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arXiv:physics/0410110 · Physical Review Letters

Precision Spectroscopy and Density-Dependent Frequency Shifts in Ultracold Sr

T. Ido, Thomas H. Loftus, Martin M. Boyd, Andrew D. Ludlow, Kevin W. Holman, Jun Ye

Published Apr 18, 2005• 99 citations
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Abstract

By varying the density of an ultracold $^{88}\mathrm{Sr}$ sample from ${10}^{9}$ to$>{10}^{12}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}3}$, we make the first definitive measurement of the density-related frequency shift and linewidth broadening of the $^{1}S_{0}\mathrm{\text{\ensuremath{-}}}^{3}P_{1}$ optical clock transition in an alkaline earth system. In addition, we report the most accurate measurement to date of the $^{88}\mathrm{Sr}$ $^{1}S_{0}\mathrm{\text{\ensuremath{-}}}^{3}P_{1}$ optical clock transition frequency. Including a detailed analysis of systematic errors, the frequency is $[434\text{ }\text{ }829\text{ }\text{ }121\text{ }\text{ }312\text{ }\text{ }334\ifmmode\pm\else\textpm\fi{}20(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}33(\mathrm{syst})]\text{ }\text{ }\mathrm{Hz}$.

DOI
10.1103/physrevlett.94.153001

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As a key component of a strontium based optical clock, we have developed an apparatus which allows laser cooling and trapping of more than 10/sup 7/ /sup 88/Sr atoms to temperatures below 1 /spl mu/K. Using this system, we have performed the first high accuracy measurement of the /sup 88/Sr /sup 1/S/sub 0/-/sup 3/P/sub 1/ clock transition using an ultra-cold sample. Detailed descriptions of both the measurement technique and corresponding systematic uncertainties is provided. In addition, by varying the density of the ultra-cold /sup 88/Sr sample over a range of three orders of magnitude we obtain the first definitive measurement of a density-related frequency shift and linewidth broadening of an optical clock transition in an ultra-cold alkaline earth system. Spectroscopy of the /sub 1/S/sub 0/-/sup 3/P/sub 0/ transition is currently underway using this narrow probe laser and an octave spanning femtosecond laser. Our most recent results are presented. The proposed measurement technique, accuracy, and stability of an optical clock based on the EIT (electromagnetically-induced-transparency) measurement in /sup 88/Sr are described.
With ultracold 87Srconfined in a magic wavelength optical lattice, we present the most precise study (2.8 Hz statistical uncertainty) to date of the 1S0-3P0 optical clock transition with a detailed analysis of systematic shifts (19 Hz uncertainty) in the absolute frequency measurement of 429 228 004 229 869 Hz. The high resolution permits an investigation of the optical lattice motional sideband structure. The local oscillator for this optical atomic clock is a stable diode laser with its hertz-level linewidth characterized by an octave-spanning femtosecond frequency comb.
Advances in ultra-stable lasers now permit sub-Hz resolution of optical atomic transitions. At this level, weak interactions by any ordinary scale can in fact dominate the dynamics of the interrogated atoms, even for spin polarized fermions at ultralow temperatures. Contrary to results obtained in radio frequency spectroscopy of alkali fermionic atoms, optical spectroscopy of 87 Sr and 171 Yb has revealed density dependent frequency shifts of the 1 S0 - 3 P 0 “clock” transition. Understanding interactions in these systems is necessary to improve their accuracy and stability. Moreover, such an understanding will enable optical lattice clock systems to serve as quantum simulators for open, driven, strongly-interacting quantum systems at the mesoscopic scale. In this talk we presented our progress towards a comprehensive evaluation and understanding of the interactions present during spectroscopy of the 87 Sr clock transition under various operating conditions. Our studies indicate that a mean-field solution of a master equation is sufficient to capture the many-body dynamics of alkaline earth atom clocks. Entering the regime in which a treatment beyond mean-field is required for a proper description of the clock dynamics is under immediate experimental reach.
We have carried out calculations towards the goal of reducing the inaccuracy of the Sr optical atomic clock to $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ and below. In particular, we focused on ac polarizabilities of the 5s25{s}^{2}5s2 1S0^{1}S_{0}1S0​ and 5s5p5s5p5s5p 3P0o^{3}P_{0}^{o}3P0o​ clock states that are important for reducing the uncertainty of black-body radiation-induced frequency shifts for the $^{1}S_{0}\text{\ensuremath{-}}^{3}P_{0}^{o}$ clock transition. Four low-lying even-parity states have been identified, whose total contribution to the static polarizability of the 3P0o^{3}P_{0}^{o}3P0o​ clock state is at the level of 90%. We show that if the contribution of these states is experimentally known with 0.1% accuracy, the same accuracy can be achieved for the total polarizability of the 3P0o^{3}P_{0}^{o}3P0o​ state. The corresponding uncertainty for the blackbody shift at a fixed room temperature will be below $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$. The calculations are confirmed by a number of experimental measurements on various Sr properties.
We present detailed analyses of our recent experiment on the three-dimensional (3D) optical lattice clock with bosonic 88Sr^{88}\mathrm{Sr}88Sr atoms in which the collisional frequency shift was suppressed by applying a single-occupancy lattice. Frequency shifts in magnetically induced spectroscopy on the 1S0−−3P0{}^{1}{S}_{0}--{}^{3}{P}_{0}1S0​−−3P0​ clock transition ($\ensuremath{\lambda}=698$ nm) of 88Sr^{88}\mathrm{Sr}88Sr were experimentally investigated by referencing a one-dimensional (1D) lattice clock based on spin-polarized 87Sr^{87}\mathrm{Sr}87Sr atoms. We discuss that the clock stability is limited by the current laser stability as well as the experimental sequence of the clock operation, which may be improved to ${\ensuremath{\sigma}}_{y}(\ensuremath{\tau})=2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}/\sqrt{\ensuremath{\tau}}$ by optimizing the cycle time of the clock operation.
Clock and inter-combination line frequency separation (3P0− 3P1^{3}P_{0} -\,^{3}P_{1}3P0​−3P1​) in 171^{171}171Yb
We have carried out concurrent optical frequency measurements of the (6s2) 1S0−(6s6p) 3P1(6s^{2})\,^{1}S_{0} -(6s6p)\,^{3}P_{1}(6s2)1S0​−(6s6p)3P1​ (F=32F=\frac{3}{2}F=23​) and (6s2) 1S0−(6s6p) 3P0(6s^{2})\,^{1}S_{0} -(6s6p)\,^{3}P_{0}(6s2)1S0​−(6s6p)3P0​ transitions in 171^{171}171Yb, and in so doing have determined the frequency separation between the 3P0^{3}P_{0}3P0​ (F=12F=\frac{1}{2}F=21​) and 3P1^{3}P_{1}3P1​ (F=32F=\frac{3}{2}F=23​) levels with an uncertainty in the ppb range. The knowledge of this frequency interval will aid experiments relying on the 1S0− 3P0^{1}S_{0}-\,^{3}P_{0}1S0​−3P0​ line in 171^{171}171Yb and 173^{173}173Yb without access to highly accurate frequency standards.