A single atom noise probe operating beyond the Heisenberg limit

Abstract

According to the Heisenberg uncertainty principle, the energy or frequency uncertainty of a measurement can be at the best inversely proportional to the observation time ($T$). The observation time in an experiment using a quantum mechanical probe is ultimately limited by the coherence time of the probe. Therefore the inverse proportionality of the statistical uncertainty of a frequency measurement to the observation time is also limited up to the coherence time of the probe, provided the systematic uncertainties are well below the statistical uncertainties. With a single laser-cooled barium ion as a quantum probe, we show that the uncertainty in the frequency measurement for a general time-dependent Hamiltonian scales as $1/T^{1.75\pm 0.03}$ as opposed to $1/T$, given by the Heisenberg limit for time-independent Hamiltonian. These measurements, based on controlled feedback Hamiltonian and implemented on a laser cooled single ion, allowed precise measurement of noise frequency in the kHz range. Moreover, based on the observed sensitivity of a single ion experiment presented here, we propose the use of a similar protocol with enhanced sensitivity as a tool to directly verify the existence of certain types of light mass axion-like dark matter particles where no direct measurement protocol exists.

arXiv comment8 figures and 9 pages

References in corpus (23)

• Advances in Quantum Metrology
• Quantum-enhanced measurements: beating the standard quantum limit
• Entanglement, Non-linear Dynamics, and the Heisenberg Limit
• First Dark Matter Search Results from the XENON1T Experiment
• An ${}^{27}$Al${}^{+}$ quantum-logic clock with systematic uncertainty below $10^{-18}$
• Generalized uncertainty relations: Theory, examples, and Lorentz invariance
• Astrophysical Axion Bounds
• Generalized Limits for Single-Parameter Quantum Estimation
• New Observables for Direct Detection of Axion Dark Matter
• Sub-millihertz magnetic spectroscopy with a nanoscale quantum sensor
• Quantum sensing with arbitrary frequency resolution
• Interaction-based quantum metrology showing scaling beyond the Heisenberg limit
• Quantum Metrology: Dynamics vs. Entanglement
• Single Ion Quantum Lock-In Amplifier
• Optimal adaptive control for quantum metrology with time-dependent Hamiltonians
• Exponentially Enhanced Quantum Metrology
• A Low-Noise High-Density Alkali Metal Scalar Magnetometer
• Indirect dark matter searches in Gamma- and Cosmic Rays
• Single-Spin Spectrum-Analyzer for a Strongly Coupled Environment
• Achieving optimal quantum acceleration of frequency estimation using adaptive coherent control
• Quantum parameter estimation with the Landau-Zener transition
• Light shift averaging in paraffin-coated alkali vapor cells
• Precision bounds for noisy nonlinear quantum metrology

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