arXiv:0902.2905 · Physical Review A

Nondestructive measurement of the transition probability in a Sr optical lattice clock

Jérôme Lodewyck, Philip G. Westergaard, P. Lemonde

Published Jun 1, 2009• 108 citations

Abstract

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 $^{87}\text{S}\text{r}$ 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 ${10}^{4}$ 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.

DOI: 10.1103/physreva.79.061401

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arXiv:0902.2905 · Physical Review A

Nondestructive measurement of the transition probability in a Sr optical lattice clock

Jérôme Lodewyck, Philip G. Westergaard, P. Lemonde

Published Jun 1, 2009• 108 citations

arXiv HTML PDF

Abstract

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

^{87}\text{S}\text{r}

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

{10}^{4}

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.

DOI: 10.1103/physreva.79.061401

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A noise-immune cavity-assisted non-destructive detection for an optical lattice clock in the quantum regime

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We present and implement a non-destructive detection scheme for the transition probability readout of an optical lattice clock. The scheme relies on a differential heterodyne measurement of the dispersive properties of lattice-trapped atoms enhanced by a high finesse cavity. By design, this scheme offers a 1st order rejection of the technical noise sources, an enhanced signal-to-noise ratio, and an homogeneous atom-cavity coupling. We theoretically show that this scheme is optimal with respect to the photon shot noise limit. We experimentally realise this detection scheme in an operational strontium optical lattice clock. The resolution is on the order of a few atoms with a photon scattering rate low enough to keep the atoms trapped after detection. This scheme opens the door to various different interrogations protocols, which reduce the frequency instability, including atom recycling, zero-dead time clocks with a fast repetition rate, and sub quantum projection noise frequency stability.We present and implement a non-destructive detection scheme for the transition probability readout of an optical lattice clock. The scheme relies on a differential heterodyne measurement of the dispersive properties of lattice-trapped atoms enhanced by a high finesse cavity. By design, this scheme offers a 1st order rejection of the technical noise sources, an enhanced signal-to-noise ratio, and an homogeneous atom-cavity coupling. We theoretically show that this scheme is optimal with respect to the photon shot noise limit. We experimentally realise this detection scheme in an operational strontium optical lattice clock. The resolution is on the order of a few atoms with a photon scattering rate low enough to keep the atoms trapped after detection. This scheme opens the door to various different interrogations protocols, which reduce the frequency instability, including atom recycling, zero-dead time clocks with a fast repetition rate, and sub quantum projection noise frequency stability.

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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 .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 .

arXiv:2505.06440Physical Review AJul 29, 20254 citations

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

^{87}\text{S}\text{r}

{^{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

{10}^{4}

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.

We present detailed analyses of our recent experiment on the three-dimensional (3D) optical lattice clock with bosonic

^{88}\mathrm{Sr}

atoms in which the collisional frequency shift was suppressed by applying a single-occupancy lattice. Frequency shifts in magnetically induced spectroscopy on the

{}^{1}{S}_{0}--{}^{3}{P}_{0}

clock transition ($\ensuremath{\lambda}=698$ nm) of

^{88}\mathrm{Sr}

were experimentally investigated by referencing a one-dimensional (1D) lattice clock based on spin-polarized

^{87}\mathrm{Sr}

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.

^1S_0(F=9/2) - {}^3P_0(F=9/2)

clock transition of the

^{87}

Sr optical lattice clock is determined as 429,228,004,229,875(4) Hz, where the uncertainty is mainly limited by that of the frequency link. The result indicates that the Sr lattice clock will play an important role in the scope of the redefinition of the ``second'' by optical frequency standards.