An analytic connection is established between exact solutions of linearly and circularly driven two-level systems by mapping to confluent Heun and Heun equations respectively, then using bilateral series and perturbative expansions to recover the rotating-wave approximation along with Stark, Bloch-S
Floquet system, Bloch oscillation, and Stark ladder
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abstract
We prove the multi-band Bloch oscillation and Stark ladder in the $nk$ and site representation from the Floquet theorem. The proof is also possible from the equivalence between the Floquet system, Bloch oscillation, and the rotator with spin. We also exactly solve the periodically driven two level atom and two band Bloch oscillation in terms of Heun function.
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quant-ph 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Analytical connection between exact and approximate solutions of the periodically-driven two-level system starting from the Heun equation
An analytic connection is established between exact solutions of linearly and circularly driven two-level systems by mapping to confluent Heun and Heun equations respectively, then using bilateral series and perturbative expansions to recover the rotating-wave approximation along with Stark, Bloch-S