  The existence of vacuum fluctuations is one of the most important predictions
of modern quantum field theory. In the vacuum state, fluctuations occurring at
different frequencies are uncorrelated. However, if a parameter in the
Lagrangian of the field is modulated by an external pump, vacuum fluctuations
stimulate spontaneous downconversion processes, creating squeezing between
modes symmetric with respect to half of the frequency of the pump. Here we show
that by double parametric pumping of a superconducting microwave cavity, it is
possible to generate another fundamental type of correlation, namely coherence
between photons in separate frequency modes. The coherence correlations are
tunable by the phases of the pumps and are established by a quantum fluctuation
that stimulates the simultaneous creation of two photon pairs. Our analysis
indicates that the origin of this vacuum-induced coherence is the absence of
'which-way' information in the frequency space.
