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Shapes of Inhomogeneously Broadened Resonance Lines in Solids (Invited Talk)

Evans, JH, Bullough, R, Arthur Marshall Stoneham

Published Jan 1, 1971• 0 citations
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A Method for Calculating the Inhomogeneously Broadened Resonance Line Shape

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Effects of strong fields on the shapes of inhomogeneously broadened spectral lines

A. S. Bankovskii, Pavel A Apanasevich

Journal of Applied Spectroscopy•Mar 1, 1969•1 citation

Crossover from inhomogeneous to homogeneous response of a resonantly driven hBN quantum emitter

Domitille Gérard, Stéphanie Buil, Jean‐Pierre Hermier +1 more

We experimentally investigate a solid-state quantum emitter---a B center in hexagonal boron nitride (hBN)---that has lifetime-limited coherence at short times, and experiences inhomogeneous broadening due to spectral diffusion at longer times. By making use of power broadening in resonant laser excitation, we explore the crossover between the inhomogeneous and the homogeneous broadening regimes. With the support of numerical simulations, we show that the line shape, count rate, second-order correlations, and long-time photon statistics evolve from a regime where they are dictated by spectral diffusion to a regime where they are simply given by the homogeneous response of the emitter, yielding restored Lorentzian shape and Poissonian photon statistics. Saturation of the count rate and line broadening occur not at the onset of the Rabi oscillations, but when the power-broadened homogeneous response becomes comparable with the inhomogeneous linewidth. Moreover, we identify specific signatures in both the second-order correlations and long-time photon statistics that are well explained by a microscopic spectral diffusion model based on discrete jumps at timescales of micro- to milliseconds. Our work provides an extensive description of the photophysics of B centers under resonant excitation, and can be readily extended to a wide variety of solid-state quantum emitters.

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Suppression of inhomogeneous broadening in optically addressed solids for quantum computing applications (Invited Paper)

Philip Hemmer

Inhomogeneous broadening in optically addressed solids provides a convenient technique for individually addressing a large number of optically active defects in a crystal. Such a capability is important for quantum computer development. However, the random nature of inhomogeneous broadening can limit scalability. Here, techniques that can be used to suppress inhomogeneous broadening will be reviewed including a recently proposed VLSI quantum computer design based on nitrogen-vacancy (NV) color centers in diamond.

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Resonance lineshapes in multi-level atomic systems

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Journal of Physics B Atomic and Molecular Physics•Oct 21, 1977•0 citations

Line Shapes of Resonant, Nonlinear, Paramagnetic Susceptibilities

Harro G. Andresen, H. Welling

Line shapes for both the absolute value and the real and imaginary components of the nonlinear, paramagnetic susceptibility ${\ensuremath{\chi}}_{\mathrm{NL}}(2\ensuremath{\omega})$ of a ruby crystal have been measured as a function of the magnetic field and crystal orientation at room temperature and "resonant" conditions, where the $X$-band driving frequency coincides with or is very close to the resonance frequencies of an equidistant or nearly equidistant paramagnetic three-level system. Though all measured line shapes were in good qualitative agreement with theoretical line-shape expressions, derived under the assumption of homogeneously broadened, Lorentzian-shaped, single-quantum resonances, a quantitative comparison between theory and experiment exhibited systematic discrepancies, such as too slowly decaying wings for the theoretical curves and too large theoretical amplitudes at "partly resonant" conditions for nearly equidistant three-level schemes. Line-shape measurements for single-quantum resonances of the linear susceptibility contradicted the Lorentzian line-shape assumption, but could satisfactorily be matched by a Gauss-type line shape. Although it was possible to fit the measured single-quantum resonance line shapes also by the convolution of a narrow, Lorentzian line shape with a proper combination of macroscopic inhomogeneous line-broadening effects such as Gaussian distributions of crystal $c$-axis orientations and crystal strains, the equivalent procedure for the nonlinear susceptibility resonances did not remove the discrepancy between theory and experiment. Since the approach towards thermal equilibrium within tightly coupled spin systems in solids has, in general, to be described by nonexponential relaxation processes, the line-shape expressions for the nonlinear susceptibility ${\ensuremath{\chi}}_{\mathrm{NL}}(2\ensuremath{\omega})$ were phenomenologically generalized and formulated in terms of non-Lorentzian-shaped, homogeneous, single-quantum resonances. By using these generalized line-shape expressions, it was possible to achieve a satisfactory quantitative agreement with all experimental results for both the line shapes of single-quantum, linear-susceptibility resonances as well as for the line shapes of the absolute value and the real and imaginary components of the nonlinear-susceptibility resonances.

