We study rotating squeezed quantum states created by a parametric resonance in an open harmonic system. As a specific realization of the phenomenon we study a mesoscopic SQUID loop where the state preparation procedure is simple in principle and feasible with currently available experimental methods. By solving dynamics and calculating spectral properties we show that quantum fluctuations of SQUID observables can be reduced below their groundstate value. The measurement is introduced by coupling the SQUID to a transmission line carrying the radiation to a secondary measurement device. Besides the theoretical interest, our studies are motivated by an opportunity for a practical quantum noise engineering.
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