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Physical Review A

Optical Ramsey spectroscopy of a single trapped Sr+88 ion

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

Published Sep 30, 2004• 33 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.70.033419

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We report on the observation of coherent excitation and spectroscopy performed using Ramsey's method of separated excitation fields on a single trapped and laser cooled ion of strontium. Single pulse Rabi excitation studies of the ion have shown linewidths approaching the transform limited value. Studies of transition rate versus pulse duration have shown a quadratic initial increase in transition rate with a duration consistent with coherent excitation and a rapid loss of Rabi oscillations, consistent with the concept of a dephasing of the thermally populated trap oscillator states as the excitation evolves. When two-pulse Ramsey excitation is applied to the single ion, fringe widths down to a linewidth of 840 Hz (FWHM) were observed with measured fringe contrasts consistent with a probe laser linewidth of 500 Hz.PACS Nos.: 32.80Qk, 32.30Jc, 06.30Ft
We experimentally demonstrate laser spectroscopy of the electric-quadrupole transition 6s2S1/2−−5d2D3/26s{}^{2}{S}_{1/2}--5d{}^{2}{D}_{3/2}6s2S1/2​−−5d2D3/2​ of a single trapped 171Yb{}^{171}\mathrm{Yb}171Yb ion. The probed transition has a natural linewidth of 3.1 Hz, and is at a wavelength of 435.5 nm. A 171Yb{}^{171}\mathrm{Yb}171Yb ion is laser cooled to the range of the Doppler limit in a radio-frequency Paul trap. The $F=0--{F}^{\ensuremath{'}}=2,$ ${m}_{{F}^{\ensuremath{'}}}=0$ hyperfine component of the 2S1/2−−2D3/2{}^{2}{S}_{1/2}{--}^{2}{D}_{3/2}2S1/2​−−2D3/2​ transition is excited by a laser source whose frequency is controlled by an optical reference cavity of high intrinsic stability. The recoilless carrier component of the vibrational sideband spectrum is resolved with a minimum linewidth of approximately 80 Hz, corresponding to a fractional frequency resolution of $1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}.$ This resolution limit is attributed to laser frequency instability. The effective decoherence rates of the residual ion motion are inferred from the observation that the axial and two radial low-frequency first-order secular-vibration sidebands show minimum linewidths in the range of 0.2--1 kHz. Prospects for an optical frequency standard based on the investigated atomic system are discussed.
The present decade has seen great advances in optical frequency standards following the development of femtosecond laser frequency combs. With this technology, combined with a stable and narrow probe laser source (50-100 Hz linewidth), we made a systematic study of the 5s 2S1/2-4d 2D5/2 (S-D) transition frequency of the 88Sr+ ion as a function of the quantization axis in the trap. This study revealed the presence of systematic shifts caused by residual micromotion in our rf Paul trap and led to an evaluation of those shifts. Also, a method was developed based on the measurement of the Zeeman spectrum of the clock transition to cancel the electric quadrupole shift caused by patch potentials on the trap electrodes. From these results, we also determined the absolute frequency of the S-D clock transition frequency at 674 nm with a fractional frequency uncertainty of 3.4 × 10-14. We have since made improvements to our probe laser system and have observed 5 Hz Fourier transform limited linewidths on a Zeeman component of the S-D transition of the 88Sr+ ion. To observe such a narrow transition it is essential to have a known and well behaved drift of the laser frequency during the few minutes it takes to measure the ion resonance using the quantum jump signal. Our approach to minimize the drift rate and its sensitivity to temperature fluctuations has been to stabilize the cavity at the temperature where its coefficient of thermal expansion is zero. We will present an overview of our recent progress made on the frequency standard based on the laser-cooled and trapped single ion of 88Sr+.
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.
We demonstrate coherent Doppler-free three-photon excitation of the $^{1}S_{0}\phantom{\rule{0.16em}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ optical clock transition and the $^{1}S_{0}\phantom{\rule{0.16em}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{0.16em}{0ex}}^{3}P_{1}$ intercombination transition in free-space thermal clouds of 88Sr^{88}\mathrm{Sr}88Sr atoms. By appropriate orientation of the wave vectors of three lasers incident on the atoms, the first-order Doppler shift can be eliminated for all velocity classes. Three-photon excitation of the $^{1}S_{0}\phantom{\rule{0.16em}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{0.16em}{0ex}}^{3}P_{1}$ transition enables high-contrast Ramsey spectroscopy with interrogation times comparable to the $21\phantom{\rule{0.16em}{0ex}}\textmu{}\mathrm{s}$ natural lifetime using a single near-resonant laser source. Three-photon spectroscopy on the $^{1}S_{0}\phantom{\rule{0.16em}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ clock transition, using only laser frequencies nearly resonant with the $^{1}S_{0}\phantom{\rule{0.16em}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ and $^{1}S_{0}\phantom{\rule{0.16em}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{0.16em}{0ex}}^{3}P_{1}$ transitions, enables a reduction in Doppler broadening by two orders of magnitude and a corresponding $\ensuremath{\sim}470\phantom{\rule{0.16em}{0ex}}\mathrm{Hz}$ linewidth without a confining potential.
An optical frequency chain referenced to a Cs atomic clock has been used to measure directly the frequency of the electric quadrupole allowed $5s^{2}S_{1/2}\ensuremath{-}4d^{2}D_{5/2}$ transition at 445 THz in a single, trapped, and laser cooled 88Sr+{}^{88}{\mathrm{Sr}}^{+}88Sr+ ion. A transition frequency, ${f}_{S\ensuremath{-}D}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}444779044095.4\mathrm{kHz}$ with an estimated standard uncertainty of 0.2 kHz has been determined. Intrinsic offsets of the probed ion transition in the current experiment are calculated to be at the ${10}^{\ensuremath{-}15}$ level.