  We demonstrate the control of quantum tunneling in an ultracold lattice gas
by the measurement backaction imposed by an imaging process. A {\em in situ}
imaging technique is used to acquire repeated images of an ultracold gas
confined in a shallow optical lattice. The backaction induced by these position
measurements modifies the coherent quantum tunneling of atoms within the
lattice. By smoothly varying the rate at which spatial information is extracted
from the atomic ensemble, we observe the continuous crossover from the 'weak
measurement regime' where position measurements have little influence on the
tunneling dynamics, to the 'strong measurement regime' where
measurement-induced localization causes a large suppression of tunneling. This
suppression of coherent tunneling is a manifestation of the Quantum Zeno
effect. Our study realizes an experimental demonstration of the paradigmatic
Heisenberg microscope in a lattice gas and sheds light on the implications of
quantum measurement on the coherent evolution of a mesoscopic quantum system.
In addition, this demonstrates a powerful technique for the control of an
interacting many-body quantum system via spatially resolved measurement
backaction.
