  We present the exact analytical solution of the explicitly time-periodic
quantum Langevin equation describing the dual-beam backaction-evasion
measurement of a single mechanical oscillator quadrature due to Braginsky,
Vorontsov and Thorne beyond the commonly used rotating-wave approximation. We
show that counterrotating terms lead to extra sidebands in the optical and
mechanical spectra and to a modification of the main peak. Physically, the
backaction of the measurement is due to periodic coupling of the mechanical
resonator to a light field quadrature that only contains cavity-filtered shot
noise. Since this fact is independent of other degrees of freedom the resonator
might be coupled to, our solution can be generalized, including to
dissipatively or parametrically squeezed oscillators, as well as recent
two-mode backaction evasion measurements.
