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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Resonance fluorescence spectrum near photonic bandgap

Ray‐Kuang Lee, Yinchieh Lai

Published Jul 7, 2003• 0 citations
Publisher

Abstract

We theoretically calculate the resonance fluorescence spectrum from a two-level atom which is embedded in a photonic bandgap crystal and is resonantly driven by a classical pump light. Non-Markovian noises caused by the non-uniform distribution of photon density states near the photonic bandgap are taken into account by a new approach which linearizes the optical Bloch equations by using the Liouville operator expansion. These linearized equations can be solved directly in the Fourier domain to obtain the correlation functions of the atomic operators and then the fluorescence spectrum from the atom. We find that if the atomic energy level is far from the bandgap, fluorescence spectra with Mollow triplets are observed. When the atomic energy level is near the bandgap, the relative magnitude and the number of the fluorescence peaks are found to be varied according to the wavelength offset.

DOI
10.1117/12.479504

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Optics and Spectroscopy•Mar 1, 2005•1 citation
We theoretically calculate the resonance fluorescence spectrum from a two-level atom which is embedded in a photonic bandgap crystal and is resonantly driven by a classical pump light. Non-Markovian noises caused by the non-uniform distribution of photon density states near the photonic bandgap are taken into account by a new approach which linearizes the optical Bloch equations by using the Liouville operator expansion. These linearized equations can be solved directly in the Fourier domain to obtain the correlation functions of the atomic operators and then the fluorescence spectrum from the atom. We find that if the atomic energy level is far from the bandgap, fluorescence spectra with Mollow triplets are observed. When the atomic energy level is near the bandgap, the relative magnitude and the number of the fluorescence peaks are found to be varied according to the wavelength offset.
Steady state resonance fluorescence spectra from a two-level atom embedded in a photonic bandgap crystal and resonantly driven by a classical pump light are calculated. The photonic crystal is considered to be with a small bandgap which is in the order of magnitude of the Rabi frequency and is modeled by the anisotropic two-band dispersion relation. Non-Markovian noises caused by the non-uniform distribution of photon density states near the photonic bandgap are taken into account by a new approach which linearizes the optical Bloch equations by using the Liouville operator expansion. Fluorescence spectra that only exhibit sidebands of the Mollow triplet are found, indicating that there is no coherent Rayleigh scattering process.
In contrast to the situation in free space where the Markovian approximation and the quantum regression theorem are valid, the atom-photon interaction in photonic bandgap materials is in general nonMarkovian. In the present paper we treat the photonic crystals as background reservoirs and introduce the nonuniform noise operators caused by such nonuniform DOS distributions near the band edge. The steady state fluorescence spectrum of a two-level atom embedded in a three-dimensional photonic bandgap crystal and driven by a monochromatic classical electrical field is calculated theoretically for the first time as we known. With the help of the Liouville operator expansion, we can calculate the stationary two-time correlation functions of the atomic operators as well as the spectral distribution of the resonance fluorescence. We also use various dispersion relations to model this nonuniform DOS distribution near the bandgap. We find that if the atomic energy level is far from the bandgap, fluorescence spectra with Mollow triplets are observed.
The fluorescence intensity and quadrature spectra from a two-level atom embedded in a photonic bandgap crystal and resonantly driven by a classical pump light are calculated. The non-Markovian nature of the problem caused by the non-uniform distribution of the photonic density of states is handled by linearizing the generalized optical Bloch equations with the Liouville operator expansion. Unlike the case in free space, we find that the bandgap effects will not only modify the fluorescence spectral shape but also cause squeezing in the in-phase quadrature spectra.
We present a quantum theory of a coherently pumped two-level atom in a photonic crystal, coupled to both a multi-mode wave-guide channel and a high quality micro-cavity embedded within the photonic crystal. The cavity field characteristics are highly distinct from that of a corresponding high Q cavity in ordinary vacuum. If the cavity field mode is resonant with the central component of the Mollow spectrum of atomic resonance fluorescence, enhanced, inversionless, nearly coherent light generation occurs when the photon density of states jump between the Mollow spectral components is large. The spectrum of the cavity field is also investigated and showed to be narrower than in the case of a conventional cavity. Moreover, enhanced, non-classical light generation is possible, if the cavity field is tuned on resonance with a Mollow sideband.
Quantum optics provides a fundamental framework for understanding the interaction between light and matter at the quantum level. Recently, it has been shown that under incoherent pumping, the resonance fluorescence spectrum dramatically changes. Engineering the resonance fluorescence spectrum paves the way towards solid-state-based single-photon sources. In this paper, we start by reviewing and reproducing some of the results concerning the resonance fluorescence spectrum, single-photon sources, dressed-state lasers, and luminescence spectrum of a quantum dot in a microcavity. Photon correlations in quantum optical systems and spectral properties of radiation emitted by atomic and semiconductor systems interacting with external fields are investigated. The well known Mollow triplet structure of the emission spectrum is discussed, together with the role of dressed states in explaining the origin of the three spectral peaks. Furthermore, the luminescence spectra of quantum emitters coupled to microcavities are reviewed. The numerical results presented here contribute to the theoretical understanding of resonance fluorescence, photon correlations, and engineered emission in quantum optical systems. These studies highlight the rich physical properties arising from light matter interaction at the quantum level and demonstrate their relevance for emerging quantum technologies.
The fluorescence of a two-level atom embedded into a two-dimensional photonic crystal is considered under the assumption that the electronic transition frequency ω 10 is close to the photonic mode frequency ω 0 in the saddle critical point of the photonic spectrum. In this case, the density of photonic states has a logarithmic peak, which manifests itself in a considerable rearrangement of the fluorescence spectrum. The Green’s function of the electron-photon system, which contains the description of the dynamics of spectroscopic transitions and the shape of fluorescence spectra, is obtained in the rotating field approximation. Using the Green’s function, the frequency-dependent Lamb shift and the broadening of the atomic transition are calculated. The shape of the fluorescence spectra is studied. At a large oscillator strength of the atomic transition, the fluorescence line splits into two components in the vicinity of the singularity caused by the saddle critical point. This splitting is associated with a specific Fano-type resonance between the discrete spectrum (the atomic states) and the continuum (the dispersion of photons with a saddle critical point). At small detunings δ = ω 10 -ω 0 , the components of the fluorescence line have considerably different intensities. As δ increases, the spectral positions of the strong and weak components tend to the frequencies of the atomic transition and the saddle point, respectively. The results obtained show that two-level atoms (or quantum dots) can be used as specific probes of the band spectra of photonic crystals.