Single Ion Quantum Lock-In Amplifier

Invented by Dicke, the lock-in measurement is a phase-sensitive detection scheme that can extract a signal with a known carrier frequency from an extremely noisy environment. Here we report on the implementation of a quantum analog to the classical lock- in amplifier. All the lock-in operations: modulation, detection and mixing, are performed via the application of non-commuting quantum operators on the electronic spin state of a single trapped Sr+ ion. We increase its sensitivity to external fields while extending phase coherence by three orders of magnitude, to more than one second. With this technique we measure magnetic fields with sensitivity of $25\ pT/\sqrt{Hz}$, and light shifts with an uncertainty below $140\ mHz$ after $1320$ seconds of averaging. These sensitivities are limited by quantum projection noise and, to our knowledge, are more than two orders of magnitude better than with other single-spin probe technologies. As a first application we perform light shift spectroscopy of a narrow optical quadruple transition. We remark that the quantum lock-in technique is generic and can potentially enhance the sensitivity of any quantum sensor. (http://arxiv.org/abs/1101.4885)