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arXiv:1202.2307 · Physical Review Letters

Shot-Noise-Limited Monitoring and Phase Locking of the Motion of a Single Trapped Ion

Pavel A. Bushev, Gabriel Hetet, L. Slodička, D. Rotter, M. A. Wilson, Ferdinand Schmidt‐Kaler, Jürgen Eschner, R. Blatt

Published Mar 26, 2013• 18 citations
arXivHTMLPDF

Abstract

We perform a high-resolution real-time readout of the motion of a single trapped and laser-cooled Ba+ ion. By using an interferometric setup, we demonstrate a shot-noise-limited measurement of thermal oscillations with a resolution of 4 times the standard quantum limit. We apply the real-time monitoring for phase control of the ion motion through a feedback loop, suppressing the photon recoil-induced phase diffusion. Because of the spectral narrowing in the phase-locked mode, the coherent ion oscillation is measured with a resolution of about 0.3 times the standard quantum limit.

DOI
10.1103/physrevlett.110.133602

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We perform a high-resolution real-time readout of the motion of a single trapped and laser-cooled Ba+ ion. By using an interferometric setup, we demonstrate a shot-noise-limited measurement of thermal oscillations with a resolution of 4 times the standard quantum limit. We apply the real-time monitoring for phase control of the ion motion through a feedback loop, suppressing the photon recoil-induced phase diffusion. Because of the spectral narrowing in the phase-locked mode, the coherent ion oscillation is measured with a resolution of about 0.3 times the standard quantum limit.
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A single trapped ion, laser cooled into its quantum ground state of motion, may be used as a very-low-temperature detector of radio-frequency signals applied to the trap end caps. If the signal source is a resonant oscillator of sufficiently high Q, the source may also be placed in its quantum ground state by coupling to the ion. Parametric couplings may be used to cool and detect source modes other than the mode directly coupled to the ion. A theoretical analysis of these cooling and detection processes is presented, and as an example, their application to single trapped electron and proton spectroscopy is examined. Squeezing and low noise detection of one quadrature component of the source oscillation are also discussed. The techniques discussed here may lead to radio-frequency measurements of improved accuracy and sensitivity. Cooling and detection of vibrations of macroscopic oscillators also appear possible.
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We discuss continuous observation of the momentum of a single atom by employing the high velocity sensitivity of the index of refraction in a driven $\ensuremath{\Lambda}$-system based on electromagnetically induced transparency. In the ideal limit of unit collection efficiency this provides a quantum-limited measurement with minimal backaction on the atomic motion. A feedback loop, which drives the atom with a force proportional to measured signal, provides a cooling mechanism for the atomic motion. We derive the master equation which describes the feedback cooling and show that in the Lamb-Dicke limit the steady state energies are close to the ground state, limited only by the photon collection efficiency. Outside of the Lamb-Dicke regime the predicted temperatures are well below the Doppler limit.
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