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The Journal of Chemical Physics

Optical dephasing in defect-rich crystals

V. Hizhnyakov, P. Reineker

Published Nov 1, 1999• 27 citations
Publisher

Abstract

The optical dephasing, caused by vibrational modulation of interactions of optical centers with defects is studied. This mechanism is essential for crystals with a substantial amount of defects, being more efficient at low temperatures than the Raman mechanism, caused by scattering of acoustic phonons at optical centers. A theory is developed, which allows one to find averaged widths and shapes of spectral holes in these systems dependending on the temperature T and concentration c of defects. The shape of the hole is found to be close to a Lorentzian, and at intermediate temperatures its width is proportional to T3, and strongly depends on c (for charged point defects as c8/3).

DOI
10.1063/1.480147

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•Jan 1, 2014•2 citations
The optical dephasing, caused by vibrational modulation of interactions of optical centers with defects is studied. This mechanism is essential for crystals with a substantial amount of defects, being more efficient at low temperatures than the Raman mechanism, caused by scattering of acoustic phonons at optical centers. A theory is developed, which allows one to find averaged widths and shapes of spectral holes in these systems dependending on the temperature T and concentration c of defects. The shape of the hole is found to be close to a Lorentzian, and at intermediate temperatures its width is proportional to T3, and strongly depends on c (for charged point defects as c8/3).
We continue the discussion of the nonperturbative theory of zero-phonon impurity lines in crystals formulated by Osad’ko and more recently by us. In that paper, a diagrammatic analysis was undertaken which led to analytic results for the thermal width and shift of the zero-phonon line. Here we evaluate these results for two model phonon densities of states: the Debye model for acoustic phonons, and a sharply peaked density of states appropriate for optical phonons. For Debye phonons we find that at low temperatures the standard (perturbative) theory of optical dephasing is qualitatively correct, but at high temperatures it becomes very inaccurate. Moreover, if one of the excited state phonon frequencies tends to zero (a soft mode), then perturbation theory breaks down completely. For optical phonons our results give an Arrhenius temperature dependence for the linewidth and place an upper bound on the value of the preexponential. In paper II of this series we will discuss dephasing by pseudo-local phonons, and in paper III we will compare our results to absorption, photon echo, and hole burning experiments.
We have applied the results of the nonperturbative theory of zero-phonon linewidths of impurities in crystals discussed by Osad’ko and us, and further developed by us in papers I and II of this series, to the analysis of several absorption, photon echo, and hole burning experiments. Two (relatively) high temperature absorption experiments on 1,3-diazaazulene in naphthalene and dilute ruby were analyzed with a model of Debye acoustic phonons. In both cases the Debye temperature was obtained from independent experiment or theory, and a one-parameter fit was performed on the temperature-dependent linewidth. It was found that (especially for diazaazulene) the systems are not in the weak coupling limit. For several low temperature experiments, where the dephasing is presumably due to pseudolocal phonons, the nonperturbative theory, coupled with the results of deBree and Wiersma, provides a reasonably complete understanding of the observed dephasing rates.
Accumulated photon echoes have been used to investigate the mechanisms of optical dephasing in CaF2 crystals activated by Nd3+ ions. Tunable picosecond laser radiation, which permits the selective excitation of various Nd3+ optical centers in the 4 I 9/2→4 G 5/2, 2 G 7/2 transition, is used. The optical phase relaxation times measured at temperatures from 9 to 50 K permit determination of the homogeneous widths of the transitions between the low-lying 4 I 9/2 Stark level and three excited 4 G 5/2, 2 G 7/2 levels, and calculation of the constants of the inter-Stark relaxation transitions in the ground and excited multiplets for the rhombic N and M Nd3+ centers in CaF2 crystals. An analysis of the temperature dependence of the homogeneous linewidth of the transitions between low-lying Stark levels of the ground and excited states shows that the mechanism of optical dephasing in the crystals investigated is described well by direct relaxation processes with resonant inter-Stark absorption of one phonon in the ground and excited states. At T=9 K, the homogeneous linewidth Γh in CaF2 crystals is almost an order of magnitude smaller than Γh in disordered CaF2-YF3 crystals. This difference can be attributed to the significantly greater spectral phonon density of states in disordered crystals.
