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arXiv:2208.06301

Inhibiting phase drift in multi-atom clocks using the quantum Zeno effect

S. U. Shringarpure, J. D. Franson

Published Aug 12, 2022• 0 citations
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Abstract

The accuracy of an atomic clock depends in part on the bandwidth of the relevant atomic transitions. Here we consider an ensemble of $N$ atoms whose transition frequencies have been independently perturbed by environmental effects or other factors. We consider the possibility of using the quantum Zeno effect to lock the relative phase of the atoms, which would decrease their effective bandwidth by a factor of $1/\sqrt{N}$. We analyze an example in which the quantum Zeno effect can be used to lock the relative phase of a pair of atoms, after which the elapsed time can be determined. Practical applications may require $N>>1$ in order to achieve a good signal-to-noise ratio.

DOI
10.48550/arxiv.2208.06301

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Inhibiting phase drift in multi-atom clocks using the quantum Zeno effect

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Abstract The accuracy of an atomic clock depends in part on the bandwidth of the relevant atomic transitions. Here we consider an ensemble of atoms whose transition frequencies have been independently perturbed by environmental effects or other factors. We consider the possibility of using the quantum Zeno effect to lock the relative phase of the atoms, which would decrease their effective bandwidth by a factor of \(1/\sqrt N .\) We analyze an example in which the quantum Zeno effect can be used to lock the relative phase of a pair of atoms, after which the elapsed time can be determined. Practical applications may require \(N>>1\) in order to achieve a good signal-to-noise ratio.

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The accuracy of an atomic clock depends in part on the bandwidth of the relevant atomic transitions. Here we consider an ensemble of NNN atoms whose transition frequencies have been independently perturbed by environmental effects or other factors. We consider the possibility of using the quantum Zeno effect to lock the relative phase of the atoms, which would decrease their effective bandwidth by a factor of 1/N1/\sqrt{N}1/N​. We analyze an example in which the quantum Zeno effect can be used to lock the relative phase of a pair of atoms, after which the elapsed time can be determined. Practical applications may require N>>1N>>1N>>1 in order to achieve a good signal-to-noise ratio.
Abstract The accuracy of an atomic clock depends in part on the bandwidth of the relevant atomic transitions. Here we consider an ensemble of atoms whose transition frequencies have been independently perturbed by environmental effects or other factors. We consider the possibility of using the quantum Zeno effect to lock the relative phase of the atoms, which would decrease their effective bandwidth by a factor of 1/N.1/\sqrt N .1/N​. We analyze an example in which the quantum Zeno effect can be used to lock the relative phase of a pair of atoms, after which the elapsed time can be determined. Practical applications may require N>>1N>>1N>>1 in order to achieve a good signal-to-noise ratio.
Optical atomic clocks that operate at frequencies up to 100,000 times higher than their microwave counterparts permit better resolutions and accuracies, while also providing more leeway in environmental control for out of lab applications. Many of the precision applications of these clocks, including relativistic geodesy and tests of fundamental physics rely on the intercomparison of at least two optical clocks. Relative comparisons that include single ion clocks, however, can require close to one month of continuous averaging to achieve measurement instabilities near 1 part in 1018. The long averaging times result from limits imposed on the quantum project noise as a result of signal detection from a single ion, as well as atom probe time limitations due to laser-atom decoherence. In this talk I will describe how the phase coherent properties of an optical frequency comb can be used to enable correlated and synchronous measurement of atomic clocks as a means to improve their relative measurement instability by close to a factor of 10, and nearly 100 times speed up in averaging time over conventional measurement techniques.
Atomic clocks have reached the Quantum Projection Noise (QPN) limit of stability and it has been proposed to use the entangled atomic ensemble in order to overcome the QPN limit. We have proposed a new method to lock the phase of the Local Oscillator (LO) to the atomic phase and call, "atomic phase lock (APL)." This APL could possibly overcome the QPN limit without need of preparing the entangled atomic ensemble. Traditional Ramsey method destroys the coherence of the atomic spin due to the projection measurement at each cycle. This destruction and initialization of the phase at each cycle introduce additional noise and the performance of the atomic clock is limited at the white frequency noise level. APL employs dispersion measurements, i.e. Faraday rotation, in order to measure the phase difference without destroying the atomic phase. By repeating the measurement cycle with sufficiently small dead time, one can suppress the LO noise down to white phase noise level, achieving the τ-1 dependence of the Allan variance that can eventually overcome the QPN limit in long term. We are preparing a proof-of-principle experiment using the ensemble of trapped 171Yb+ ions with hyperfine splitting (12.6 GHz) as a clock transition and report the current status of the experiment as well.
In trapped-atom clocks, the primary source of decoherence is often the phase noise of the oscillator. For this case, we derive theoretical performance gains by combining several atomic ensembles. For example, M ensembles of N atoms can be combined with a variety of probe periods, to reduce the frequency variance to M 2^-M times that of standard Ramsey clocks. A similar exponential improvement is possible if the atomic phases of some of the ensembles evolve at reduced frequencies. These ensembles may be constructed from atoms or molecules with lower-frequency transitions, or generated by dynamical decoupling. The ensembles with reduced frequency or probe period are responsible only for counting the integer number of 2 pi phase wraps, and do not affect the clock's systematic errors. Quantum phase measurement with Gaussian initial states allows for smaller ensemble sizes than Ramsey spectroscopy.
The effect of the anti-rotating terms on the short-time evolution and the quantum Zeno (QZE) and anti-Zeno (AQZE) effects is studied for a two-level system coupled to a bosonic environment. A unitary transformation and perturbation theory are used to obtain the electron self-energy, energy shift and the enhanced QZE or the AQZE, simultaneously. The calculated Zeno time depends on the atomic transition frequency sensitively. When the atomic transition frequency is smaller than the central frequency of the spectrum of boson environment, the Zeno time is prolonged and the anti-rotating terms enhance the QZE; when it is larger than that the Zeno time is reduced and the anti-rotating terms enhance the AQZE. PACS numbers: 03.65.Xp; 42.50.Ct; 03.65.Yz 1 The quantum Zeno effect (QZE) and anti-Zeno effects (AQZE) have been widely discussed for decades theoretically [** * early papers and recent papers] and recently experimentally [***the paper of Ref. B and others]. In an unstable quantum twolevel (multi-level) system, frequently measurement can reduce or accelerate the decay