Fixing the rotating-wave approximation for strongly-detuned quantum oscillators

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