For a periodically driven open quantum system, the Floquet theorem states that the time evolution operator $Λ(t,0)$ of the system can be factorized as $Λ(t,0)=\mathcal{D}(t)e^{\mathcal{L}_{eff}t}$ with micro-motion operator $\mathcal{D}(t)$ possessing the same period as the external driving, and time-independent operator $\mathcal{L}_{eff}$ . In this work, we extend this theorem to open systems that follow a modulated periodic evolution, in which the fast part is periodic while the slow part breaks the periodicity. We derive a factorization for the time evolution operator that separates the long time dynamics and the micro-motion for the open quantum system. High-frequency expansions for the effective evolution operator control the long time dynamics, and the micro-motion operator is also given and discussed. It may find applications in quantum engineering with open systems following modulated periodic evolution.For a periodically driven open quantum system, the Floquet theorem states that the time evolution operator $Λ(t,0)$ of the system can be factorized as $Λ(t,0)=\mathcal{D}(t)e^{\mathcal{L}_{eff}t}$ with micro-motion operator $\mathcal{D}(t)$ possessing the same period as the external driving, and time-independent operator $\mathcal{L}_{eff}$. In this work, we extend this theorem to open systems that follow a modulated periodic evolution, in which the fast part is periodic while the slow part breaks the periodicity. We derive a factorization for the time evolution operator that separates the long time dynamics and the micro-motion for the open quantum system. High-frequency expansions for the effective evolution operator control the long time dynamics, and the micro-motion operator is also given and discussed. It may find applications in quantum engineering with open systems following modulated periodic evolution.

arXiv:1707.05030Jul 17, 20174 citations

Theory of open systems

L. A. Lugiato

Physica A Statistical Mechanics and its ApplicationsJan 1, 19766 citations

TIME EVOLUTION OF ATOMIC RESPONSE AND LIGHT AMPLIFICATION MECHANISM IN AN OPEN I NVERSIONLESS LASING SYSTEM

Fan Xi-jun, Shufen Tian, LI JIAN +3 more

We study the law of time evolution of atomic response in an open Λ-type inversi onless lasing system,elucidate the light amplification mechanism without inversi on,and find that the character of the time evolution of atomic response in an open system is obviously different from that in a corresponding closed system. Weconsider that the variation of the oscillation frequency and anharmonic oscillat ion in the process of time evolution originate from the stochastic coherence pro perty of atom oscillators in the system.We study the law of time evolution of atomic response in an open Λ-type inversi onless lasing system,elucidate the light amplification mechanism without inversi on,and find that the character of the time evolution of atomic response in an open system is obviously different from that in a corresponding closed system. Weconsider that the variation of the oscillation frequency and anharmonic oscillat ion in the process of time evolution originate from the stochastic coherence pro perty of atom oscillators in the system.

Acta Physica SinicaJan 1, 20005 citations

For a periodically driven open quantum system, the Floquet theorem states that the time evolution operator

Λ(t,0)

of the system can be factorized as

Λ(t,0)=\mathcal{D}(t)e^{\mathcal{L}_{eff}t}

with micro-motion operator

\mathcal{D}(t)

possessing the same period as the external driving, and time-independent operator

\mathcal{L}_{eff}

. In this work, we extend this theorem to open systems that follow a modulated periodic evolution, in which the fast part is periodic while the slow part breaks the periodicity. We derive a factorization for the time evolution operator that separates the long time dynamics and the micro-motion for the open quantum system. High-frequency expansions for the effective evolution operator control the long time dynamics, and the micro-motion operator is also given and discussed. It may find applications in quantum engineering with open systems following modulated periodic evolution.