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Physical Review A

Coupled ion pairs in solids under the influence of a coherent radiation field

Nico Bodenschatz, Johann Heber

Published Nov 1, 1996• 15 citations
Publisher

Abstract

The coupled ion pairs were modeled by two coupled two-level systems. The resulting Bloch equations were derived by the density-matrix formalism. They were solved numerically for identical ions and for slightly detuned ions with identical wave functions as a first approximation to the problem of inhomogeneous line broadening in solids. The following results were found: (1) intrinsic optical bistability as a function of the applied laser field; (2) regions of stability, instability, and multistability for different detunings and couplings of the ions at different laser fields; (3) asymmetric shapes of the absorption lines with unstable regions; and (4) suppression of the photon echo due to the nonlinear chaotic dynamics of the coupled ions. Experimental evidence is given which supports the computer calculations. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.4428

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The coupled ion pairs were modeled by two coupled two-level systems. The resulting Bloch equations were derived by the density-matrix formalism. They were solved numerically for identical ions and for slightly detuned ions with identical wave functions as a first approximation to the problem of inhomogeneous line broadening in solids. The following results were found: (1) intrinsic optical bistability as a function of the applied laser field; (2) regions of stability, instability, and multistability for different detunings and couplings of the ions at different laser fields; (3) asymmetric shapes of the absorption lines with unstable regions; and (4) suppression of the photon echo due to the nonlinear chaotic dynamics of the coupled ions. Experimental evidence is given which supports the computer calculations. \textcopyright{} 1996 The American Physical Society.
Coupled ion pairs in solids have played an important role in the development of new solid-state lasers. The long-range interaction among two or more ions provides a channel for the inversion of population, leading to the discovery of new emission lines. Because of the relatively large optical cross sections, coupled ion pairs may provide new media for the implementation of a solid-state phase conjugate mirror. We present a theory of optical phase conjugation via four-wave mixing in such novel materials. For a model ion-doped solid-state system, the calculations give the following conclusions. First, the spectral linewidth is proportional to the square root of the intensity of the radiation field in an inhomogenously broadened material for fixed ion density. Second, the linewidth decreases with increasing ion density for the fixed intensity level. And last, the saturation intensity also decreases with increasing ion density for the fixed optical intensity. The behavior of the linewidth and the saturation intensity are attributed to the strong interaction among two nearest-neighbor ion pairs, which leads to the generation of additional energy dumping pathways.
The effects of intense laser pulse trains in coupled multilevel systems (such as pure or mixed molecular crystals) are analyzed by calculating exact density matrix evolutions. It is shown that two-level approximations are inadequate. The contributions of exchange couplings, inhomogeneous broadening, permanent multipole interactions and transition multipole interactions to absorption and photon echo line shapes are calculated. The absorption line shape of 1,4-dibromonaphthalene (DBN) is shown to be predominantly an isotopic substitution effect, as our Monte Carlo results give quantitative agreement with experiment for this model. Average t-matrix approximations to the Green’s function, which have been used to propose a different mechanism for the DBN line shape are shown to be qualitatively inadequate. Dipole–dipole interactions are shown to be an important photon echo decay mechanism in mixed crystals, with the relative importance of permanent and transition multipole interactions dependent on the resonance frequency distribution. Multiple pulse trains, including multiple pulse echoes and optical multiple-quantum sequences, are shown to be capable of distinguishing different types of interactions in the molecular Hamiltonian and reducing optical density effects. Specific pulse sequences are proposed and their effects are calculated.
We introduce a non-Hermitian Schrödinger-type approximation of optical Bloch equations for two-level systems. This approximation provides a complete and accurate description of the coherence and decoherence dynamics in both weak and strong laser fields at the cost of losing accuracy in the description of populations. In this approach, it is sufficient to propagate the wave function of the quantum system instead of the density matrix, providing that relaxation and dephasing are taken into account via automatically adjusted time-dependent gain and decay rates. The developed formalism is applied to the problem of scattering and absorption of electromagnetic radiation by a thin layer comprised of interacting two-level emitters.
The optical Bloch equations, which give the time evolution of the elements of the density matrix of an atomic system subject to radiation, are generalized so that they can be applied when transitions between pairs of states can proceed by more than one stimulated route. The case considered is that for which the time scale of interest in the problem is long compared with that set by the differences in detuning of the radiation fields stimulating via the different routes. It is shown that the Bloch equations then reduce to the standard form of linear differential equations with constant coefficients. The theory is applied to a two-state system driven by two lasers with different intensities and frequencies and to a three-state Λ-system with one laser driving one transition and two driving the second. It is also shown that the theory reproduces well the observed response of a cold 40Ca+ ion when subject to a single laser frequency driving the 4S1/2–4P1/2 transition and a laser with two strong sidebands driving 3D3/2–4P1/2.
We have studied the case of optical multistability in a four-level system interacting with two coherent fields. The system, shown in fig. 1, consists of two pairs of energy levels, 1, 2, and 3, 4, absorption occurs between levels 1- 4 and emission takes place from 3-2. The 'intra-band' transitions, 4-3 and 2- 1 are assumed non-radiative and extremely fast. The system is irradiated by two beams, one tuned to the absorption spectrum, the other to the emission spectrum, in a Fabry-Perot cavity. Solution of the optical Bloch equations following [1] enables us to write the input-output equations, la and lb, in the form where Yi, Xi, are the appropriately scaled input and output fields, Ci the 'bistability' parameter, and Δi, ϕi, the atomic and cavity detuning respectively, of field i.