How much knowledge can we gain about a physical system and to
what degree can we control it? In quantum optical systems, such as
ion traps or neutral atoms in cavities, single particles and their
correlations can now be probed in a way that is fundamentally
limited only by the laws of quantum mechanics. In contrast, quantum
many-body systems pose entirely new challenges due to the enormous
number of microscopic parameters and their small length- and short
time-scales.
This thesis describes a new approach to probing quantum many-body
systems at the level of individual particles: Using
high-resolution, single-particle-resolved imaging and manipulation
of strongly correlated atoms, single atoms can be detected and
manipulated due to the large length and time-scales and the precise
control of internal degrees of freedom. Such techniques lay
stepping stones for the experimental exploration of new quantum
many-body phenomena and applications thereof, such as quantum
simulation and quantum information, through the design of systems
at the microscopic scale and the measurement of previously
inaccessible observables.
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