Fixing the rotating-wave approximation for strongly detuned quantum oscillators

Periodically driven oscillators are commonly described in a frame corotating with the drive and using rotating-wave approximation (RWA). This description, however, is known to induce errors for off-resonant driving. Here, we show that standard quantum creation annihilation of particles oscillators' natural frequency, necessarily leads incorrect results when combined RWA. We demonstrate this on simple (quantum) harmonic oscillator present an alternative operator basis reconciles RWA The approach also applicable more complex models, where it accounts discrepancies. As example, advantage our scheme Duffing oscillator.