  We minimize the stray electric field in a linear Paul trap quickly and
accurately, by applying interferometry pulse sequences to a trapped ion optical
qubit. The interferometry sequences are sensitive to the change of ion
equilibrium position when the trap stiffness is changed, and we use this to
determine the stray electric field. The simplest pulse sequence is a two-pulse
Ramsey sequence, and longer sequences with multiple pulses offer a higher
precision. The methods allow the stray field strength to be minimized beyond
state-of-the-art levels, with only modest experimental requirements. Using a
sequence of nine pulses we reduce the 2D stray field strength to
$(10.5\pm0.8)\,\mathrm{mV\,m^{-1}}$ in $11\,\mathrm{s}$ measurement time. The
pulse sequences are easy to implement and automate, and they are robust against
laser detuning and pulse area errors.
  We use interferometry sequences with different lengths and precisions to
measure the stray field with an uncertainty below the standard quantum limit.
This marks a real-world case in which quantum metrology offers a significant
enhancement. Also, we minimize micromotion in 2D using a single probe laser, by
using an interferometry method together with the resolved sideband method; this
is useful for experiments with restricted optical access.
  Furthermore, a technique presented in this work is related to quantum
protocols for synchronising clocks; we demonstrate these protocols here.