Physical Review•Jul 5, 1965•1 citation
We experimentally investigate a solid-state quantum emitter---a B center in hexagonal boron nitride (hBN)---that has lifetime-limited coherence at short times, and experiences inhomogeneous broadening due to spectral diffusion at longer times. By making use of power broadening in resonant laser excitation, we explore the crossover between the inhomogeneous and the homogeneous broadening regimes. With the support of numerical simulations, we show that the line shape, count rate, second-order correlations, and long-time photon statistics evolve from a regime where they are dictated by spectral diffusion to a regime where they are simply given by the homogeneous response of the emitter, yielding restored Lorentzian shape and Poissonian photon statistics. Saturation of the count rate and line broadening occur not at the onset of the Rabi oscillations, but when the power-broadened homogeneous response becomes comparable with the inhomogeneous linewidth. Moreover, we identify specific signatures in both the second-order correlations and long-time photon statistics that are well explained by a microscopic spectral diffusion model based on discrete jumps at timescales of micro- to milliseconds. Our work provides an extensive description of the photophysics of B centers under resonant excitation, and can be readily extended to a wide variety of solid-state quantum emitters.
Inhomogeneous broadening in optically addressed solids provides a convenient technique for individually addressing a large number of optically active defects in a crystal. Such a capability is important for quantum computer development. However, the random nature of inhomogeneous broadening can limit scalability. Here, techniques that can be used to suppress inhomogeneous broadening will be reviewed including a recently proposed VLSI quantum computer design based on nitrogen-vacancy (NV) color centers in diamond.
Line shapes for both the absolute value and the real and imaginary components of the nonlinear, paramagnetic susceptibility ${\ensuremath{\chi}}_{\mathrm{NL}}(2\ensuremath{\omega})$ of a ruby crystal have been measured as a function of the magnetic field and crystal orientation at room temperature and "resonant" conditions, where the XXX-band driving frequency coincides with or is very close to the resonance frequencies of an equidistant or nearly equidistant paramagnetic three-level system. Though all measured line shapes were in good qualitative agreement with theoretical line-shape expressions, derived under the assumption of homogeneously broadened, Lorentzian-shaped, single-quantum resonances, a quantitative comparison between theory and experiment exhibited systematic discrepancies, such as too slowly decaying wings for the theoretical curves and too large theoretical amplitudes at "partly resonant" conditions for nearly equidistant three-level schemes. Line-shape measurements for single-quantum resonances of the linear susceptibility contradicted the Lorentzian line-shape assumption, but could satisfactorily be matched by a Gauss-type line shape. Although it was possible to fit the measured single-quantum resonance line shapes also by the convolution of a narrow, Lorentzian line shape with a proper combination of macroscopic inhomogeneous line-broadening effects such as Gaussian distributions of crystal ccc-axis orientations and crystal strains, the equivalent procedure for the nonlinear susceptibility resonances did not remove the discrepancy between theory and experiment. Since the approach towards thermal equilibrium within tightly coupled spin systems in solids has, in general, to be described by nonexponential relaxation processes, the line-shape expressions for the nonlinear susceptibility ${\ensuremath{\chi}}_{\mathrm{NL}}(2\ensuremath{\omega})$ were phenomenologically generalized and formulated in terms of non-Lorentzian-shaped, homogeneous, single-quantum resonances. By using these generalized line-shape expressions, it was possible to achieve a satisfactory quantitative agreement with all experimental results for both the line shapes of single-quantum, linear-susceptibility resonances as well as for the line shapes of the absolute value and the real and imaginary components of the nonlinear-susceptibility resonances.