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Optics Express

Double photonic bandgaps dynamically induced in a tripod system of cold atoms

Cui-Li Cui, Jin‐Hui Wu, Jin-Wei Gao, Yan Zhang, Nuo Ba

Published Feb 19, 2010• 17 citations
Publisher

Abstract

A tripod atomic system driven by two standing-wave fields (a coupling and a driving) is explored to generate tunable double photonic bandgaps in the regime of electromagnetically induced transparency. Both photonic bandgaps depend critically on frequency detunings, spatial periodicities, and initial phases of the two standing-wave fields. When the coupling and driving detunings are very close, a small fluctuation of one standing-wave field may demolish both photonic bandgaps. If the two detunings are greatly different, however, each standing-wave field determines only one photonic bandgap in a less sensitive way. Dynamic generation and elimination of a pair of photonic bandgaps shown here may be exploited toward the end of simultaneous manipulation of two weak light signals even at the single-photon level.

DOI
10.1364/oe.18.004538

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Acta Physica Sinica•Jan 1, 2014•1 citation
A tripod atomic system driven by two standing-wave fields (a coupling and a driving) is explored to generate tunable double photonic bandgaps in the regime of electromagnetically induced transparency. Both photonic bandgaps depend critically on frequency detunings, spatial periodicities, and initial phases of the two standing-wave fields. When the coupling and driving detunings are very close, a small fluctuation of one standing-wave field may demolish both photonic bandgaps. If the two detunings are greatly different, however, each standing-wave field determines only one photonic bandgap in a less sensitive way. Dynamic generation and elimination of a pair of photonic bandgaps shown here may be exploited toward the end of simultaneous manipulation of two weak light signals even at the single-photon level.
In this chapter, we give a brief review of our recent research works on photonic bandgaps induced by standing-wave (SW) coupling fields in the regime of electromagnetically induced transparency (EIT). EIT refers to the absorption suppression or elimination of a weak probe going through an atomic ensemble at the presence of a strong coupling, which is a result of laser induced destructive quantum interference. On the other hand, a light signal cannot freely propagate in the media with periodic refractive indices (the so-called photonic crystals) if its carrier frequencies fall inside the photonic bandgaps. Utilizing a SW coupling to attain the periodically modulated refractive index with little absorption, one can establish an induced photonic bandgap with its width and position dynamically tunable. The potential media may be either cold atomic ensembles or solid materials exhibiting defect states, such as Pr3+: Y2SiO5 and diamond containing N-V color centers. We first consider the steady optical responses of the atomic and solid media with dynamically induced bandgaps to a time- independent probe by focusing on the dispersion curves of Bloch wave vectors and the spectra of reflection and transmission. Then, we examine the propagation dynamics of a probe pulse through a cold atomic sample in two different situations where a dynamically induced bandgap exists or not. We find that the SW coupling field can be easily modulated to mold the traveling-light flow and to control the stationary-light generation with quite high flexibility, and thus may have applications in the fields of classical and quantum information processing of optical signals. In performing theoretical simulations, we also demonstrated several different but almost equivalent mathematical methods, i.e. the two-mode approximation method, the transfer-matrix method, and the Maxwell-Liouville equation method, to deal with the problems of SW-EIT. Comparison of these methods is quite helpful to understand the underlying physics of the formation of dynamically induced photonic bandgaps.
Double photonic bandgaps (PBGs) can simultaneously appear when double dark resonances in uniform cold atoms are spatially modulated by a resonance standing-wave. Theoretical calculations show that variable and efficient coherent optical control of the PBGs can be achieved by modulating the coupling field and standing-wave. The structures of double PBGs induced by the atomic coherence effect are better than those obtained in the photonic crystal heterostructures. We anticipate that this scheme has potential applications in optical networks for dual-channel all-optical switching or a dual-frequency optical Bragg reflector.
In this chapter, we give a brief review of our recent research works on photonic bandgaps induced by standing-wave (SW) coupling fields in the regime of electromagnetically induced transparency (EIT). EIT refers to the absorption suppression or elimination of a weak probe going through an atomic ensemble at the presence of a strong coupling, which is a result of laser induced destructive quantum interference. On the other hand, a light signal cannot freely propagate in the media with periodic refractive indices (the so-called photonic crystals) if its carrier frequencies fall inside the photonic bandgaps. Utilizing a SW coupling to attain the periodically modulated refractive index with little absorption, one can establish an induced photonic bandgap with its width and position dynamically tunable. The potential media may be either cold atomic ensembles or solid materials exhibiting defect states, such as Pr3+: Y2SiO5 and diamond containing N-V color centers. We first consider the steady optical responses of the atomic and solid media with dynamically induced bandgaps to a time- independent probe by focusing on the dispersion curves of Bloch wave vectors and the spectra of reflection and transmission. Then, we examine the propagation dynamics of a probe pulse through a cold atomic sample in two different situations where a dynamically induced bandgap exists or not. We find that the SW coupling field can be easily modulated to mold the traveling-light flow and to control the stationary-light generation with quite high flexibility, and thus may have applications in the fields of classical and quantum information processing of optical signals. In performing theoretical simulations, we also demonstrated several different but almost equivalent mathematical methods, i.e. the two-mode approximation method, the transfer-matrix method, and the Maxwell-Liouville equation method, to deal with the problems of SW-EIT. Comparison of these methods is quite helpful to understand the underlying physics of the formation of dynamically induced photonic bandgaps.
Using the technique of electromagnetically induced transparency, three photonic bandgaps can be established and manipulated at any time due to the refraction modulated periodically by the one-dimensional optical lattice in a tripod atomic system which is trapped in a one-dimensional optical lattice with a Gaussian density distribution. Using the density-matrix equations to describe the interaction between laser and atoms and the transfer-matrix equation to describe the scattering of light waves in periodic media, we can obtain the steady reflection and transmission spectra. It can be found that the position and width as well as the reflectivity of the photonic band-gap could be tuned by changing the detunings and intensities of the coupling fields and the geometric Bragg detuning.
We study a four-level double-Lambda system with spontaneously generated coherence driven by a standing-wave coupling field. It is found that two well-developed photonic bandgaps with reflectivities of about 90% can be generated on the probe resonance in the presence of maximal spontaneously generated coherence. The induced double photonic bandgaps become, however, severely malformed when spontaneously generated coherence vanishes. Dynamic control of the double photonic bandgaps may be exploited to achieve a novel two-port double-channel routing scheme for weak light signals in quantum networks.
We study the steady optical responses of a four-level Tripod cold 87Rb atomic system, which is driven by two mutually perpendicular strong standing-wave laser fields. It is found that satisfying the condition of a proper detuning between two strong fields, one nearly perfect structure of double photonic band-gap, where reflectivity can reach 95%, can be generated along each direction, respectively. Shifting a strong field (two strong fields) to a travelling-wave field (two travelling-wave fields), we can achieve a reflectivity platform and a transmissivity window (two transmissivity windows). Our new findings are beneficial to a novel all-optical switching and routing, which may have applications in complex all-optical information networks.