Quantum-limited cooling and detection of radio-frequency oscillations by laser-cooled ions

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.