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arXiv:quant-ph/0308100 · Journal of Optics B Quantum and Semiclassical Optics

Fluorescence squeezing spectra near a photonic bandgap

Ray‐Kuang Lee, Yinchieh Lai

Published Jul 28, 2004• 6 citations
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Abstract

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.

DOI
10.1088/1464-4266/6/8/014

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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 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.
A new possibility of generating one-mode squeezed light by coupling a system of two-level atom with a bichromatic pump field in an optical cavity is suggested. The non-classical character of light in this process is caused by two-photon radiation at the central frequency of the spectrum of resonance fluorescence in the bichromatic field. The intensity of the resonance fluorescence cavity output field as well as the variance of the quadrature amplitudes and the second-order correlation function of intensity are calculated.
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.
We observe squeezing in the phase-dependent fluorescence spectra of two-level atoms that are coherently driven by a near-resonant laser field in free space. In contrast to previous predictions that emphasized the in- and out-of-phase quadratures, we find that maximum squeezing occurs for homodyne detection at a phase near $\ifmmode\pm\else\textpm\fi{}{45}^{\ensuremath{\circ}}$ relative to the exciting field. A new physical picture of phase-dependent noise is developed that incorporates quantum collapses into a Bloch vector model and yields a very simple form for the complete squeezing spectrum.