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URSI General Assembly and Scientific Symposium

Synchronous frequency comparison of optical lattice clocks to approach the quantum limit

Hidetoshi Katori, T. Takano, Masao Takamoto

Published Aug 1, 2011• 0 citations
Publisher

Abstract

We demonstrate a synchronous frequency comparison of two optical lattice clocks operated using87Sr and88Sr atoms, whose Allan standard deviation achieved 1 × 10-17in an averaging time of 1,600 s by cancelling out the Dick effect to approach the QPN limit. The scheme manifests an advantage of using a large number N ≈ 2,000 of atoms in optical clocks and paves the way to investigate clocks' inherent uncertainties and relativistic geodesy on a time scale of tens of minutes.

DOI
10.1109/ursigass.2011.6050325

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We demonstrate the frequency comparison of two optical lattice clocks at the relative stabilities close to the quantum projection noise (QPN) limit of optical lattice clocks. This stable frequency comparison is accomplished by synchronous interrogations of two clocks by a common probe laser, which allows us to cancel out the probe laser's frequency noise. We perform the frequency comparison of a one-dimensional (1D) optical lattice clock with spin-polarized fermions 87Sr and a three-dimensional (3D) optical lattice clock with unity-occupation bosons 88Sr and achieve the Allan standard deviation of σγ(τ)=4×10-16 τ-1/2, which corresponds to the QPN limited stability for N=1,000 atoms and the spectrum linewidth γ=8 Hz. The relative stability reaches 1×10-17 with an averaging time of 1,600 s. Finally, we discuss the prospects to realize 10-18 fractional inaccuracies and the possible application of frequency comparison with synchronous interrogations to remote clocks' comparison for relativistic geodesy.

