  We propose an efficient method for controlled generation of field squeezing
with cold atomic clouds trapped close to a superconducting transmission line
resonator. It is shown that, based on the coherent strong magnetic coupling
between the collective atomic spins and microwave fields in the transmission
line resonator, two-mode or single mode field squeezed states can be generated
through coherent control on the dynamics of the system. The degree of squeezing
and preparing time can be directly controlled through tuning the external
classical fields. This protocol may offer a promising platform for implementing
scalable on-chip quantum information processing with continuous variables.
