Shapes of Inhomogeneously Broadened Resonance Lines in Solids

Stoneham, A. M.

doi:10.1103/revmodphys.41.82

Cited by 620 publications

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“…Stoneham's theory [15] of inhomogeneous line broadening in defected crystal, is based on long-range forces and parts of it can be interpreted in terms of Lévy stable laws [9]. Stoneham's approach [15] is inherently static, while the SM line shape model considers both dynamical and static contributions from the defects. An important issue is the slow and fast modulation limits [6,11].…”

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confidence: 99%

“…Lévy statistics is known to describe several long range interaction systems in diverse fields such as astronomy [12], turbulence [13] and spin glass [14]. Stoneham's theory [15] of inhomogeneous line broadening in defected crystal, is based on long-range forces and parts of it can be interpreted in terms of Lévy stable laws [9]. Stoneham's approach [15] is inherently static, while the SM line shape model considers both dynamical and static contributions from the defects.…”

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confidence: 99%

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Lévy Distribution of Single Molecule Line Shape Cumulants in Glasses

2000

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We investigate the distribution of single molecule line shape cumulants, κ1, κ2, · · ·, in low temperature glasses based on the sudden jump, standard tunneling model. We find that the cumulants are described by Lévy stable laws, thus generalized central limit theorem is applicable for this problem.Pacs: 05.40.Fb, 61.43.FS, 78.66.Jg Recent experimental advances [1] have made it possible to measure the spectral line shape of a single molecule (SM) embedded in a condensed phase. Because each molecule is in a unique static and dynamic environment, the line shapes of chemically identical SMs vary from molecule to molecule [2]. In this way, the dynamic properties of the host are encoded in the distribution of single molecule spectral line shapes [1][2][3][4][5][6][7][8][9]. We examine the statistical properties of the line shapes and show how these are related to the underlying microscopic dynamical events occurring in the condensed phase.We use the Geva-Skinner [5] model for the SM line shape in a low temperature glass based on the sudden jump picture of Kubo and Anderson [10,11]. In this model, a random distribution of low-density (and noninteracting) dynamical defects [e.g., spins or two level systems (TLS)] interacts with the molecule via long range interaction (e.g., dipolar). We show that Lévy statistics fully characterizes the properties of the SM spectral line both in the fast and slow modulation limits, while far from these limits Lévy statistics describes the mean and variance of the line shape. We then compare our analytical results, derived in the slow modulation limit, with results obtained from numerical simulation. The good agreement indicates that the slow modulation limit is correct for the parameter set relevant to experiment.Lévy stable distributions serve as a natural generalization of the normal Gaussian distribution. The importance of the Gaussian in statistical physics stems from the central limit theorem. Lévy stable laws are used when analyzing sums of the type x i , with {x i } being independent identically distributed random variables characterized by a diverging variance. In this case the ordinary Gaussian central limit theorem must be replaced with the generalized central limit theorem. With this generalization, Lévy stable probability densities, L γ,η (x), replace the Gaussian of the standard central limit theorem. Khintchine and Lévy found that stable characteristic functions,L γ,η (k), are of the form [12] ln L γ,η (k) = iµk − z γ |k| γ 1 − iη k |k| tan πγ 2for 0 < γ ≤ 2 (for the case η = 0, γ = 1 see [12]). Four parameters are needed for a full description of a stable law. The constant γ is called the characteristic exponent, the parameter µ is a location parameter which is unimportant in the present case, z γ > 0 is a scale parameter and −1 ≤ η ≤ 1 is the index of symmetry. When An important issue is the slow and fast modulation limits [6,11]. Briefly, the fast (slow) modulation limit is valid if important contributions to the line shape are from TLSs which satisfy ν ≪ K (...

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Lévy Distribution of Single Molecule Line Shape Cumulants in Glasses

2000

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“…55,56 The broad and symmetric peaks associated with Fe and Cu for the unannealed sample show presence of inhomogeneous strain. The unannealed sample is also strained due to the rapid solidification of the alloy from the molten state with the Fe and Cu nano regions randomly distributed, as shown by the electron microscopy studies.…”

Section: Effect Of Annealingmentioning

confidence: 99%

Experimental investigation of inhomogeneities, nanoscopic phase separation, and magnetism in arc melted Fe-Cu metals with equal atomic ratio of the constituents

