Validity of many-mode Floquet theory with commensurate frequencies

Abstract

Many-mode Floquet theory [T.-S. Ho, S.-I. Chu, and J. V. Tietz, Chem. Phys. Lett. 96, 464 (1983)] is a technique for solving the time-dependent Schrödinger equation in the special case of multiple periodic fields, but its limitations are not well understood. We show that for a Hamiltonian consisting of two time-periodic couplings of commensurate frequencies (integer multiples of a common frequency), many-mode Floquet theory provides a correct expression for unitary time evolution. However, caution must be taken in the interpretation of the eigenvalues and eigenvectors of the corresponding many-mode Floquet Hamiltonian, as only part of its spectrum is directly relevant to time evolution. We give a physical interpretation for the remainder of the spectrum of the Hamiltonian. These results are relevant to the engineering of quantum systems using multiple controllable periodic fields.

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

“…This is consistent with the previous finding that the phases of the bichromatic field are found to have no influence on the quasienergies. [ 37,38 ] For this reason, we consider $$\phi _1=\phi _2=0$$ throughout this work. Third, it is evident that when $$d=0$$, $$\overline{P}$$ takes on the maximal value 1/2, which signifies the resonance response of the qubit to the external field.…”

Engineering, control and longitudinal readout of Floquet qubits

“…MMFT has been implemented into a numerical solver using truncated Fourier bases [25], which we do not make use of in this work. However, the generalization of quasienergies and Floquet Modes provides an analytical approach to understand the dynamics of driven systems with additional drives such as naturally occurs in Floquet qubits.…”

Harmonic dual dressing of spin one-half systems

“…Using the perturbation Eqs. ( 30) and (31) for synthetic field and g-tensor, the compensation of such field is produced by an Ω xz strong dressing field applied along the x axis, and (Ω y5 , Ω y6 ) weak dressing fields along the y axis, at even and odd high harmonics as in Sec.IV B. In an experiment this dressing scheme may be produced by a single source feeding separate coils for the x and z axes, with different amplitudes producing the required orthogonality to the ω 0xz static field.…”

“…Tunneling suppression in a dual well with harmonic bichromatic driving with is examined theoretically in [29] and for a tight-binding model in [30]. For the same driving a recent work [31] compares different theoretical approaches combined to a careful study of the dressing field phase. In most cases numerical solutions are the final tool.…”