  Understanding the effects of interactions in complex quantum systems beyond
the mean-field paradigm constitutes a fundamental problem in physics. Here, we
show how the atom numbers and interactions in a Bose-Bose mixture can be tuned
to cancel mean-field interactions completely. The resulting system is entirely
governed by quantum fluctuations -- specifically the Lee-Huang-Yang
correlations. We derive an effective one-component Gross-Pitaevskii equation
for this system, which is shown to be very accurate by comparison with a full
two-component description. This allows us to show how the Lee-Huang-Yang
correlation energy can be accurately measured using two powerful probes of
atomic gases: collective excitations and radio-frequency spectroscopy.
Importantly, the behavior of the system is robust against deviations from the
atom number and interaction criteria for canceling the mean-field interactions.
This shows that it is feasible to realize a setting where quantum fluctuations
are not masked by mean-field forces, allowing investigations of the
Lee-Huang-Yang correction at unprecedented precision.
