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Canadian Journal of Physics

Optical Ramsey spectroscopy and coherence measurements of the clock transition in a single trapped Sr ion

L. Marmet, Alan A. Madej

Published Jan 1, 2000• 14 citations
Publisher

Abstract

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

DOI
10.1139/cjp-78-5-6-495

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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
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.
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+.
The 435 mum171Yb+transition is a good candidate for an atomic clock based on an optical transition. We have stored single171Yb ions for several months in RF traps. The ions are cooled, repumped and the clock transition is interrogated by (frequency-doubled) diode lasers. The interrogation laser linewidth was 30 Hz determining the resolvable linewidth of the Yb+transition interrogated. The absolute frequency of this transition was measured using an optical comb generator, self referenced by broadening the spectrum to above one octave, with respect to a Cs fountain clock. Of all systematic frequency shifts to which this transition is subject an estimate indicates that the electric quadruple shift appears is the largest. To obtain a magnitude of the quadruple shift (and the quadruple moment) the clock frequencies of two independently stored and cooled171Yb ions were compared while varying the static electric field in one trap. The measured frequency shift amounting to ~1 Hz/V. This result would seem to permit clocks with much higher accuracy than the clocks based on microwave transition, particularly if the technique of aligning the ions with respect to the electric field were applicable. Anticipating even more precise clocks, we are presently investigating a blue nuclear transition in229Th. Such a nuclear transition should be even better shielded from environmental influences than transitions in the electron shell. This nuclear transition has not yet been directly optically observed. We are presently investigating the luminescence after incoherent broad band optical excitation. The triply ionized223Th is then a suitable system for trapped single ion spectroscopy. The cooling transition lies conveniently in the near infrared and the nuclear clock transition can be read out by nuclear/electron shell double resonance
Single ions trapped and laser cooled provide ideal objects for high resolution spectroscopy and frequency standards. For the latter purpose we are investigating the 5s2 1S0 → 5s5p 3P0 transition of In+. With a natural linewidth of only 1.1 Hz this resonance offers very high resolution and is highly immune to frequency shifts due to external electromagnetic fields, because it connects two levels with vanishing electronic magnetic momenta [1]. The wavelength of this clock transition is 236.5 nm and is technically very convenient, since it coincides with the fourth harmonic of the 946 nm Nd:YAG laser line. So this intrinsically frequency stable solid-state laser can be used to excite the transition [2]. For laser cooling and fluorescence detection of the indium ion the 5s2 1So -> 5s5p 3P1 transition at 230.6 nm can be employed. The use of the relatively narrow intercombination line for laser cooling allows us to study optical sideband cooling in the strong binding regime, where the oscillation frequencies of the ion in the trap (around 1 MHz) are larger than the optical linewidth of 360 kHz. In this parameter range laser cooling is possible to the quantum ground state of the vibrational motion in the trap corresponding to a temperature of roughly 100 μK. The same low temperature was obtained with sideband cooling of a small Coulomb crystal consisting of two ions, creating an interesting new quantum few-particle system.
We experimentally investigate an optical frequency standard based on the (2)S1/2(F=0)→(2)F7/2(F=3) electric octupole (E3) transition of a single trapped (171)Yb+ ion. For the spectroscopy of this strongly forbidden transition, we utilize a Ramsey-type excitation scheme that provides immunity to probe-induced frequency shifts. The cancellation of these shifts is controlled by interleaved single-pulse Rabi spectroscopy, which reduces the related relative frequency uncertainty to 1.1×10(-18). To determine the frequency shift due to thermal radiation emitted by the ion's environment, we measure the static scalar differential polarizability of the E3 transition as 0.888(16)×10(-40) J m(2)/V(2) and a dynamic correction η(300 K)=-0.0015(7). This reduces the uncertainty due to thermal radiation to 1.8×10(-18). The residual motion of the ion yields the largest contribution (2.1×10(-18)) to the total systematic relative uncertainty of the clock of 3.2×10(-18).
An optical frequency standard, based on the 674 nm 2S1/2-2D5/2 'clock' transition in a laser cooled trapped strontium ion is currently being evaluated at the UK National Physical Laboratory. The probe laser is a narrowed AlGaInP diode laser locked to a highly-stable and ultra-low- expansion high-finesse cavity. Laser linewidths of less than 200 Hz have been observed, measured by scanning over a single Zeeman component at 674 nm. The development of this laser is described, together with factors currently limiting the observed linewidth. Three 88Sr+ traps are now in operation, and the probe laser source can be simultaneously locked to the center of the 2S1/2 - 2D5/2 Zeeman multiplet in any two of the three traps, allowing a comparison between them. Recent results on this comparison are presented.