Non-Hermitian wave packet approximation of Bloch optical equations

Abstract

We introduce a non-Hermitian approximation of Bloch optical equations. This approximation provides a complete description of the excitation, relaxation, and decoherence dynamics of ensembles of coupled quantum systems in weak laser fields, taking into account collective effects and dephasing. In the proposed method, one propagates the wave function of the system instead of a complete density matrix. Relaxation and dephasing are taken into account via automatically adjusted time-dependent gain and decay rates. As an application, we compute the numerical wave packet solution of a time-dependent non-Hermitian Schrödinger equation describing the interaction of electromagnetic radiation with a quantum nano-structure, and compare the calculated transmission, reflection, and absorption spectra with those obtained from the numerical solution of the Liouville-von Neumann equation. It is shown that the proposed wave packet scheme is significantly faster than the propagation of the full density matrix while maintaining small error. We provide the key ingredients for easy-to-use implementation of the proposed scheme and identify the limits and error scaling of this approximation.

Molecular plasmonics: The role of rovibrational molecular states in exciton-plasmon materials under strong-coupling conditions

“…With the knowledge of the electric field E( r, t) the molecular dynamics is described by solving the non-Hermitian Schrödinger equation that we have developed recently 14,15 .…”

“…Such matrix elements are given in Ref. [14] and for the potential curves we use Table I. These parameters have been chosen such that the absorption spectra of the molecules lie in the energy domain of the SPP resonance.…”

“…In terms of rotation, the molecules are assumed to be initially isotropically distributed (with N = M = 0) or pre-aligned (see Section III). The essence of our non-Hermitian Schrödinger approach lies in the introduction of time-dependent gain and decay rates 14,15 for the ground and excited electronic states. These rates can be viewed as the positive and negative imaginary parts of the ground and excited states energies which are simple functions 14,15 that depend on the nonradiative decay rate of the excited state, the pure dephasing rate of the molecular system, and the population difference between the ground and excited electronic states.…”

Theoretical analysis of dipole-induced electromagnetic transparency

“…The idea is to separate the description of EM waves from the dynamics of quantum emitters considering the spatiotemporal evolution of EM radiation using classical Maxwell's equations while applying the full machinery of quantum mechanics to describe the response of quantum emitters to EM excitation. This results in a system of coupled Maxwell-Bloch equations [30], If one wants to observe collective effects, it is imperative to solve the corresponding equations of motion self-consistently without any decoupling [31].…”

“…However, the splitting of the excited state leaves spectral holes in the reflection spectra [ Fig. 9(c)], If the system is com prised o f em itters with many optically active excited states that can be populated by the incident laser pulse (such as m olecules w ith rovibrational levels, for instance [31]), each transition interacts w ith the others and interferes constructively or destructively at different frequencies, leading to reflected pulses w ith m ore than a single frequency am plified or rem oved from the spectrum . In particular, the spectra o f the transm itted pulse in Figs.…”