The optical dephasing, caused by a quadratic interaction with acoustic phonons, is studied on the basis of the nonperturbative theory. The effect of a strong weakening of the elastic springs on the electronic transition is studied. It is found that, if the weakening brings the system close to the dynamical instability, then the usual ∝ T7 dependence of the homogeneous width of a zero-phonon line (ZPL) is replaced by the ∝ T3 dependence in a broad temperature interval. An equation is derived which describes the additional broadening of a ZPL caused by the dynamical instability of the final state. The model explains the temperature broadening and shift of the zero-phonon lines of some nitrogen-containing centers in diamond crystals.
We identify and analyze dephasing mechanisms that broaden the optical transitions of rare-earth ions in randomly oriented transparent ceramics. The study examines the narrow $^{7}F_{0}\phantom{\rule{4pt}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{4pt}{0ex}}^{5}D_{0}$ transition of Eu3+{\mathrm{Eu}}^{3+}Eu3+ dopants in a series of Y2O3{\mathrm{Y}}_{2}{\mathrm{O}}_{3}Y2​O3​ ceramic samples prepared under varying conditions. We characterize the temperature and magnetic field dependence of the homogeneous linewidth, as well as long-term spectral diffusion on time scales up to 1 s. The results highlight significant differences between samples with differing thermal treatments and Zr4+{\mathrm{Zr}}^{4+}Zr4+ additive concentrations. In particular, several distinct magnetic interactions from defect centers are observed, which are clearly distinguished from the broadening due to interactions with two-level systems and phonons. By minimizing the broadening due to the different defect centers, linewidths of the order of 4 kHz are achieved for all samples. The linewidths are limited by temperature-dependent interactions and by an interaction that is yet to be identified. Although the homogeneous linewidth can be narrowed further in these ceramic samples, the broadening is now comparable to the linewidths achieved in rare-earth-ion--doped single crystals. Thus, this work emphasizes the usefulness of studying ceramics to gain insights into dephasing mechanisms relevant to single crystals and suggests that ceramics may be an interesting alternative for applications in classical and quantum information processing.
The work presents the results of optical studies of Xe-related defect in diamond. This defect is one of a few having narrow zero-phonon line in the near-infrared part of the photo-luminescence spectra. It appears in diamond after Xe+ ion implantation followed by thermal annealing. Given unique physical properties of diamond (hardness, optical transparency in wide spectral range, chemical inertness, high thermal conductivity, low thermal expansion coefficient) and stability of Xe-related center it can be viewed as an potential candidate for the source of single-photons, or as optically manipulated qubit, not unlike nitrogen-vacancy center. However, compared to the latter Xe-related center is not as well understood and it is necessary to gain thorough understanding of its spatial structure, symmetry, electronic states and mechanisms of interaction with the host diamond lattice. This thesis addresses several questions, in regard to Xe-related center: 1) How efficiently this center is formed in the implantation/annealing process; 2) How does it interact with the host lattice to produce both homogeneous and inhomogeneous shape of the 811.7 nm zero-phonon line; and 3) What is the type and nature of transitions responsible for the 811.7 nm zero-phonon line. In answering the first question two methods for measuring the conversion efficiency of any kind of optically active defect have been developed and applied to Xe-related center in diamond. The study of line-broadening mechanisms showed how this center interacts with the strain produced by other neighboring Xe-centers, distributed in a plane-like geometry. Also, interaction with vibrational motions of the diamond lattice localized in the vicinity of the Xe-centers is analyzed and the parameters of this pseudo-local mode are found. Finally, using the effects of optical saturation in photo-luminescence under excitation with Gaussian laser beams it has been shown that 811.7 nm zero-phonon line is due to absorption and emission by circular magnetic dipole. Also, the site symmetry of Xe-related center has been confirmed as trigonal with the threefold axis oriented alongdirection in the diamond crystal.