Jaffari

Aftab²,

Anjum

et al. 2015

Journal of Applied Physics

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Composition gradient and phase separation at the nanoscale have been investigated for arc-melted and solidified with equiatomic Fe-Cu. Diffraction studies revealed that Fe and Cu exhibited phase separation with no trace of any mixing. Microscopy studies revealed that immiscible Fe-Cu form dense bulk nanocomposite. The spatial distribution of Fe and Cu showed existence of two distinct regions, i.e., Fe-rich and Cu-rich regions. Fe-rich regions have Cu precipitates of various sizes and different shapes, with Fe forming meshes or channels greater than 100 nm in size. On the other hand, the matrix of Cu-rich regions formed strips with fine strands of nanosized Fe. Macromagnetic response of the system showed ferromagnetic behavior with a magnetic moment being equal to about 2.13 μB/Fe atom and a bulk like negligible value of coercivity over the temperature range of 5–300 K. Anisotropy constant has been calculated from various laws of approach to saturation, and its value is extracted to be equal to 1350 J/m3. Inhomogeneous strain within the Cu and Fe crystallites has been calculated for the (unannealed) sample solidified after arc-melting. Annealed sample also exhibited local inhomogeneity with removal of inhomogeneous strain and no appreciable change in magnetic character. However, for the annealed sample phase separated Fe exhibited homogenous strain.

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“…The various molecules in the solid have intrinsically narrow widths (called the homogeneous width), but the overall absorption line profile represents the range of different center frequencies for the molecules arising from different local environments (illustrated in Figure 3(c)) which shift the absorption energies over a range. These perturbations arise from effects like local stresses and strains arising from crystal imperfections, or from other defects, or possibly from local electric fields, and so on, and a number of theoretical models were proposed for the mechanisms of inhomogeneous broadening (12). FIGURE 3 HERE:…”

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Nobel Lecture: Single-molecule spectroscopy, imaging, and photocontrol: Foundations for super-resolution microscopy

Moerner

2015

Rev. Mod. Phys.

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The initial steps toward optical detection and spectroscopy of single molecules in condensed matter arose out of the study of inhomogeneously broadened optical absorption profiles of molecular impurities in solids at low temperatures. Spectral signatures relating to the fluctuations of the number of molecules in resonance led to the attainment of the single-molecule limit in 1989 using frequency-modulation laser spectroscopy. In the early 90's, many fascinating physical effects were observed for individual molecules, and the imaging of single molecules as well as observations of spectral diffusion, optical switching and the ability to select different single molecules in the same focal volume simply by tuning the pumping laser frequency provided important forerunners of the later superresolution microscopy with single molecules. In the room temperature regime, imaging of single copies of the green fluorescent protein also uncovered surprises, especially the blinking and photoinduced recovery of emitters, which stimulated further development of photoswitchable fluorescent protein labels. Because each single fluorophore acts a light source roughly 1 nm in size, microscopic observation and localization of individual fluorophores is a key ingredient to imaging beyond the optical diffraction limit. Combining this with active control of the number of emitting molecules in the pumped volume led to the super-resolution imaging of Eric Betzig and others, a new frontier for optical microscopy beyond the diffraction limit. The background leading up to these observations is described and current developments are summarized. The early days Introduction and early inspirationsI want to thank the Nobel Committee for Chemistry, the Royal Swedish Academy of Sciences, and the Nobel Foundation for selecting me for this prize recognizing the development of super-resolved fluorescence microscopy. I am truly honored to share the prize with my two esteemed colleagues, Stefan Hell and Eric Betzig. My primary contributions center on the first optical detection and spectroscopy of single molecules in the condensed phase(1), and on the observations of imaging, blinking and photocontrol not only for single molecules at low temperatures in solids, but also for useful variants of the green fluorescent protein at room temperature (2). This lecture describes the context of the events leading up to these advances as well as a portion of the subsequent developments both around the world and in my laboratory.In the mid-1980's, I derived much early inspiration from amazing advances that were occurring around the world where single nanoscale quantum systems were detected and explored for both scientific and technological reasons. Some of these were (i) the spectroscopy of single electrons or ions confined in vacuum electromagnetic traps (3-5), (ii) scanning tunneling microscopy (STM) (6) and atomic force microscopy (AFM) (7), and (iii) the study of ion currents in single membrane-embedded ion channels (8). But why not optical detection and ...

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Shapes of Inhomogeneously Broadened Resonance Lines in Solids

Cited by 620 publications

References 78 publications

Lévy Distribution of Single Molecule Line Shape Cumulants in Glasses

Lévy Distribution of Single Molecule Line Shape Cumulants in Glasses

Experimental investigation of inhomogeneities, nanoscopic phase separation, and magnetism in arc melted Fe-Cu metals with equal atomic ratio of the constituents

Nobel Lecture: Single-molecule spectroscopy, imaging, and photocontrol: Foundations for super-resolution microscopy

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