A trapped-ion phonon laser and the detection of ultra-weak forces

This dissertation reports on the demonstration of a mechanical analogue to an optical laser, a ”phonon laser”, using a single trapped ion. Furthermore, we show that the dynamics of this system are surprisingly sensitive to external fields; we demonstrate phase synchronization (”injection locking”) to an external signal by applying forces as weak as 5 yN (yocto=10). This enormous sensitivity might allow the detection of the nuclear spin of a single atom or molecule. A single magnesium ion is trapped in a linear radio-frequency ion trap and illuminated by two laser beams. One is tuned slightly above an atomic transition, blue-detuned, and amplifies an existing motion. A second, red-detuned laser beam damps the motion. For certain parameters, the ion starts to oscillate from noise. The forces on the ion saturate, so it oscillates with a stable amplitude. This oscillation is sustained by the stimulated generation of phonons similar to an optical laser. The simplicity of this system allows an in-depth theoretical description which precisely matches our observations. Thus, we report on the first mechanical analogue to an optical laser, a trapped-ion phonon laser. In contrast to an optical laser, our single trapped-ion phonon laser does not emit phonons. In order to coherently manipulate this system from outside, we demonstrate phase synchronization, also known as injection locking, to an external signal. This is a technologically important phenomenon, e.g., used to transfer stability in optical lasers. We have developed two techniques to investigate the injection locking dynamics: We analyze the motional spectrum of the ion with a spatially selective Fourier transform method and retrieve the phase between the injected signal and the oscillator using stroboscopic imaging. In both cases we find excellent agreement between theory and experiment, and obtain unique insight into the underlying mechanisms. The forces which induce phase synchronization are minute–the smallest force we observed is 5 yN. In comparison: This displaces the ion by one nanometer only, which is 2000 times less than the resolution of our imaging system or the extent of the thermal motion of the ion. Therefore, we conclude that this system appears promising for the detection of ultra-weak forces. Conceivable would be the detection of nuclear spin flips of a single trapped atomic or molecular ion.