Abstract
We investigate the quantum dynamics of a two-level system driven by a bichromatic field, using a non-perturbative analysis. We make special emphasis in the case of two large frequencies, where the Magnus expansion can fail, and in the case of a large and a small frequency, where resonances can dominate. In the first case, we show that two large frequencies can be combined to produce an effective adiabatic evolution. In the second case, we show that high frequency terms (which naturally arise as corrections to the adiabatic evolution obtained in the first case) can be used to produce a highly tunable adiabatic evolution over the whole Bloch sphere, controlled by multi-photon resonances.
Highlights
Perturbing a system out of equilibrium is at the heart of physics, as it allows one to extract information about its properties by just measuring the response to the perturbation
Applying periodic perturbations has been shown to be a versatile tool to manipulate physical systems. They allow one to control spin qubits in quantum dots [7,8,9,10,11], or to induce new electronic, dynamical, and topological properties [12,13,14,15,16]. These works typically consider monochromatic driving, bichromatic fields have been used in a few occasions [17,18,19,20], showing that their potential has not been fully explored
We show the dynamics for the off-diagonal component of U (t ) in the Appendix B, Fig. 7, to confirm that the long-time behavior is controlled by the nonperturbative correction u1(τ1), which produces the rotation proportional to σy in Eq (19)
Summary
Perturbing a system out of equilibrium is at the heart of physics, as it allows one to extract information about its properties by just measuring the response to the perturbation. Applying periodic perturbations has been shown to be a versatile tool to manipulate physical systems They allow one to control spin qubits in quantum dots [7,8,9,10,11], or to induce new electronic, dynamical, and topological properties [12,13,14,15,16]. These works typically consider monochromatic driving, bichromatic fields have been used in a few occasions [17,18,19,20], showing that their potential has not been fully explored. Our analysis can be extended to the analysis of a multilevel system under multichromatic driving in a straightforward manner
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