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arXiv:1703.04609 · New Journal of Physics

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

Grégoire Vallet, Eva Bookjans, Ulrich Eismann, Sławomir Bilicki, Rodolphe Le Targat, Jérôme Lodewyck

Published Aug 7, 2017• 51 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1367-2630/aa7c84

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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.
SummaryThe short-term frequency instability of the best optical atomic clock lies in the mid 10−17. However, the Dick effect is still an obstacle for a single operational clock closely followed by the quantum projection noise. To improve the frequency stability of the strontium optical lattice clock, we present a quantum non-demolition detection scheme based on the cavity mediated interaction between the atoms and a probe light that has a large-frequency detuning to the atomic resonance, aiming to bring the detection scheme proposed in [1] to the quantum regime. We obtained a rather small photon scattering rate, measured to be less than 0.1 photon/μs/atom, which allows us to not only preserve the atoms in the lattice but also the atomic wave function as long as the total probe time is on the order of a few microseconds. The detection noise for the number of atoms is 48/√photons atoms, implying that the frequency stability can surpass the standard quantum limit when the number of trapped atoms is larger than 2.3×104with spin squeezing protocols.
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.
The work achieved in the frame of this PhD training consisted in the implementation of a cavity enhanced non destructive detection system of atoms trapped in an optical lattice aiming at improving the stability of an optical strontium clock.The characterization of the system in its classical regime, for which a sufficiently low number of photons are scattered per atom to avoid expelling them off the trap, highlighted significant improvements in term of signal to noise ratio, with gain factor around 100 compared with the previously used fluorescence scheme. Yet, gains in terms of stability via Dick effect reduction still have to be demonstrated.Regarding the quantum regime, for which less than one photon is scattered per atom over the detection, new ideas and significant changes have been carried out on the system and a theoretical study was has been undertaken to determine the strategy for the improvement of the clock stability by quantum projection noise reduction via quantum non demolition measurement.It was as well the opportunity to study the effect of the hot collisions between the trapped strontium atoms and the residual vacuum background gas particles, allowing for the improvement of the clock uncertainty. This work reports in particular on the first measurement of strontium clock hot collisions shifts as well as its theoretical study.
We present an analysis of the different types of noise from the detection and interrogation laser in our strontium lattice clock. We develop a noise model showing that in our setup quantum projection noise-limited detection is possible if more than 130 atoms are interrogated. Adding information about the noise spectrum of our clock laser with sub-${10}^{\ensuremath{-}16}$ fractional frequency instability allows one to infer the clock stability for different modes of operation. Excellent agreement with experimental observations for the instability of the difference between two interleaved stabilizations is found. We infer a clock instability of $1.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}/\sqrt{\ensuremath{\tau}}$ as a function of averaging time $\ensuremath{\tau}$ expressed in seconds for normal clock operation.
In this paper, we review several aspects of the frequency stability of optical lattice clocks. We describe a new ultra-stable cavity design with reduced thermal noise and record frequency stability (below 10 −15 ), as well as a non-destructive detection scheme for measuring the clock transition probability. Given the experimental parameters we measured, we simulate different sequence strategies for optimizing the stability. Finally, we report on the development of a second optical lattice clock and simulate several comparison strategies. In particular, we show by a numerical method that a stability as low as 2 × 10 −16 τ −1/2 can be reached with optical lattice clocks, and we show how to demonstrate this stability with a double clock system.