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We analyze two-time correlators as the most natural characteristic of apropagating quadrature-squeezed field in the transient regime. The consideredsystem is a parametrically driven resonator with a time-dependent drive. Usinga semiclassical approach derived from the input-output theory, we develop atechnique for calculation of the two-time correlators, which are directlyrelated to fluctuations of the measured integrated signal. While in the steadystate the correlators are determined by three parameters (as for thephase-space ellipse describing a squeezed state), four parameters are necessaryin the transient regime. The formalism can be generalized to weakly nonlinearresonators with additional coherent drive. We focus on squeezed microwavefields relevant to the measurement of superconducting qubits; however, ourformalism is also applicable to optical systems. The results can be readilyverified experimentally.

Two-time correlators for propagating squeezed microwave in transients