  Josephson parametric amplifiers (JPA) are promising devices for applications
in circuit quantum electrodynamics (QED) and for studies on propagating quantum
microwaves because of their good noise performance. In this work, we present a
systematic characterization of a flux-driven JPA at millikelvin temperatures.
In particular, we study in detail its squeezing properties by two different
detection techniques. With the homodyne setup, we observe squeezing of vacuum
fluctuations by superposing signal and idler bands. For a quantitative analysis
we apply dual-path cross-correlation techniques to reconstruct the Wigner
functions of various squeezed vacuum and thermal states. At 10 dB signal gain,
we find 4.9+-0.2 dB squeezing below vacuum. In addition, we discuss the physics
behind squeezed coherent microwave fields. Finally, we analyze the JPA noise
temperature in the degenerate mode and find a value smaller than the standard
quantum limit for phase-insensitive amplifiers.
