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Chinese Physics Letters

Controlled Photonic Stop Bands in a Four-Level Atomic System of an Inhomogeneously Broadened Solid

Lili Han, Xiaojun Zhang, Chengze Liu, Cunbo Fan, Xingwei Han, Jin‐Hui Wu, Jin-Yue Gao

Published Mar 1, 2013• 0 citations
Publisher

Abstract

A neatly controllable photonic band gap formed in a four-level tripod system in the solid material, Pr 3+ -doped yttrium orthosilicate (Pr:YSO) is investigated. Driven by two standing waves, the sample is just like a photonic crystal to the weak probe. Based on the numerical simulation and the analytic result we present a clear and full-scale view on the induced band gap in the inhomogeneously broadened tripod system.

DOI
10.1088/0256-307x/30/3/034203

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A neatly controllable photonic band gap formed in a four-level tripod system in the solid material, Pr 3+ -doped yttrium orthosilicate (Pr:YSO) is investigated. Driven by two standing waves, the sample is just like a photonic crystal to the weak probe. Based on the numerical simulation and the analytic result we present a clear and full-scale view on the induced band gap in the inhomogeneously broadened tripod system.
When a three-level system is coherently driven by a strong modified standing wave, photonic band gaps are viable to realize. Theoretically detailed calculations, for Pr3+{\mathrm{Pr}}^{{3}^{+}}Pr3+-doped yttrium orthosilicate crystal with inhomogeneously broadening, further show that the gap structure can be dynamically controlled and optimized by modulating the Rabi frequency, the spatial periodicity of the standing wave, the reflectivity of mirror, and the angle of incidence. This adjustable photonic band gap determined by the external pump control parameters in a doped solid crystal should hold more potential for applications than that in typical photonic crystals which are determined once for all by the way the material periodic structure is grown.
Inhomogeneously broadened doped solids supporting electromagnetically induced transparency are viable materials where optically tunable photonic band gaps may be observed and results are shown for Pr:YSO and nitrogen-vacancy color center materials. Such crystals, when coherently driven by a strong pump beam in a suitably designed standing wave configuration, exhibit a tunable stop-band with rather different values of the reflectivity. The different propagating behavior is investigated and characterized for a weak probe across the gap region of the two materials.
We illustrate a mechanism based on coherent optical nonlinearities to realize optically tunable photonic crystals built from media supporting electromagnetically induced transparency. These exhibit specific periodic patterns where a light probe can experience a fully developed photonic band-gap with negligible absorption. An analytical method based on a two-mode approximation is developed to study the optical response of such a periodically modulated medium driven into a regime of standing-wave electromagnetically induced transparency. A comparison with a transfer matrix approach and with techniques based on the coupled Maxwell–Liouville equations shows that our method is very accurate to describe the optical properties of such photonic metamaterials in the frequency region of interest. Nearly perfect reflectivities may be attained for ultracold 87Rb atoms samples which are seen to reflect with little loss and deformation light pulses whose frequency components are contained within the gap. When the same mechanism is implemented for inhomogeneously broadened optical transitions of nitrogen-vacancy centers in diamond, which is more amenable to device applications, fully developed photonic band-gap structures with negligible absorption, reflectivities very close to unity and sufficiently large bandwidths may also be attained. We further examine more flexible schemes based on four level systems under double driving conditions showing more accurate and efficient coherent optical control of the photonic band-gap. The remarkable experimental simplicity of the schemes that we presented is set to ease quantum nonlinear optics applications.
Abstract Inhomogeneously broadened optical transitions in nitrogen‐vacancy color centers in diamond and Pr3+ doped yttrium orthosilicate may be employed to attain all‐optically controlled Bragg structures with photonic band‐gaps of high reflectivities and large bandwidths. Such a control mechanism is valuable for improving performance and scalability of solid quantum memory devices. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 2722–2726, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24723
We study a cold atomic sample coherently driven into the five-level triple-$\ensuremath{\Lambda}$ configuration for attaining a dynamically controlled triple photonic band-gap structure. Our numerical calculations show that three photonic band gaps with homogeneous reflectivities up to 9292%92 can be induced on demand around the probe resonance by a standing-wave driving field in the presence of spontaneously generated coherence. All these photonic band gaps are severely malformed with probe reflectivities declining rapidly to very low values when spontaneously generated coherence is gradually weakened. The triple photonic band-gap structure can also be attained in a five-level chain-$\ensuremath{\Lambda}$ system of cold atoms in the absence of spontaneously generated coherence, which however requires two additional traveling-wave fields to couple relevant levels.
The probe absorption-dispersion spectra of a radio-frequency (RF)-driven five-level atom embedded in a photonic crystal are investigated by considering the isotropic double-band photonic-band-gap (PBG) reservoir. In the model used, the two transitions are, respectively, coupled by the upper and lower bands in such a PBG material, thus leading to some curious phenomena. Numerical simulations are performed for the optical spectra. It is found that when one transition frequency is inside the band gap and the other is outside the gap, there emerge three peaks in the absorption spectra. However, for the case that two transition frequencies lie inside or outside the band gap, the spectra display four absorption profiles. Especially, there appear two sharp peaks in the spectra when both transition frequencies exist inside the band gap. The influences of the intensity and frequency of the RF-driven field on the absorptive and dispersive response are analyzed under different band-edge positions. It is found that a transparency window appears in the absorption spectra and is accompanied by a very steep variation of the dispersion profile by adjusting system parameters. These results show that the absorption-dispersion properties of the system depend strongly on the RF-induced quantum interference and the density of states (DOS) of the PBG reservoir.