  We experimentally study the influence of dissipation on the driven Dicke
quantum phase transition, realized by coupling external degrees of freedom of a
Bose-Einstein condensate to the light field of a high-finesse optical cavity.
The cavity provides a natural dissipation channel, which gives rise to
vacuum-induced fluctuations and allows us to observe density fluctuations of
the gas in real-time. We monitor the divergence of these fluctuations over two
orders of magnitude while approaching the phase transition and observe a
behavior which significantly deviates from that expected for a closed system. A
correlation analysis of the fluctuations reveals the diverging time scale of
the atomic dynamics and allows us to extract a damping rate for the external
degree of freedom of the atoms. We find good agreement with our theoretical
model including both dissipation via the cavity field and via the atomic field.
Utilizing a dissipation channel to non-destructively gain information about a
quantum many-body system provides a unique path to study the physics of
driven-dissipative systems.
