Improving the $Q$ Factor of an Optical Atomic Clock Using Quantum Nondemolition Measurement

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Improving the $Q$ Factor of an Optical Atomic Clock Using Quantum Nondemolition Measurement

William Bowden, Alvise Vianello, Ian R. Hill, Marco Schioppo, and Richard Hobson

Phys. Rev. X 10, 041052 – Published 15 December 2020

Abstract

Quantum nondemolition (QND) measurement is a remarkable tool for the manipulation of quantum systems. It allows specific information to be extracted while still preserving fragile quantum observables of the system. Here we apply cavity-based QND measurement to an optical lattice clock—a type of atomic clock with unrivaled frequency precision—preserving the quantum coherence of the atoms after readout with 80% fidelity. We apply this technique to stabilize the phase of an ultrastable laser to a coherent atomic state via a series of repeated QND measurements. We exploit the improved phase coherence of the ultrastable laser to interrogate a separate optical lattice clock, using a Ramsey spectroscopy time extended from 300 ms to 2 s. With this technique we maintain 95% contrast and observe a sevenfold increase in the clock’s $Q$ factor to $1.7 \times 10^{15}$ .

Received 24 July 2020
Revised 20 September 2020
Accepted 13 October 2020

DOI:https://doi.org/10.1103/PhysRevX.10.041052

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Atomic, optical & lattice clocks Cavity quantum electrodynamics Coherent control Quantum measurements Squeezing of quantum noise

Atomic, Molecular & Optical

Authors & Affiliations

William Bowden ^1,*, Alvise Vianello ^1,2,*, Ian R. Hill ¹, Marco Schioppo ¹, and Richard Hobson ¹

¹National Physical Laboratory, Hampton Road, Teddington TW11 0LW, United Kingdom
²Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom

^*These authors contributed equally to this work.

Popular Summary

The past two decades have seen rapid progress in atomic clocks, with the best clocks now demonstrating an extraordinary 18 digits of precision. Even so, scientists always want to go further—could the next decimal place yield new technologies or uncover new physics? To that end, we experimentally demonstrate a fundamentally new way to run an atomic clock that could provide a several-fold improvement to its precision.

In an optical atomic clock, the “ticks” of an optical oscillator (a laser) are regularly steered to match the ticks between two quantum states of an atom, which gather phase at a constant rate. In earlier realizations of atomic clocks, the ticks of the oscillator were steered by detecting the phase of the atoms via fluorescence from a strong probe laser. The measurement allows one to steer the oscillator but erases the phase of the atoms, forcing a pause to reinitialize the atoms for further spectroscopy.

We demonstrate an alternative approach in which a very weak laser measures the phase of the atoms without destroying their quantum state. Instead of reinitializing atoms after each measurement, now we can repeatedly measure the same atoms and steer the oscillator toward the atoms’ phase. As an application of this technique, we show that the phase-locked oscillator can be used to probe a separate cloud of atoms very efficiently, forming a compound clock with state-of-the-art frequency resolution.

Our results show that “quantum nondemolition measurements” are an effective tool for improving the phase coherence of a laser, thus enhancing the precision of atomic clocks. If applied to atom interferometers instead of atomic clocks, the same methods could also lead to the detection of low-frequency gravitational waves.

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Issue

Vol. 10, Iss. 4 — October - December 2020

Subject Areas

Atomic and Molecular Physics

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Images

Figure 1
Overview of the QND measurement scheme. (a) Sketch of the dual-wavelength in-vacuum cavity used to trap the atoms and to carry out the QND measurement. Atoms are trapped at the 813 nm intensity maxima represented in red, while they also interact with the nearest blue- and red-detuned cavity modes at 461 nm represented in blue and purple. (b) Simplified level scheme for Sr showing the 461 nm transition used for nondestructive detection and the 698 nm optical clock transition. (c) Diagram of the optical setup used for the QND measurement, and a sketch of the optical spectrum transmitted through the Mach-Zehnder interferometer (MZI). The six probe frequency components generated by the electro-optic modulator (EOM) chain are depicted in blue, interacting with the cavity modes in gray which surround the atomic transition in purple. The padlocks represent Pound-Drever-Hall loops used to stabilize the laser frequencies and the cavity lengths.
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Figure 2
Coherence preservation after the QND measurement. (a) Timing sequence used to measure coherence after QND measurement, and sketches of the atomic state in the Bloch sphere representation at each step of the sequence. The projection of atoms into the ground or excited state due to scattering of QND probe photons is represented by the shrinking radius of the Bloch sphere compared to its original size $N / 2$ (gray halo). The final Bloch sphere (top right) shows the case where the final $π / 2$ -pulse phase is $ϕ = 0 °$ . (b) The measured atomic coherence $S_{x}$ remaining after QND measurement as a function of total probe time. For the data with spin echo we use the total measurement time summed over the two QND probes, and fit an exponential decay with time constant $317 μ s$ (blue dashed line). The model for coherence decay without spin echo (green dashed line, also displayed in the inset) is described in the main text.
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Figure 3
Experimental setup and Sr1-Sr2 correlations. (a) LO light is distributed to Sr1 and Sr2 along separate optical paths, the lengths of which are actively stabilized. When the APL is engaged, phase corrections from Sr2 are applied to an acousto-optic modulator (AOM) shared by both systems, thereby increasing the coherence time of the light sent to Sr1. (b) Allan deviation of the frequency ratio between Sr1 and Sr2, with the APL disengaged and the OLCs independently stabilized using synchronous 300 ms Rabi pulses. Both clocks experience the same LO frequency fluctuations, resulting in highly correlated frequency corrections $ν_{1}$ , $ν_{2}$ . However, there are residual sources of noise—for example, linear Zeeman shift fluctuations, which are suppressed using a less sensitive Zeeman transition. After minimizing noise (see Supplemental Material [39]), the frequency instability approaches the quadrature sum of QPN from both clocks, $4 \times 10^{- 17} / \sqrt{τ}$ . The cycle time is 1.75 s and atom numbers are $7 \times 10^{3}$ and $1.3 \times 10^{4}$ atoms in Sr1 and Sr2, respectively.
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Figure 4
Enhanced Ramsey spectroscopy via APL. (a) Timing sequence for the synchronous spectroscopy scheme, and Bloch sphere representation of the atomic state during the APL sequence. Atomic data from the Rabi time in Sr1 are used only when scanning over Sr1 Ramsey fringes. Prior to and during each scan, the Rabi data measure frequency drift of the free-running LO (typically between 0 and $3 mHz s^{- 1}$ ), and allows us to apply LO drift compensation in a double-integrator control loop with attack time of approximately 100 clock cycles. (b) Results using Ramsey spectroscopy in Sr1, cointerrogated with Sr2 using the same LO. Left: excitation fractions with the LO frequency locked to the central Sr1 Ramsey fringe under three conditions: 300 ms Ramsey dark time with the APL to Sr2 disengaged (orange), 2 s dark time with the APL disengaged (red), and 2 s dark time with the APL engaged (green). Frequency scans over the Sr1 Ramsey fringes are shown on the right under the same conditions as above. With the APL engaged, the fringe width is measured to be 254(1) mHz for a 2 s dark time.
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