  Fast control of quantum systems is essential in order to make use of quantum
properties before they are degraded by decoherence. This is important for
quantum-enhanced information processing, as well as for pushing quantum systems
into macroscopic regimes at the boundary between quantum and classical physics.
Bang-bang control attains the ultimate speed limit by making large changes to
control fields on timescales much faster than the system can respond, however
these methods are often challenging to implement experimentally. Here we
demonstrate bang-bang control of a trapped-ion oscillator using nano-second
switching of the trapping potentials. We perform controlled displacements which
allow us to realize quantum states with up to 10,000 quanta of energy. We use
these displaced states to verify the form of the ion-light interaction at high
excitations which are far outside the usual regime of operation. These methods
provide new possibilities for quantum-state manipulation and generation,
alongside the potential for a significant increase in operational clock speed
for ion-trap quantum information processing.
