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arXiv:1802.02945 · Physical Review A

Lattice-induced photon scattering in an optical lattice clock

Sören Dörscher, R. Schwarz, Ali Al-Masoudi, Stephan Falke, Uwe Sterr, Christian Lisdat

Published Jun 25, 2018• 59 citations
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Abstract

Off-resonant scattering of lattice laser radiation by ${}^{87}$Sr atoms in the two states ${}^{1}{S}_{0}$ and ${}^{3}{P}_{0}$ and its effect on clock operation are investigated. It is found that Raman scattering eventually limits the achievable frequency instability and thus limits the useful interrogation time in optical lattice clocks at presently used lattice depths.

DOI
10.1103/physreva.97.063419

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Off-resonant scattering of lattice laser radiation by 87{}^{87}87Sr atoms in the two states 1S0{}^{1}{S}_{0}1S0​ and 3P0{}^{3}{P}_{0}3P0​ and its effect on clock operation are investigated. It is found that Raman scattering eventually limits the achievable frequency instability and thus limits the useful interrogation time in optical lattice clocks at presently used lattice depths.
We explore the limits of atomic coherence and measurement precision in a ^{87}Sr optical lattice clock. We perform a detailed characterization of key effects, including lattice Raman scattering and atomic collisions in a shallow lattice configuration, determining a 174(28) s ^{3}P_{0} clock state lifetime. Investigation of atomic coherence across a range of lattice depths and atomic densities reveals decoherence mechanisms related to photon scattering and atomic interaction. At a reduced density, we observe a coherence time of 118(9) s, approaching the fundamental limit set by spontaneous emission. Guided by this coherence understanding, we demonstrate a clock instability for an atomic ensemble of 1.5×10^{-18} at 1 s in fractional frequency units. Our results are important for further advancing the state of the art of an optical lattice clock for fundamental physics applications.
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.
Increasing coherent interrogation times is central to advancing the precision of optical clocks. Synchronous differential optical clock comparisons have now demonstrated atomic coherence times that far exceed the coherence time of the clock laser. While atom coherence times are then primarily limited by errors induced by lattice Raman scattering, excited clock state radiative decay, and broadening from two-body collisions, many of these errors take the atoms out of the clock transition subspace, and can therefore be converted into “erasure” errors if the appropriate readout scheme is employed. Here we experimentally demonstrate a hyperfine-resolved readout technique for 87 Sr optical lattice clocks that mitigates decoherence from Raman scattering induced by the lattice as well as radiative decay. By employing hyperfine-resolved readout in synchronous differential comparisons between 87 Sr ensembles with both Ramsey and spin-echo spectroscopy sequences, we achieve enhanced atomic coherence times exceeding 100 and 150 s, respectively, enabling longer coherent measurements without a reduction in performance. We anticipate that this hyperfine-resolved readout technique will benefit applications of state-of-the-art optical lattice clock comparisons in which the coherence times are constrained by Raman scattering or radiative decay.
We explore the limits of atomic coherence and measurement precision in a 87Sr optical lattice clock. We perform a detailed characterization of key effects, including lattice Raman scattering and atomic collisions in a shallow lattice configuration, determining a 174(28) s 3P0 clock state lifetime. Investigation of atomic coherence across a range of lattice depths and atomic densities reveals decoherence mechanisms related to photon scattering and atomic interaction. At a reduced density, we observe a coherence time of 118(9) s, approaching the fundamental limit set by spontaneous emission. Guided by this coherence understanding, we demonstrate a clock instability of 1.5E-18 at 1 s in fractional frequency units. Our results are important for further advancing the state-of-the-art of an optical lattice clock for fundamental physics applications.
We present the experimental demonstration of nondestructive probing of the ${^{1}S}_{0}\text{\ensuremath{-}}{^{3}P}_{0}$ clock transition probability in an optical lattice clock with 87Sr^{87}\text{S}\text{r}87Sr atoms. It is based on the phase shift induced by the atoms on a weak off-resonant laser beam. The method we propose is a differential measurement of this phase shift on two modulation sidebands with opposite detuning with respect to the ${^{1}S}_{0}\text{\ensuremath{-}}{^{1}P}_{1}$ transition, allowing a detection limited by the photon shot noise. We have measured an atomic population of 104{10}^{4}104 atoms with a signal-to-noise ratio of 100 per cycle, while keeping more than 95% of the atoms in the optical lattice with a depth of 0.1 mK. The method proves simple and robust enough to be operated as part of the whole clock setup. This detection scheme enables us to reuse atoms for subsequent clock state interrogations, dramatically reducing the loading time and thereby improving the clock frequency stability.
We investigate the effects of stimulated scattering of optical lattice photons on atomic coherence times in a state-of-the art ^{87}Sr optical lattice clock. Such scattering processes are found to limit the achievable coherence times to less than 12 s (corresponding to a quality factor of 1×10^{16}), significantly shorter than the predicted 145(40) s lifetime of ^{87}Sr's excited clock state. We suggest that shallow, state-independent optical lattices with increased lattice constants can give rise to sufficiently small lattice photon scattering and motional dephasing rates as to enable coherence times on the order of the clock transition's natural lifetime. Not only should this scheme be compatible with the relatively high atomic density associated with Fermi-degenerate gases in three-dimensional optical lattices, but we anticipate that certain properties of various quantum states of matter-such as the localization of atoms in a Mott insulator-can be used to suppress dephasing due to tunneling.