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arXiv:1411.5561 · Physical Review A

Linear and nonlinear Rabi oscillations of a two-level system resonantly coupled to an Anderson-localized mode

Nicolas Bachelard, Rémi Carminati, Patrick Sebbah, C. Vanneste

Published Apr 7, 2015• 4 citations
arXivHTMLPDF

Abstract

We use time-domain numerical simulations of a two-dimensional scattering system to study the interaction of a collection of emitters resonantly coupled to an Anderson-localized mode. For a low electric-field intensity, we observe strong coupling between the emitters and the mode, which is characterized by linear Rabi oscillations. Remarkably, a higher intensity induces a nonlinear interaction between the emitters and the mode, referred to as the dynamical Stark effect, resulting in nonlinear Rabi oscillations. The transition between the two regimes is observed and an analytical model is proposed which accurately describes our numerical observations.

DOI
10.1103/physreva.91.043810

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We use time-domain numerical simulations of a two-dimensional scattering system to study the interaction of a collection of emitters resonantly coupled to an Anderson-localized mode. For a low electric-field intensity, we observe strong coupling between the emitters and the mode, which is characterized by linear Rabi oscillations. Remarkably, a higher intensity induces a nonlinear interaction between the emitters and the mode, referred to as the dynamical Stark effect, resulting in nonlinear Rabi oscillations. The transition between the two regimes is observed and an analytical model is proposed which accurately describes our numerical observations.
We study the dynamics of a set of two-level systems coupled by dipolar interactions under a resonant external Rabi drive. The two-level systems are prepared initially in a coherent product state, and we ask how the nonequilibrium conditions caused by the drive affect this coherence. We study the full nonlinear dynamics of the coupled two-level systems within a classical approximation by analyzing numerically the equations of motion and determining the stability of the collective coherent state within classical Floquet theory. We establish the behavior analytically in the high Rabi coupling limit by employing a Magnus expansion and spin-wave analysis. Our results show that, typically, the dipole interactions between the two-level systems lead to instabilities that cause a breakdown of the collective Rabi oscillations. However, we identify parameter regimes for which the two-level systems undergo collective coherent Rabi oscillations even in the presence of the dipole interactions.
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We investigate excitation dynamics in the system of a quantum dipole emitter (QDE) coupled to a located nearby metal nanoparticle (MNP), which exhibits a dipolar localized surface plasmon (LSP) resonance at the frequency of the QDE radiative transition, in the presence of a strong external resonant electromagnetic field. Considering the QDE-field interactions in the regime of strong QDE-field coupling, we show that the feedback provided by the MNP on the QDE (due to the LSP excitation with the field generated by the dipole moment of the QDE transition) influences significantly the coherent process of Rabi oscillations, resulting in the occurrence of additional satellite frequencies in the radiation spectrum scattered by the QDE-MNP configuration. The relative ratio of high harmonics depends strongly on the QDE-MNP separation, an important characteristic feature that can be used for observing this effect and can be exploited, for example, for controlling distances at the nanoscale.
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.
Rabi oscillations is a key phenomenon among the variety of quantum optical effects that manifests itself in the periodic oscillations of a two-level system between the ground and excited states when interacting with electromagnetic field. Commonly, the rate of these oscillations scales proportionally with the magnitude of the electric field probed by the two-level system. Here, we investigate the interaction of light with a two-level quantum emitter possessing permanent dipole moments. The semi-classical approach to this problem predicts slowing down and even full suppression of Rabi oscillations due to asymmetry in diagonal components of the dipole moment operator of the two-level system. We consider behavior of the system in the fully quantized picture and establish the analytical condition of Rabi oscillations collapse. These results for the first time emphasize the behavior of two-level systems with permanent dipole moments in the few photon regime, and suggest observation of novel quantum optical effects.
We study the interaction of an ac electric field with a semiconductor quantum well by using the effective nonlinear Bloch equations. Only the first two electron subbands in the well are considered. We apply the rotating wave approximation and derive analytical solutions for the Bloch equations for two different values of the detuning. At exact resonance we find a critical value of the Rabi frequency around which the dynamics of the system changes abruptly. Above this critical value one obtains electron oscillations with complete inversion in the two-subband system, while below this value we obtain electron oscillations without complete inversion and with the majority of the electron population on average in the lower subband. We also present numerical calculations for a specific quantum well structure and assess the limits of validity of the analytical results.