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Physical Review A

Tunable non-Markovian dynamics with a three-level atom mediated by the classical laser in a semi-infinite photonic waveguide

Xin Li, Shuang Xu, X. X. Yi, H. Z. Shen

Published May 6, 2022• 28 citations
Publisher

Abstract

In this work, we investigate the non-Markovian (NM) dynamical evolution of a three-level atom coupled to a semi-infinite one-dimensional photonic waveguide and driven by a classical driving field. The single-end of waveguide behaves as a perfect mirror while light can pass through the opposite end with no backreflection. We derive the exact analytical expressions for the wave function of the driven three-level atom by solving a set of delay differential equations and give the conditions of atom-photon bound state formation that can inhibit the dissipation, which appears in the atom-mirror interspace in order to trap a considerable amount of initial atomic excitation. We show that when the evolution time of the system is shorter than the time delay taken by a photon to perform a round trip between the atom and mirror, the atomic dynamics exhibits Markovian properties, which depend on the driving strength and rescaled parameters. If the evolution time of the system exceeds the time delay, the photon can be reabsorbed by the atom with the photon emitted by the atom having completed the round trip, which exhibits NM memory effects, where the population eventually convergences to the finite-steady values. We also study the influence of the loss and dephasing on the formation of a bound state. Finally, the above results are extended to a more general quantum system involving single-end photonic waveguide coupled to an arbitrary number of noninteracting three-level atoms driven by the driving fields. The presented formalism might open a way to better understand exactly the NM dynamics of driven multilevel atoms coupled to a semi-infinite waveguide.

DOI
10.1103/physreva.105.053706

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In this work, we investigate the non-Markovian (NM) dynamical evolution of a three-level atom coupled to a semi-infinite one-dimensional photonic waveguide and driven by a classical driving field. The single-end of waveguide behaves as a perfect mirror while light can pass through the opposite end with no backreflection. We derive the exact analytical expressions for the wave function of the driven three-level atom by solving a set of delay differential equations and give the conditions of atom-photon bound state formation that can inhibit the dissipation, which appears in the atom-mirror interspace in order to trap a considerable amount of initial atomic excitation. We show that when the evolution time of the system is shorter than the time delay taken by a photon to perform a round trip between the atom and mirror, the atomic dynamics exhibits Markovian properties, which depend on the driving strength and rescaled parameters. If the evolution time of the system exceeds the time delay, the photon can be reabsorbed by the atom with the photon emitted by the atom having completed the round trip, which exhibits NM memory effects, where the population eventually convergences to the finite-steady values. We also study the influence of the loss and dephasing on the formation of a bound state. Finally, the above results are extended to a more general quantum system involving single-end photonic waveguide coupled to an arbitrary number of noninteracting three-level atoms driven by the driving fields. The presented formalism might open a way to better understand exactly the NM dynamics of driven multilevel atoms coupled to a semi-infinite waveguide.
We study the non-Markovian dynamics of a two-level giant atom interacting with a one-dimensional semi-infinite waveguide through multiple coupling points, where a perfect mirror is located at the endpoint of the waveguide. The system enters a non-Markovian process when the travel time of the photon between adjacent coupling points is sufficiently large compared to the inverse of the bare relaxation rate of the giant atom. The photon released by the spontaneous emission of the atom transfers between multiple coupling points through the waveguide or is reabsorbed by the atom with the photon emitted via the atom having completed the round trip after reflection of the mirror, which leads to the photon being trapped and forming bound states. We find that three different types of bound states can be formed in the system, containing the static bound states with no inversion of population, the periodic equal amplitude oscillation with two bound states, and the periodic nonequal amplitude oscillation with three bound states. The physical origins of the three bound states' formation are revealed. Moreover, we consider the influences of the dissipation of unwanted modes and dephasing on the bound states. Finally, we extend the system to a more general case involving many giant atoms coupled into a one-dimensional semi-infinite waveguide. The obtained set of delay differential equations for the giant atoms might open a way to better understand the non-Markovian dynamics of many giant atoms coupled to a semi-infinite waveguide.
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Non-Markovian dynamics with ΛΛΛ-type atomic systems in a single end photonic waveguide
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We investigate the spontaneous emission of a two-level system, e.g., an atom or atomlike object, coupled to a single-end, i.e., a semi-infinite, one-dimensional photonic waveguide such that one end behaves as a perfect mirror while light can pass through the opposite end with no backreflection. Through a quantum microscopic model we show that such geometry can cause nonexponential and long-lived atomic decay. Under suitable conditions, a bound atom-photon stationary state appears in the atom-mirror interspace so as to trap a considerable amount of initial atomic excitation. Yet this can be released by applying an atomic frequency shift, causing a revival of photon emission. The resilience of such effects to typical detrimental factors is analyzed.
Non‐Markovian Dynamics with ΛΛ\LambdaΛ‐Type Atomic Systems in a Single‐End Photonic Waveguide
Abstract In this work, the non‐Markovian dynamical evolution of a ‐type atom interacting with a semi‐infinite 1D photonic waveguide via two atomic transitions is investigated. The waveguide terminates at a perfect mirror, which reflects the light and introduces boundary effects. Exact analytical expressions are derived and it is shown that, under suitable conditions, the instantaneous and retarded decay rates reach equilibrium, leading to the formation of an atom‐photon bound state that suppresses dissipation. Consequently, the atom retains a long‐lived population in the asymptotic time limit. Furthermore, the output field intensity is analyzed and it is demonstrated that blocking one of the coupling channels forces the atomic system to emit photons of a single frequency. Finally, the model is extened to a two‐atom system and the disentanglement dynamics of the two spatially separated atoms are examined. These findings elucidate the dynamic process of spontaneous emission involving multi‐frequency photons from multi‐level atoms and provide insights into the complex interference between different decay pathways.
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