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We study the resonance and dynamics of a qubit exposed to a strong aperiodicbichromatic field by using a periodic counter-rotating hybridized rotating wave(CHRW) Hamiltonian, which is derived from the original Hamiltonian with theunitary transformations under a reasonable approximation and enables theapplication of the Floquet theory. It is found that the consistency between theCHRW results and numerically exact generalized-Floquet-theory (GFT) results inthe valid regime of the former while the widely used rotating-waveapproximation (RWA) breaks down. We illustrate that the resonance exhibits bandstructure and the Bloch-Siegert shifts induced by the counter-rotatingcouplings of the bichromatic field become notable at the multiphoton resonanceband. In addition, the CHRW method is found to have a great advantage ofefficiency over the GFT approach particularly in the low beat-frequency casewhere the latter converges very slowly. The present CHRW method provides ahighly efficient way to calculate the resonance frequency incorporating theBloch-Siegert shift and provides insights into the effects of thecounter-rotating couplings of the bichromatic field in the strong-drivingregimes.

Multiphoton resonance band and Bloch-Siegert shift in a bichromatically driven qubit