  High-quality superconducting oscillators have been successfully used for
quantum control and readout devices in conjunction with superconducting qubits.
Also, it is well known that squeezed states can improve the accuracy of
measurements to subquantum, or at least subthermal, levels. Here we show
theoretically how to produce squeezed states of microwave radiation in a
superconducting oscillator with tunable parameters. The circuit impedance, and
thus the resonance frequency, can be changed by controlling the state of an RF
SQUID inductively coupled to the oscillator. By repeatedly shifting the
resonance frequency between any two values, it is possible to produce squeezed
and subthermal states of the electromagnetic field in the (0.1--10) GHz range,
even when the relative frequency change is small. We propose experimental
protocols for the verification of squeezed state generation, and for their use
to improve the readout fidelity when such oscillators serve as quantum
transducers.
