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Chinese Physics Letters

Abnormal Dielectric Response in an Optical Range Based on Electronic Transition in Rare-Earth-Ion-Doped Crystals

Xiaojian Fu, Yuanda Xu, Ji Zhou

Published Feb 1, 2012• 3 citations
Publisher

Abstract

A new scheme to realize an abnormal dielectric response at optical wavelength is developed on the basis of two-level electronic transition of rare-earth ion doped crystals. Based on the semi-classical theory and the Judd—Ofelt theory, the electric dipole transition under a weak field is analyzed, and a general expression for the frequency-dependent dielectric constant is obtained. As an example, the permittivity of (Er x Y 1−x ) 3 Al 5 O 12 is calculated numerically in consideration of the transition between 4 I 15/2 and 4 F 9/2 . An optimized dielectric property with a negative real part and low absorption is achieved. This proposes a new mechanism for building extraordinary electromagnetic media at optical frequencies by using a quantum process.

DOI
10.1088/0256-307x/29/2/027805

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A new scheme to realize an abnormal dielectric response at optical wavelength is developed on the basis of two-level electronic transition of rare-earth ion doped crystals. Based on the semi-classical theory and the Judd—Ofelt theory, the electric dipole transition under a weak field is analyzed, and a general expression for the frequency-dependent dielectric constant is obtained. As an example, the permittivity of (Er x Y 1−x ) 3 Al 5 O 12 is calculated numerically in consideration of the transition between 4 I 15/2 and 4 F 9/2 . An optimized dielectric property with a negative real part and low absorption is achieved. This proposes a new mechanism for building extraordinary electromagnetic media at optical frequencies by using a quantum process.
The change of intensities of optical transitions of atoms, molecules, and their ions in the near field of nanoobjects is of interest for researchers from both basic and applied points of view. The concept of a near field was used as early as the 1960s to study the mechanisms of hypersensitive transitions of rare-earth (RE) ions. In this work, it is once more emphasized that, precisely for these transitions, changes in characteristics under the action of local properties of the medium are especially strong and, correspondingly, these transitions are especially promising for use. The Judd method for the calculation of the intensities of hypersensitive transitions of RE ions taking into account the inhomogeneous ligand field is extended to RE ions in the near field of nanoobjects. A simple analytical expression for the Judd-Ofelt intensity parameter Ω 2 for RE ions in the field of spherical nanoparticles of a subwavelength size is derived.
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.
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 present a scheme for quantum computing in rare-earth-ion doped inorganic crystals. We use two of the ground state hyperfine levels as the qubit states, with different qubits absorbing light at different frequencies within an inhomogeneously broadened optical transition. Interaction between different qubits is accomplished using the change in permanent dipole moment that is induced at the optical excitation of the ions. The two most important aspects of the scheme have been accomplished experimentally: The isolation of a single qubit in a pure state and interaction between ions absorbing at different frequencies.
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.
The paper reports on the experimental realization on the possibility of isolating ions in a selected frequency channel. In the scheme, this interaction is mediated by the change in permanent dipole moment experienced by the rare-earth ions when they are optically excited from the ground state to an excited state. The change in dipole moment changes the electric field experienced by ions situated close to the excited ion, thus their absorption frequencies are changed. The important aspect, in order to use this frequency shift for controlled logic, is that the shift is large enough for ions, originally resonant with a certain laser frequency, to be shifted out of resonance with this laser field. Excitation induced frequency shifts are experimentally observed, which opens the way for the realisation of the first quantum gate in this type of solid state materials.