical Ramsey spectra have been observed with fringe visibilities up to $\ensuremath{\sim}90%$. The visibility decreased as the free precession period was increased, and was limited by the interrogation laser's coherence. The effect of varying the relative phase of the second Ramsey pulse was investigated. By measuring the difference in excitation probability on reversing a $90\ifmmode^\circ\else\textdegree\fi{}$ relative phase shift between the two Ramsey pulses, we have demonstrated Ramsey's anti-symmetric line shape in the optical domain. A significant advantage of this line shape is the zero crossing at line center and the independence of this center frequency on drifts in signal amplitude. This optical Ramsey line shape is suitable for stabilizing a local oscillator to an atomic reference transition in an optical frequency standard. All observed optical Ramsey signals are well described by a model using the optical Bloch equations.