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arXiv:2207.10207 · Physical Review A

Undamped Rabi oscillations due to polaron-emitter hybrid states in a nonlinear photonic waveguide coupled to emitters

Jugal Talukdar, D. Blume

Published Jul 29, 2022• 7 citations
arXivHTMLPDF

Abstract

The collective dynamics of two noninteracting two-level emitters, which are coupled to a structured wave guide that supports two-photon bound states, is investigated. Tuning the energy of the two emitters such that they are in resonance with the two-photon bound-state energy band, we identify parameter regimes where the system displays fractional populations and essentially undamped Rabi oscillations. The Rabi oscillations, which have no analog in the single-emitter dynamics, are attributed to the existence of a collective polaron-like photonic state that is induced by the emitter-photon coupling. The full dynamics is reproduced by a two-state model in which the photonic polaron interacts with the state $|e,e,\text{vac}\ensuremath{\rangle}$ (two emitters in their excited state and empty wave guide) through a Rabi coupling frequency that depends on the emitter separation. Our work demonstrates that emitter-photon coupling can lead to an all-to-all momentum space interaction between two-photon bound states and tunable non-Markovian dynamics, opening up exciting directions for emitter arrays coupled to a waveguide.

DOI
10.1103/physreva.106.013722

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The collective dynamics of two noninteracting two-level emitters, which are coupled to a structured wave guide that supports two-photon bound states, is investigated. Tuning the energy of the two emitters such that they are in resonance with the two-photon bound-state energy band, we identify parameter regimes where the system displays fractional populations and essentially undamped Rabi oscillations. The Rabi oscillations, which have no analog in the single-emitter dynamics, are attributed to the existence of a collective polaron-like photonic state that is induced by the emitter-photon coupling. The full dynamics is reproduced by a two-state model in which the photonic polaron interacts with the state ∣e,e,vac\ensuremath⟩|e,e,\text{vac}\ensuremath{\rangle}∣e,e,vac\ensuremath⟩ (two emitters in their excited state and empty wave guide) through a Rabi coupling frequency that depends on the emitter separation. Our work demonstrates that emitter-photon coupling can lead to an all-to-all momentum space interaction between two-photon bound states and tunable non-Markovian dynamics, opening up exciting directions for emitter arrays coupled to a waveguide.
We consider two noninteracting two-level emitters that are coupled weakly to a one-dimensional nonlinear waveguide. Due to the Kerr-like nonlinearity, the waveguide considered supports---in addition to the scattering continuum---a two-body bound state. As such, the waveguide models a bath with nontrivial mode structure. Solving the time-dependent Schr\"odinger equation, the radiation dynamics of the two emitters, initially prepared in their excited states, is presented. Changing the emitter frequency such that the two-emitter energy is in resonance with one of the two-body bound states, radiation dynamics ranging from exponential decay to fractional populations to Rabi oscillations is observed. Along with the detuning, the dependence on the separation of the two emitters is investigated. Approximate reduced Hilbert-space formulations, which result in effective emitter separation and momentum dependent interactions, elucidate the underlying physical mechanisms and provide an avenue to showcase the features that would be absent if the one-dimensional waveguide did not contain a nonlinearity. Our theoretical findings apply to a number of experimental platforms and the predictions can be tested with state-of-the-art technology. In addition, the weak-coupling Schr\"odinger equation based results provide critical guidance for the development of master equation approaches.
Waveguide quantum electrodynamics platforms have emerged as promising candidates for exploring and implementing non-Markovian quantum phenomena. In this work, we investigate the formation and dynamics of superpositions of bound states in a cavity array waveguide coupled to two spatially separated quantum emitters. By tuning the system parameters, we show that spontaneous emission can drive the system into non-local equilibrium states in which both photonic and emitter populations exhibit persistent oscillations. These states arise from the coexistence of bound states embedded in the energy continuum and bound states outside it, leading to hybrid oscillatory modes. We analytically derive the conditions required for the emergence of these states, numerically simulate their formation through spontaneous emission, and predict their long-time behaviour. Our results demonstrate that such bound-state superpositions enable the generation of emitter-emitter interaction through free evolution, while supporting oscillatory breathing modes of the photon density between the emitters.
We study the dynamics of two giant atoms interacting with a coupled resonator waveguide (CRW) beyond the Markovian approximation. The distinct atomic configurations determine the number of bound states in the continuum (BICs), leading to different dynamical behaviors. Our results show that when the system supports two BICs, Rabi oscillations dominate the dynamics, whereas fractional population dynamics emerge in the presence of a single BIC. The connection between these dynamics and the existence of BICs is further verified by analyzing the photonic distribution in the CRW during time evolution. These findings challenge the conventional notion that the environment always induces dissipation and decoherence. Instead, the bound states in the CRW-emitter coupled system can suppress complete dissipation of the emitters. We also quantitatively illustrate the memory effect of the waveguide, which serves as the environment of the giant-atom feature that can only be captured within our non-Markovian treatment. This work offers an effective approach for controlling dissipative dynamics in open quantum systems.
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Abstract We investigate the quantum dynamics of two two-level atoms coupled to a one-dimensional resonator waveguide. Using the resolvent method, we obtain exact analytical solutions for the atomic evolution and photon scattering processes within the single-excitation subspace. The photonic band structure of the waveguide dictates distinctly different dynamical regimes. For atomic frequencies at the band center and small interatomic separation, the system exhibits Markovian decay and relaxes into a steady-state subradiant Bell entangled state. In contrast, near the band edge, non-Markovian dynamics dominates, leading to the formation of atom-photon bound states that mediate persistent, coherent interactions between the atoms. Furthermore, we demonstrate that the atomic detuning and separation provide effective control over singlephoton scattering, enabling a tunable quantum interface.