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Acta Physica Sinica

The quantum coherent left handness of Λ-type four level system in Er3+：YAlO3 crystal

Liu Chun-Xu, Zhang Ji-Sen, Liu Jun-Ye, Jin Guang, (1)中国科学院长春光学精密机械与物理研究所，长春 130033; (2)中国科学院长春光学精密机械与物理研究所激发态物理重点实验室，长春 130033

Published Jan 1, 2009• 3 citations
Publisher

Abstract

We first calculated the negative refractive index on the solid Er3+：YAlO3 crystal with a Λ-type four-level scheme proposed for atomic vapour by Thommen and Mandel and Kastel using quantum interference and electromagnetically induced transparency （EIT）. It is shown that the frequency band with the negative index is wider （～1 MHz） than that reported previously. Usually，Im［n］ is always positive，corresponding to absorption，and the ratio of refraction to absorption，|Re［n］/Im［n］|，is only of the order of unity. In our case the ratio |Re［n］/Im［n］|=4.6，which indicates that the absorption has been well suppressed by EIT approach. The negative Im［n］ may be related to the stimulated emission of 4I13/2→4I15/2 of rare earth ion Er3+. It indicates that the rare earth ion doped material with abundant energy levels and various electric and magnetic transitions is an outstanding and practical candidate for electromagnetically induced negative refractive index material.

DOI
10.7498/aps.58.5778

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We first calculated the negative refractive index on the solid Er3+：YAlO3 crystal with a Λ-type four-level scheme proposed for atomic vapour by Thommen and Mandel and Kastel using quantum interference and electromagnetically induced transparency （EIT）. It is shown that the frequency band with the negative index is wider （～1 MHz） than that reported previously. Usually，Im［n］ is always positive，corresponding to absorption，and the ratio of refraction to absorption，|Re［n］/Im［n］|，is only of the order of unity. In our case the ratio |Re［n］/Im［n］|=4.6，which indicates that the absorption has been well suppressed by EIT approach. The negative Im［n］ may be related to the stimulated emission of 4I13/2→4I15/2 of rare earth ion Er3+. It indicates that the rare earth ion doped material with abundant energy levels and various electric and magnetic transitions is an outstanding and practical candidate for electromagnetically induced negative refractive index material.
We carried out the negative refractive index in the solid medium Er3+:YAlO3 crystal with a Λ-type four-level scheme proposed for atomic vapour by Thommen and Mandel, and Kastel (Phys. Rev. Lett. 2006 96 053601 and 2007 98 069301) based on quantum interference and electromagnetically induced transparency (EIT). The results show that the frequency band with the negative index is much wider (~1 MHz) than reported previously. Usually, Im[n] is always positive, corresponding to absorption, and the figure of merit (FOM, the ratio of real to imaginary, namely |Re[n]/Im[n]|) is only on the order of unity. We achieve FOM = |Re[n]/Im[n]| = 4.6. The corresponding negative Im[n] is related to the stimulated emission of 4I13/2 → 4I15/2 of the rare earth ion Er3+ under external electromagnetic fields. It is concluded that the rare earth ion doped material with abundant energy levels and various electric and magnetic transitions is an outstanding and practical candidate for the electromagnetically induced negative refractive index material.
The electromagnetically induced left-handedness with zero absorption and large negative refractive index was investigated in a solid Er3+:YAG crystal with a four-level system proposed for an atomic medium. It was found that the frequency region with simultaneous negative permittivity and negative permeability, the zero absorption intervals, and the maximum values of the negative refractive index can be adjusted by changing the signal field, the coherent field, as well as the concentration of Er3+ ion in crystal. It is shown that wider zero absorption intervals with a higher index of refraction can be easily obtained when the signal field is only off resonance. The slab fabricated by the left-handed solid medium Er3+:YAG crystal with zero absorption may be a practical candidate for designing perfect lenses.
We propose a scheme for realizing negative refractive index in a V-type four-level atomic system. It is shown that the negative refractive index can be achieved in a wide frequency band based on the effect of quantum coherence. It is also found that the frequency band of negative refractive index and the absorption property of left-handed material are manipulated by the pump and control fields. Furthermore, left-handed material with reduced absorption is possible by choosing appropriate parameters. (c) 2006 Elsevier B.V. All rights reserved.
This paper intends to realize negative refraction with absorption suppressed by the electromagneticly induced transparency(EIT) in a dense four-level atomic system. Without the two equal transition frequencies responding to the probe field, the atomic system displays a negative refraction with the simultaneously negative permittivity and negative permeability(Left-handedness). The response of the probe field is amplified and propagates transparency in some frequency extents. Therefore, our aim for searching the low-loss negative refraction can be achieved in the scheme, given the main applied limitation of the negative refractive materials is the large amount of dissipation and absorption. However, an excessive signal field intensity would increase the absorption near the resonance in our scheme.
We propose two dense gas schemes of four-level 'Lambda'-type and V-type atoms based on the effect of quantum coherence. It is shown that under certain conditions the dense gas can simultaneously exhibit negative permittivity and negative permeability, and thus become a negative refractive-index material. Furthermore, by analyzing the absorption property of the left-handed materials, we find that the absoption can be reduced via choosing appropriate parameters. Such schemes might be used to fabricate isotropic and homogeneous left-handed material with vanishing absorption in a wider optical frequency band.
A new mechanism for realizing negative refractive index with a four-level atomic system is suggested. The explicit expressions for the electric permittivity and magnetic permeability at probe frequency are presented. It is shown that there is a frequency band in which the four-level photonic-resonant atomic vapour may exhibit simultaneously negative permittivity and permeability, and that such an atomic vapour may become a left-handed material (negatively refracting medium). Compared with the previous schemes to realize negative refraction within the framework of classical electromagnetic theory, the most remarkable features of the present scenario are as follows: (i) isotropic material with microscopic structure units at atomic-scale level, (ii) negative refraction in visible and infrared frequency bands, (iii) controllable manipulation by external fields and (iv) based on quantum coherence in a multilevel atomic system.