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Periodically-driven oscillators are commonly described in a frame co-rotatingwith the drive and using the rotating-wave approximation (RWA). Thisdescription, however, is known to induce errors for off-resonant driving. Herewe show that the standard quantum description, using creation and annihilationof particles with the oscillator's natural frequency, necessarily leads toincorrect results when combined with the RWA. We demonstrate this on the simpleharmonic oscillator and present an alternative operator basis which reconcilesthe RWA with off-resonant driving. The approach is also applicable to morecomplex models, where it accounts for known discrepancies. As an example, wedemonstrate the advantage of our scheme on the driven quantum Duffingoscillator.

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