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Journal of Luminescence

Peak value of the cross-section of zero-phonon line's absorption

Karl K. Rebane, Inna Rebane

Published Oct 1, 1993• 27 citations
Publisher
DOI
10.1016/0022-2313(93)90051-n

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Magnetometry with nitrogen-vacancy (NV) centers in diamond has shown great promise in recent years. In particular, absorption-based magnetometry techniques, employing a cavity to enhance the absorption length, can improve the contrast and sensitivity compared to conventional techniques based on reading out the NV$^-$ triplet fluorescence. The absorption techniques rely on magnetic-field-dependent absorption at the NV$^-$ singlet zero phonon line at 1042$\,$nm and its phonon sideband. In a cavity-enhanced spectroscopy approach, we study pump-laser- and microwave-induced cavity signal changes at room temperature over a spectral range of 680-1050$\,$nm. Through normalization, we eliminate the cavity-enhancement effect and provide quasi-single-pass values for the absorption and optically detected magnetic resonance (ODMR) contrast. The highest contrast is found at 1042$\,$nm, but multiple points of high contrast are found at the peaks of the phonon sideband. Additionally, cavity-enhanced ODMR contrasts in the range of 50-80$\,\%$ are presented. We further measure the broadband singlet absorption cross section at room temperature with a novel method through microwave-induced signal changes. This method is insensitive to pump-laser-induced signal changes by other defects and quantifies the room-temperature absorption strength of the singlet transition and its entire phonon sideband. We determine the absorption cross section at 1042$\,$nm to be $σ^{\,\bigstar}_{1042}=(0.89\pm0.14)\cdot 10^{-21}\,\text{m}^2$ or $σ^{\,\blacktriangle}_{1042}=(2.9\pm0.5)\cdot 10^{-21}\,\text{m}^2$. depending on the employed 532$\,$nm NV$^-$ absorption cross section.

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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.

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Magnetometry with nitrogen-vacancy (NV) centers in diamond has shown great promise in recent years. In particular, absorption-based magnetometry techniques, employing a cavity to enhance the absorption length, can improve the contrast and sensitivity compared to conventional techniques based on reading out the NV−^-− triplet fluorescence. The absorption techniques rely on magnetic-field-dependent absorption at the NV−^-− singlet zero phonon line at 1042 \,nm and its phonon sideband. In a cavity-enhanced spectroscopy approach, we study pump-laser- and microwave-induced cavity signal changes at room temperature over a spectral range of 680-1050 \,nm. Through normalization, we eliminate the cavity-enhancement effect and provide quasi-single-pass values for the absorption and optically detected magnetic resonance (ODMR) contrast. The highest contrast is found at 1042 \,nm, but multiple points of high contrast are found at the peaks of the phonon sideband. Additionally, cavity-enhanced ODMR contrasts in the range of 50-80 %\,\%% are presented. We further measure the broadband singlet absorption cross section at room temperature with a novel method through microwave-induced signal changes. This method is insensitive to pump-laser-induced signal changes by other defects and quantifies the room-temperature absorption strength of the singlet transition and its entire phonon sideband. We determine the absorption cross section at 1042 \,nm to be σ1042 ★=(0.89±0.14)⋅10−21 m2σ^{\,\bigstar}_{1042}=(0.89\pm0.14)\cdot 10^{-21}\,\text{m}^2σ1042★​=(0.89±0.14)⋅10−21m2 or σ1042 ▲=(2.9±0.5)⋅10−21 m2σ^{\,\blacktriangle}_{1042}=(2.9\pm0.5)\cdot 10^{-21}\,\text{m}^2σ1042▲​=(2.9±0.5)⋅10−21m2. depending on the employed 532 \,nm NV−^-− absorption cross section.
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.