High-resolution imaging of a single atom for direct detection of atomic motion*

We present the high-resolution detection of the motion of a single trapped 171Yb$+$ ion using high quality imaging optical elements. Light scattered from a trapped ion is collected in a lens system with 0.6 input numerical aperture and working distance of 11.5 mm.~ Near diffraction-limited performance from the imaging system is verified through the use of a Zernike expansion over the point spread function, giving a minimum spot size (FWHM) of 375nm.~ By means of a position sensitive detector, we measure a photon shot-noise limited sensitivity on the position of the trapped ion to be $\sim$ 5 nm/sqrt(Hz), bottoming out to an minimum absolute sensitivity of $\sim$ 1nm. We use this technique perform to directly measure the rf-induced micromotion of the trapped ion, and this technique can also be used to directly sense the thermal or driven secular motion of the trapped ion.