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Chinese Physics Letters

Resonance Fluorescence Spectrum by Two-Level System Without the Rotating Wave Approximation

Renhong Liu, Weihan Tan

Published Jan 1, 1999• 5 citations
Publisher

Abstract

In this paper the theory of resonance fluorescence spectrum by two-level system is presented without the assumption of rotating wave approximation. However, in this case, the application of quantum fluctuation-regression theorem to evaluate the resonance fluorescence spectrum takes a more complicated form. The prominent features of the spectrum calculated are the double splitting on the central and side bands and the emergence of harmonics in the asymmetric spectra.

DOI
10.1088/0256-307x/16/1/009

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In this paper the theory of resonance fluorescence spectrum by two-level system is presented without the assumption of rotating wave approximation. However, in this case, the application of quantum fluctuation-regression theorem to evaluate the resonance fluorescence spectrum takes a more complicated form. The prominent features of the spectrum calculated are the double splitting on the central and side bands and the emergence of harmonics in the asymmetric spectra.
We examine the transient resonance fluorescence (RF) spectrum from a two-level atom excited by a rectangular laser pulse containing many frequency modes. We predict exactly the qualitative features of the spectra in which the number of components and their locations in the spectra are precisely specified. The extreme case of the infinite-mode limit is also analysed. The RF spectra (with and without the rotating wave approximation) of a harmonic oscillator excited by a similar pulse have been calculated.
We study the fluorescence spectrum of a strongly driven two-level system (TLS) with modulated transition frequency, which is a bichromatically driven TLS and has multiple resonance frequencies. We are aiming to provide a reliable description of the fluorescence in a regime that is difficult to tackle with perturbation theory and the rotating-wave approximation (RWA), and illustrate the spectral features of the fluorescence under off- and multiphoton-resonance conditions. To go beyond the RWA, we use a semianalytical counter-rotating-hybridized rotating-wave method that combines a unitary transformation and Floquet theory to calculate the two-mode Floquet states and quasienergies for the bichromatically driven TLS. We then solve the master equation accounting for the spontaneous decay in the bases of the two-mode Floquet states, and derive a physically transparent fluorescence spectrum. In comparison with the numerically exact spectrum from the generalized Floquet-Liouville approach, the present spectrum is found to be applicable in a wide range of the parameters where the RWA and the secular approximation may break down. We find that the counter-rotating (CR) terms of the transverse field omitted in the RWA have non-negligible contributions to the spectrum under certain conditions. Particularly, at the multiphoton resonance the width of which is comparable with the Bloch-Siegert shift, the RWA and non-RWA spectra markedly differ from each other because of the CR-induced shift. We also analyze the symmetry of the spectrum in terms of the transition matrix elements between the two-mode Floquet states. We show that the strict symmetry of the spectrum cannot be expected without the RWA but the almost symmetric spectrum can be obtained at the single-photon resonance that takes the Bloch-Siegert shift into account if the driving is moderately strong and at the multiphoton resonance with a sufficiently weak transverse field.
Abstract We theoretically study the resonance fluorescence spectra of the lambda (Λ), vee (V) and cascade (Ξ) type three-level configurations. It is shown that each system with two detuning frequencies can be modelled using the SU(3) symmetry group to derive a generalized optical Bloch equation. For each configuration, this equation is solved to calculate the two-time correlation function by invoking the quantum regression theorem. The incoherent part of the power spectra gives the characteristic multi-peak fluorescence profiles which are different for different configurations. We also discuss how the dressed-state structure of such system can explain the origin of quintuplet profile of the fluorescent spectrum.