  Noiseless measurement of a single quadrature in systems of parametrically
coupled oscillators is theoretically possible by pumping at the sum and
difference frequencies of the two oscillators, realizing a backaction-evading
(BAE) scheme. Although this would hold true in the simplest scenario for a
system with pure three-wave mixing, implementations of this scheme are hindered
by unwanted higher-order parametric processes that destabilize the system and
add noise. We show analytically that detuning the two pumps from the sum and
difference frequencies can stabilize the system and fully recover the BAE
performance, enabling operation at otherwise inaccessible cooperativities. We
also show that the acceleration demonstrated in a weak signal detection
experiment [PRX QUANTUM 4, 020302 (2023)] was only achievable because of this
detuning technique.
