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Single-ion quantum lock-in amplifier


Quantum metrology1 uses tools from quantum information science to improve measurement signal-to-noise ratios. The challenge is to increase sensitivity while reducing susceptibility to noise, tasks that are often in conflict. Lock-in measurement is a detection scheme designed to overcome this difficulty by spectrally separating signal from noise. Here we report on the implementation of a quantum analogue to the classical lock-in amplifier. All the lock-in operations—modulation, detection and mixing—are performed through the application of non-commuting quantum operators to the electronic spin state of a single, trapped Sr+ ion. We significantly increase its sensitivity to external fields while extending phase coherence by three orders of magnitude, to more than one second. Using this technique, we measure frequency shifts with a sensitivity of 0.42 Hz Hz−1/2 (corresponding to a magnetic field measurement sensitivity of 15 pT Hz−1/2), obtaining an uncertainty of less than 10 mHz (350 fT) after 3,720 seconds of averaging. These sensitivities are limited by quantum projection noise and improve on other single-spin probe technologies2,3 by two orders of magnitude. Our reported sensitivity is sufficient for the measurement of parity non-conservation4, as well as the detection of the magnetic field of a single electronic spin one micrometre from an ion detector with nanometre resolution. As a first application, we perform light shift spectroscopy of a narrow optical quadrupole transition. Finally, we emphasize that the quantum lock-in technique is generic and can potentially enhance the sensitivity of any quantum sensor.

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Figure 1: Measurement scheme.
Figure 2: Sensitivity of the quantum lock-in measurement.
Figure 3: Lock-in measurement of a small signal.
Figure 4: Light shift spectroscopy.

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We thank G. Bensky, G. Gordon and G. Kurizki for discussions. We acknowledge the support by the ISF Morasha program, the Crown Photonics Center and the Minerva Foundation.

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All authors participated in the building of the experimental apparatus. S.K. led the data-taking effort, with help from N.A. Data analysis and development of the analytic theory were performed by S.K. S.K. and R.O. wrote the manuscript. R.O. designed the experiment and supervised the work. All authors participated in discussions, contributed ideas along the way and edited the manuscript.

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Correspondence to Shlomi Kotler.

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The authors declare no competing financial interests.

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Kotler, S., Akerman, N., Glickman, Y. et al. Single-ion quantum lock-in amplifier. Nature 473, 61–65 (2011).

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