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Journal of Modern Optics

Observation of electromagnetically induced photonic band gaps in hot two-level atoms

Z.R. Chen, Xue Mei Su, J. B. Kim, Z. C. Zhuo

Published May 6, 2014• 3 citations
Publisher

Abstract

In this paper, two-level thermal Cs atoms are used to observe electromagnetically induced photonic band gaps with a strong symmetric and two types of asymmetric standing-wave (SW) driving fields. One main band and two sidebands are measured for the transmitted and reflected spectra. We carry out physical interpretation about the observations in SW-dressed atom picture and employ method of Fourier transformation to solve density-matrix equations for hot two-level system to simulate the experimental results. The numerical analyses are consistent with the experimental observations for properties of electromagnetically induced photonic band gaps.

DOI
10.1080/09500340.2014.914588

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In this paper, two-level thermal Cs atoms are used to observe electromagnetically induced photonic band gaps with a strong symmetric and two types of asymmetric standing-wave (SW) driving fields. One main band and two sidebands are measured for the transmitted and reflected spectra. We carry out physical interpretation about the observations in SW-dressed atom picture and employ method of Fourier transformation to solve density-matrix equations for hot two-level system to simulate the experimental results. The numerical analyses are consistent with the experimental observations for properties of electromagnetically induced photonic band gaps.
Three-level Λ-type thermal Cs atoms are used to demonstrate the phenomenon of a photonic bandgap induced by quantum coherence with a standing wave (SW). We observed the transmitted signals of probe field driven by several kinds of SW, which are formed by a strong forward-traveling field and a backward-traveling field when a mirror reflects the forward-traveling beam. Considering Doppler inhomogeneous broadenings with a SW drive, we employ Fourier transformation to solve density-matrix equations for simulation results. The simulation results are found to be consistent with the experimental results.
By using the technique of electromagnetically induced transparency and solving density matrix equations for atoms and transfer matrix equations of fields, we study the steady optical properties of a four-level system of cold atoms driven by a traveling-wave field and a standing-wave field. It is found that a nearly perfect structure of double photonic band-gap can be generated with specific parameters. In particular, the reflectivity inside each photonic band-gap is homogeneous over 95%. It is convenient to modulate the positions and widths of both photonic band-gaps by changing intensities and frequencies of the driving fields. The double photonic band-gaps can be used to achieve all-optical routing and switching and therefore may have applications in all-optical information networks.
The phenomenon of electromagnetically induced transparency has been studied when a four-level atom is located in a photonic band gap material. Quantum interference is introduced by driving the two upper levels of the atom with a strong pump laser field. The top level and one of the ground levels are coupled by a weak probe laser field and absorption takes place between these two states. The susceptibility due to the absorption for this transition has been calculated by using the master equation method in linear response theory. Numerical simulations are performed for the real and imaginary parts of the susceptibility for a photonic band gap material whose gap-midgap ratio is 21%. It is found that when resonance frequencies lie within the band, the medium becomes transparent under the action of the strong pump laser field. More interesting results are found when one of the resonance frequencies lies at the band edge and within the band gap. When the resonance frequency lies at the band edge, the medium becomes nontransparent even under a strong pump laser field. On the other hand, when the resonance frequency lies within the band gap, the medium becomes transparent even under a weak pump laser field. In summary, we found that the medium can be transformed from the transparent state to the nontransparent state just by changing the location of the resonance frequency. We call these two effects anomalous electromagnetically induced transparency.
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.
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.
We experimentally investigate transmission of the probe field, the reflected four-wave mixing photonic band gap signal, and fluorescence signal in a five-level atomic system. In addition, we compared the single-dressing, double-dressing, and triple-dressing on the three types of signals. These three types of signals can be controlled by frequency detunings, powers, and relative phases of the dressing beams. Such a scheme could have potential applications in amplification processing of triode and quantum information processing.