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arXiv:1108.1431 · Physical Review A

Inelastic collisions and density-dependent excitation suppression in a 87 Sr optical lattice clock

Michael Bishof, Michael J. Martin, Matthew D. Swallows, Craig Benko, Yige Lin, Goulven Quéméner, Ana María Rey, J. Ye

Published Nov 17, 2011• 56 citations
arXivHTMLPDF

Abstract

We observe two-body loss of ${}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{0}$ ${}^{87}$Sr atoms trapped in a one-dimensional optical lattice. We measure loss rate coefficients for atomic samples between 1 and 6 $\ensuremath{\mu}$K that are prepared either in a single nuclear-spin sublevel or with equal populations in two sublevels. The measured temperature and nuclear-spin preparation dependence of rate coefficients agree well with calculations and reveal that rate coefficients for distinguishable atoms are only slightly enhanced over those of indistinguishable atoms. We further observe a suppression of excitation and losses during interrogation of the ${}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}$--${}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{0}$ transition as density increases and Rabi frequency decreases, which suggests the presence of strong interactions in our dynamically driven many-body system.

DOI
10.1103/physreva.84.052716

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We observe two-body loss of 3P0{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{0}3P0​ 87{}^{87}87Sr atoms trapped in a one-dimensional optical lattice. We measure loss rate coefficients for atomic samples between 1 and 6 \ensuremathμ\ensuremath{\mu}\ensuremathμK that are prepared either in a single nuclear-spin sublevel or with equal populations in two sublevels. The measured temperature and nuclear-spin preparation dependence of rate coefficients agree well with calculations and reveal that rate coefficients for distinguishable atoms are only slightly enhanced over those of indistinguishable atoms. We further observe a suppression of excitation and losses during interrogation of the 1S0{}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}1S0​--3P0{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{0}3P0​ transition as density increases and Rabi frequency decreases, which suggests the presence of strong interactions in our dynamically driven many-body system.
We have quantified collisional losses, decoherence and the collision shift in a one-dimensional optical lattice clock on the highly forbidden transition (1)S(0)-(3)P(0) at 698 nm with bosonic (88)Sr. We were able to distinguish two loss channels: inelastic collisions between atoms in the upper and lower clock state and atoms in the upper clock state only. Based on the measured coefficients, we determine the operation parameters at which a 1D-lattice clock with (88)Sr shows no degradation due to collisions on the fractional uncertainty level of 10(-16).
Recently, ppp-wave cold collisions were shown to dominate the density-dependent shift of the clock transition frequency in a 171{}^{171}171Yb optical lattice clock. Here we demonstrate that by operating such a system at the proper excitation fraction, the cold-collision shift is canceled below the $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}$ fractional frequency level. We report inelastic two-body loss rates for 3P0{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{0}\phantom{\rule{0.16em}{0ex}}3P0​-3P0{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{0}3P0​ and 1S0{}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}\phantom{\rule{0.16em}{0ex}}1S0​-3P0{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{0}3P0​ scattering. We also measure interaction shifts in an unpolarized atomic sample. Collision measurements for this spin-1/2 171{}^{171}171Yb system are relevant for high-performance optical clocks as well as strongly interacting systems for quantum information and quantum simulation applications.
Optical lattice clocks based on the narrow ( 5 s 2 ) S 0 1 − ( 5 s 5 p ) P 0 3 transition in neutral strontium (Sr) are among the most precise and accurate measurement devices in existence. Although this transition is completely forbidden by selection rules, state mixing from the hyperfine interaction in Sr 87 provides a weakly allowed transition that can be coherently driven with practical clock laser intensities. While the coherent interrogation times of optical clocks are typically set by the linewidth of the probe laser, this limitation can be overcome in synchronous differential comparisons between ensembles. In such measurements the natural lifetime of the S 0 1 – P 0 3 clock transition becomes the fundamental limiting factor to the duration of a single run of the experiment. However, a direct measurement of the decay rate of the clock excited state is quite challenging due to the competing effects of other loss channels such as Raman scattering, inelastic collisions, and atom loss due to background gas. In this work, we monitor the decay of Sr atoms trapped in an optical lattice and initialized in the P 0 3 state. By making measurements of high and low density ensembles of both Sr 87 and Sr 88 across varying lattice trap depths, we isolate radiative decay, which accounts for a significant fraction of the observed decays at low depths. We obtain a natural radiative decay lifetime of 167 − 40 + 79 s for the P 0 3 clock state in Sr 87 , a value that is consistent with previously reported measurements and theoretical predictions. We also introduce an additional measurement scheme that involves repeated measurements of the ground-state population within a single experimental sequence, validating our model and the consistency of the measured rates. We expect that the techniques introduced in this work are applicable to lifetime measurements of long-lived metastable states in other atoms and ions used for clocks and quantum computing. The results presented in this work inform performance estimates of proposed gravitational wave detectors and long-baseline atom interferometers making use of Sr 87 .
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 report precise measurements of inter-level interactions in a bosonic optical lattice clock based on 88^{88}88Sr atoms. We observe a nonlinear density dependence of the clock shift, even without reaching quantum degeneracy. In a 2D lattice, the Rabi line shape exhibits an interaction sideband consistent with a collective spin model, while in a 1D lattice the shift is modified by density-induced dephasing. These findings, combined with a careful choice of interrogation detuning and atomic density, can enable operation at a net-zero systematic density shift in 88^{88}88Sr lattice clocks. We discuss the implications of these findings in many-body physics, quantum simulation, and precision isotope shift measurements, which provide a powerful probe for new physics beyond the Standard Model.
In this work we study the effect of interactions in an optical lattice clock based on fermionic Sr atoms. In current one-dimensional lattice clocks nuclear spin-polarized atoms are known to have contact interactions of p-wave character and collective in nature. Here we focus on interactions that will influence the design of future optical lattice clocks. We study the case where atoms are no longer confined to a single nuclear spin state. By using samples of atoms with different distributions among the ten nuclear spin states of Sr we show that these interactions are SU(N) symmetric up to a 3% uncertainty in our measurements. Through these measurements we are also able to determine all the s-wave and p-wave scattering lengths.\nWe also study the case of nuclear spin-polarized interacting atoms that are allowed to tunnel between different lattice sites where the electronic spin and the motion of these atoms become coupled. We observe spectroscopically the precession of the collective magnetization and evolution of spin locking effects arising from the interplay between p-wave interactions and interactions induced by the spin-orbit coupling. The many-body dynamics are captured by a spin model that describes a broad class of condensed matter systems ranging from superconductors to quantum magnets.\nBy loading a dense sample of atoms into a magneto-optical trap we are able to observe long-range dipole-dipole interactions between our Sr atoms. These interactions will be important for atomic clocks based on a three dimensional lattice, such as the one recently demonstrated in our lab. In these clocks it is possible to remove the contact interactions between the atoms by loading only one atom per lattice site. In this case the dominant interactions will be from the long-range dipole-dipole interactions that will take place between the atoms.