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•May 1, 2026•0 citations
We demonstrate a synchronous frequency comparison of two optical lattice clocks operated using87Sr and88Sr atoms, whose Allan standard deviation achieved 1 × 10-17in an averaging time of 1,600 s by cancelling out the Dick effect to approach the QPN limit. The scheme manifests an advantage of using a large number N ≈ 2,000 of atoms in optical clocks and paves the way to investigate clocks' inherent uncertainties and relativistic geodesy on a time scale of tens of minutes.
We demonstrate the frequency comparison of two optical lattice clocks at the relative stabilities close to the quantum projection noise (QPN) limit of optical lattice clocks. This stable frequency comparison is accomplished by synchronous interrogations of two clocks by a common probe laser, which allows us to cancel out the probe laser's frequency noise. We perform the frequency comparison of a one-dimensional (1D) optical lattice clock with spin-polarized fermions 87Sr and a three-dimensional (3D) optical lattice clock with unity-occupation bosons 88Sr and achieve the Allan standard deviation of σγ(τ)=4×10-16 τ-1/2, which corresponds to the QPN limited stability for N=1,000 atoms and the spectrum linewidth γ=8 Hz. The relative stability reaches 1×10-17 with an averaging time of 1,600 s. Finally, we discuss the prospects to realize 10-18 fractional inaccuracies and the possible application of frequency comparison with synchronous interrogations to remote clocks' comparison for relativistic geodesy.
We consider designs of optical lattice clocks in view of the quantum statistics, relevant atomic spins, and atom-lattice interactions. The first two issues lead to two optimal constructions for the clock: a one-dimensional (1D) optical lattice loaded with spin-polarized fermions and a 3D optical lattice loaded with bosons. By taking atomic multipolar interactions with the lattice fields into account, an "atomic motion insensitive" wavelength is proposed to provide a precise definition of the "magic wavelength." We then present a frequency comparison of these two optical lattice clocks: spin-polarized fermionic 87 Sr and bosonic 88 Sr prepared in 1D and 3D optical lattices, respectively. Synchronous interrogations of these two optical lattice clocks by the same probe laser allowed canceling out its frequency noise as a common mode noise to achieve a relative stability of 3 × 10 −17 for an averaging time of τ = 350 s. The scheme, therefore, provides us with a powerful means to investigate intrinsic uncertainty of the clocks regardless of the probe laser stability. We discuss prospects of the synchronous operation of the clocks on the measurement of the geoid height difference and on the search of constancy of fundamental constants.
We present a synchronous frequency comparison method based on one cold-atom ensemble by using the dual-excitation spectrum technique, which can simultaneously detect the probabilities of two different clock transitions. We experimentally verify this synchronous frequency comparison method between |mF|=9/2 and |mF|=7/2 in a one-dimensional 87Sr optical lattice clock and the comparison instability is well below the Dick limit. We also extend the dual-excitation spectrum method to shorten the clock feedback cycle by a half in optical lattice clocks and experimentally demonstrate that the interleaved self-comparison instability is 1.4 times lower than that of the traditional operation method.
Many-particle optical lattice clocks have the potential for unprecedented measurement precision and stability due to their low quantum projection noise. However, this potential has so far never been realized because clock stability has been limited by frequency noise of optical local oscillators. By synchronously probing two 87Sr^{87}\mathrm{Sr}87Sr lattice systems using a laser with a thermal noise floor of $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$, we remove classically correlated laser noise from the intercomparison, but this does not demonstrate independent clock performance. With an improved optical oscillator that has a $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$ thermal noise floor, we demonstrate an order of magnitude improvement over the best reported stability of any independent clock, achieving a fractional instability of $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ in 1000 s of averaging time for synchronous or asynchronous comparisons. This result is within a factor of 2 of the combined quantum projection noise limit for a 160 ms probe time with $\ensuremath{\sim}{10}^{3}$ atoms in each clock. We further demonstrate that even at this high precision, the overall systematic uncertainty of our clock is not limited by atomic interactions. For the second Sr clock, which has a cavity-enhanced lattice, the atomic-density-dependent frequency shift is evaluated to be $\ensuremath{-}3.11\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ with an uncertainty of $8.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$.
The experimental comparison of two thulium optical lattice clocks in a time interval of up to one hour has been carried out. The synchronous comparison of a clock transition in two independent atomic ensembles using a single ultrastable laser has allowed us to eliminate fluctuations of the laser frequency from the measured frequency difference and to reach a relative measurement error of 10–16 after 500-s averaging, which corresponds to a relative instability of 2×10−15/τ2 \times {{10}^{{ - 15}}}{\text{/}}\sqrt \tau 2×10−15/τ​ . The successful demonstration of the long-term operation of two systems using the synchronous comparison of clock transitions opens the possibility of studying systematic shifts in thulium optical clocks with an uncertainty of 10–17.
Optical atomic clocks have spurred a range of precision frequency comparison experiments and proposals including tests of general relativity, gravitational wave detection, and relativistic geodesy. Current measurements using optical atomic clocks are often limited by the coherence of the clock laser rather than the atomic samples used as a frequency reference. In order to overcome the performance limits imposed by clock laser coherence, we realize a multiplexed optical clock system where multiple spatially resolved ensembles each consisting of thousands of strontium atoms trapped in a 1D optical lattice function as separate atomic frequency references that can be simultaneously interrogated with a shared clock laser. This scheme allows us to make differential frequency comparisons with a quantum projection noise limited fractional instability of 9.7(4)×10−18/ √τ and a differential fractional uncertainty of 8.9×10−20 after 3.3 hours of averaging. We then use this system to perform a lab-based test of the gravitational redshift at the centimeter scale, where we measure a fractional frequency gradient of [−12.4±0.7stat ±2.5sys]×10−19/cm, consistent with the predicted value of 10.9×10−19/cm. Having demonstrated that our differential comparisons are no longer limited by the local oscillator, we turn to fundamental limits on atom–atom coherence. We perform a direct decay measurement of the natural lifetime of the excited clock state 3P0 in 87Sr, in which we use measurements of simultaneously loaded high and low density atomic ensembles and compare decay rates of 87Sr and 88Sr to help isolate natural lifetime decay from other population dynamics. We measure a lifetime of 167+79 −40, which is consistent with previously reported experimental and theoretical values. Lastly, we demonstrate a hyperfine-resolved readout scheme in 87Sr that converts depolarization errors during interrogation into erasure errors, extending coherence times between ensembles in our optical lattice clock up to 150s using spin-echo measurements. These results taken together demonstrate the advantages of differential clock measurements that aren’t limited by clock laser coherence and how to characterize and improve on the performance limits that arise in that regime.