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Physical Review A

Dressed-state mixed-parity transitions for realizing negative refractive index

Clifford M. Krowne, Jian Qi Shen

Published Feb 17, 2009• 43 citations
Publisher

Abstract

The dressed states that are linear combinations of two bare levels of an atom (e.g., an alkali-metal atom) can be realized by a strong-coupling laser beam. As the dressed states have mixed parities, both electric- and magnetic-dipole-allowed transitions can occur between the dressed states and a third level with a definite (pure) parity. It is shown that such dressed-state mixed-parity transitions in an atomic vapor (the concept also applies in the solid state) can give rise to a negative refractive index. The produced negative refractive index is isotropic with atomic-scale microscopic structure units, and the negative real part can emerge in the optical frequency band. Also examined is the case of a fully quantized probe photonic field which interrogates the bottom dressed state and the third-level state. Similarities between the semiclassical approach for the weaker probe field and its fully quantum mechanical second-quantization treatment are discussed in regard to the off-diagonal density matrix element for the reduced $2\ifmmode\times\else\texttimes\fi{}2$ manifold, and its implications for the refractive index.

DOI
10.1103/physreva.79.023818

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The dressed states that are linear combinations of two bare levels of an atom (e.g., an alkali-metal atom) can be realized by a strong-coupling laser beam. As the dressed states have mixed parities, both electric- and magnetic-dipole-allowed transitions can occur between the dressed states and a third level with a definite (pure) parity. It is shown that such dressed-state mixed-parity transitions in an atomic vapor (the concept also applies in the solid state) can give rise to a negative refractive index. The produced negative refractive index is isotropic with atomic-scale microscopic structure units, and the negative real part can emerge in the optical frequency band. Also examined is the case of a fully quantized probe photonic field which interrogates the bottom dressed state and the third-level state. Similarities between the semiclassical approach for the weaker probe field and its fully quantum mechanical second-quantization treatment are discussed in regard to the off-diagonal density matrix element for the reduced 2\ifmmode×\else\texttimes\fi22\ifmmode\times\else\texttimes\fi{}22\ifmmode×\else\texttimes\fi2 manifold, and its implications for the refractive index.
Abstract—A scheme of double-negative left-handed atomic vapor medium based on dressed-state assisted simultaneous electric and magnetic resonances is suggested. In this mechanism, simultaneous electric- and magnetic-dipole allowed transitions of atoms are driven by an optical wave by taking full advantage of both mixed-parity dressed-state assisted resonance and incoherent population pumping in a quantum-coherent atomic medium (e.g., alkali-metal atomic vapor). Since the simultaneously negative permittivity and permeability can be achieved in a same frequency band, such an atomic vapor will exhibit an incoherent-gain double-negative refractive index that is three-dimensionally isotropic and homogeneous. The imaginary part of the negative refractive index of the present atomic vapor would be drastically suppressed or would become negative because of loss compensation through incoherent population transfer. The quantum-coherent left-handed atomic vapor presented here will have four characteristics: i) three-dimensionally isotropic and homogeneous negative refractive index, ii) double-negative atomic medium at visible (and infrared) wavelengths, iii) tunable negative refractive index based on dressed-state quantum coherence, and iv) high gain due to incoherent pumping action.
The existing Quantum Optics- based models of negative refractive index in atomic-vapor medium (e.g. Ne, Na) require unrealistically strong magnetic response of atoms combined with high atomic density. In contrast to these gas-based models, our approach explores solid-state n-type semiconductor with well-defined hydrogen-like donor atomic states within the band gap. Based on methods of Quantum Optics, we have found that optically transparent indium oxide is negative refractive index material if doped with tin and zinc (In 2-x Sn x/2 Zn x/2 O 3 (zinc-doped ITO)). The desirable negative refractive index effect is due to coherent coupling an electric dipole transition with magnetic transition with proper detunings of the probe and support laser beams (A.-G. Kussow and A. Akyurtlu, Int. J. Mod. Physics (2010)). The calculations demonstrate the feasibility of the effect at ~ 10 THz with extremely high figure of merit FOM >> 10.
A new scenario for realizing a gain left-handed atomic vapor medium based on both dressed-state mixed-parity transitions (for simultaneous electric- and magnetic-dipole resonance) and incoherently-pumped population transfer (for high gain amplification) in a four-level atomic system is suggested. Dressed-state assisted simultaneous electric- and magnetic-dipole allowed transitions in such a four-level atomic system (of, e.g., neutral alkali-metal atoms such as lithium and potassium atoms) are utilized for achieving negative refractive index with impedance perfectly matched to vacuum. The attractive features of the present scenario include: i) three-dimensionally isotropic negative indices; ii) incoherent-gain wave amplification; iii) perfect impedance matching to vacuum. All these important properties of the double-negative medium would have potential applications in designing some optical and photonic devices, including particularly subwavelength focusing system and negative-index superlens for perfect imaging.
A scenario for realizing simultaneously negative permittivity and permeability of a two-photon quantum-coherent atomic vapor is suggested in order to achieve a left-handed atomic medium with a negative refractive index. One of the remarkable features of the present scheme is that it can lead to a controllable manipulation of the negative refractive index of the atomic vapor. Since the electric- and magnetic-dipole allowed transitions of atoms can be excited by visible and infrared lightwaves, the refractive index of the atomic vapor can exhibit its negative refractive index at optical and near-optical frequency bands. This may be a new scheme to fabricate a negatively refracting material based on the quantum optical approach. Such a three-dimensionally isotropic negative refractive index at visible and infrared wavelengths induced by the two-photon-resonant quantum coherence would find a potential application in fabrication of superlenses for perfect imaging and subwavelength focusing.
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.
Based on methods of quantum optics, we discuss the possibility of achieving the negative index of refraction in a semiconductor with donor-like impurities. The quantum states of hydrogen-like donor atom and states of an electron in conduction band constitute a discrete-level atomic medium within the optical range. The coherent coupling of an electric dipole transition with a magnetic dipole transition leads to permeability and permittivity responses and, within some frequency band, ensures the negative refractive index. The magnetic moment between two quasi-atomic states separated by optical frequencies is induced by a low-frequency electromagnetic field. The implementation of this scheme is carried out in tin-doped indium oxide, and the calculations show feasibility of the effect within a broad bandwidth ∼2% with a high figure of merit greater than 10 in the optical regime.