Multiphoton Resonance Band and Bloch–Siegert Shift in a Bichromatically Driven Qubit

Abstract

AbstractThe resonance and dynamics of a qubit exposed to a strong aperiodic bichromatic field are studied by using a periodic counter‐rotating hybridized rotating wave (CHRW) Hamiltonian, which is derived from the original Hamiltonian with the unitary transformations under a reasonable approximation and enables the application of the Floquet theory. It is found that the consistency between the CHRW results and numerically exact generalized‐Floquet‐theory (GFT) results in the valid regime of the former while the widely used rotating‐wave approximation breaks down. It is illustrated that the resonance exhibits band structure and the Bloch–Siegert shifts induced by the counter‐rotating couplings of the bichromatic field become notable at the multiphoton resonance band. In addition, the CHRW method is found to have a great advantage of efficiency over the GFT approach particularly in the low beat‐frequency case where the latter converges very slowly. The present CHRW method provides a highly efficient way to calculate the resonance frequency incorporating the Bloch–Siegert shift and provides insights into the effects of the counter‐rotating couplings of the bichromatic field in the strong‐driving regimes.