  We analyze the dynamics of a superconducting qubit and the phenomenon of
multiorder Rabi oscillations in the presence of a time-modulated external
field. Such a field is also presented as a bichromatic field consisting of two
spectral components, which are symmetrically detuned from the qubit resonance
frequency. This approach leads to obtaining qualitative quantum effects beyond
those for the case of monochromatic excitation of qubits. We calculate Floquet
states and quasienergies of the composite system "superconducting qubit plus
time-modulated field" for various resonant regimes. We analyze the dependence
of quasienergies from the amplitude of an external field, demonstrating the
zeros of difference between quasienergies. We show that, as a rule, populations
of qubit states exhibit aperiodic oscillations, but we demonstrate the specific
important regimes in which dynamics of populations becomes periodically
regular.

Quantum Physics;Mesoscale and Nanoscale Physics;Superconductivity