Coherence from vacuum fluctuations

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 in the ground state, it is possible to generate another fundamental type of correlation, namely coherence between photons in separate frequency modes that are not directly connected through a single downconversion process. The coherence is tunable by the phases of the pumps and it is established by a quantum fluctuation that takes simultaneously part in 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.