Floquet states in dissipative open quantum systems

(submitted), (2019)

Floquet states in dissipative open quantum systems

S. A. Sato, U. De Giovannini, S. Aeschlimann, I. Gierz, H. Hübener, A. Rubio

We theoretically investigate basic properties of nonequilibrium steady states of periodically-driven open quantum systems based on the full solution of the Maxwell-Bloch equation. In a resonantly driving condition, we find that the transverse relaxation, also known as decoherence, significantly destructs the formation of Floquet states while the longitudinal relaxation does not directly affect it. Furthermore, by evaluating the quasienergy spectrum of the nonequilibrium steady states, we demonstrate that the Rabi splitting can be observed as long as the decoherence time is as short as one third of the Rabi-cycle. Moreover, we find that Floquet states can be formed even under significant dissipation even when the decoherence time is substantially shorter than the cycle of driving, once the driving field strength becomes strong enough. In an off-resonant condition, we demonstrate that the Floquet states can be realized even in weak field regimes because the system is not excited and the decoherence mechanism is not activated. Once the field strength becomes strong enough, the system can be excited by nonlinear processes and the decoherence process becomes active. As a result, the Floquet states are significantly disturbed by the environment even in the off-resonant condition. Thus, we show here that the suppression of heating is a key condition for the realization of Floquet states in both on and off-resonant conditions not only because it prevents material damage but also because it contributes to preserving coherence.

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We acknowledge fruitful discussions with M. A. Sentef and P. Tang. This work was supported by the European Research Council (ERC-2015-AdG694097) and JST-CREST under Grant No. JP-MJCR16N5. The Flatiron Institute is a division of the Simons Foundation. S.A.S. gratefully acknowledges the fellowship from the Alexander von Humboldt Foundation. A.R. acknowledges support from the Cluster of Excellence 'Advanced Imaging of Matter' (AIM).

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