The effect of instantaneous spectral diffusion (ISD) on gate operations in rare-earth-ion-doped crystals is an important question to answer for the future of rare-earth quantum computing. Here we present a microscopic modeling that highlights the stochastic nature of the phenomenon and use it to investigate ISD errors on single-qubit gate operations. Furthermore, we present a method to estimate the total error from many different error sources by only studying subsystems containing one error source at a time. This allows us to estimate the total ISD error from all nonqubit dopants in the vicinity of a qubit. We conclude that optical pumping techniques must be used to empty the frequency regions around the qubit transitions from absorption (transmission windows) in order to suppress the ISD errors. Despite using such windows, there remains a roughly $0.3%$ risk that a qubit has an ISD error larger than the error from other sources. In those cases, the qubit can be discarded and its frequency channel can be reused by another qubit. However, in most cases the ISD errors are significantly smaller than other errors, thus opening up the possibility to perform noisy intermediate-scale quantum (NISQ) algorithms despite ISD being present.The effect of instantaneous spectral diffusion (ISD) on gate operations in rare-earth-ion-doped crystals is an important question to answer for the future of rare-earth quantum computing. Here we present a microscopic modeling that highlights the stochastic nature of the phenomenon and use it to investigate ISD errors on single-qubit gate operations. Furthermore, we present a method to estimate the total error from many different error sources by only studying subsystems containing one error source at a time. This allows us to estimate the total ISD error from all nonqubit dopants in the vicinity of a qubit. We conclude that optical pumping techniques must be used to empty the frequency regions around the qubit transitions from absorption (transmission windows) in order to suppress the ISD errors. Despite using such windows, there remains a roughly $0.3%$ risk that a qubit has an ISD error larger than the error from other sources. In those cases, the qubit can be discarded and its frequency channel can be reused by another qubit. However, in most cases the ISD errors are significantly smaller than other errors, thus opening up the possibility to perform noisy intermediate-scale quantum (NISQ) algorithms despite ISD being present.

arXiv:2110.09884Physical Review AMar 11, 20226 citations

Spectral and Laser Characteristics of Activated Crystals

Alexander A. Kaminskii

Springer series in optical sciences/SPringer series in optical sciencesJan 1, 19900 citations

Optical Spectra of Single Impurity Molecules in a Polymer: Spectral Diffusion and Persistent Spectral Hole-Burning

Th. Basché, W. E. Moerner

Recent advances in the optical detection and spectroscopy of single impurity centers in crystals has provided the possibility of obtaining information about defect-solid interactions on a truly local level. For the system composed of pentacene impurity molecules in the crystal p-terphenyl, single molecules have been studied using both absorption1 and fluorescence excitation2 techniques at liquid helium temperatures. The superior signal-to-noise of the latter technique has led to direct observations of the lifetime-limited Lorentzian homogeneous profile of a single pentacene impurity3 as well as the surprising observation of spontaneous spectral diffusion4. Spectral diffusion, or changes in the resonance frequency of an impurity molecule with time as a result of low-energy excitations (two-level system transitions (TLS)),5 is generally expected in amorphous hosts. Indeed, the presence of TLSs in amorphous solids is intimately connected with nonphotochemical mechanisms for persistent spectral hole-burning (PSHB) in amorphous materials6-8. Using perylene impurity molecules in poly(ethylene), we have observed the optical spectra of single molecules in a polymeric host for the first time. At 1.5K, individual perylene molecules show the expected spectral diffusion; moreover, we observe light-induced changes in resonance frequency, i.e., persistent spectral hole-burning, which allows one to envision optical storage on the single-molecule level.Recent advances in the optical detection and spectroscopy of single impurity centers in crystals has provided the possibility of obtaining information about defect-solid interactions on a truly local level. For the system composed of pentacene impurity molecules in the crystal p-terphenyl, single molecules have been studied using both absorption1 and fluorescence excitation2 techniques at liquid helium temperatures. The superior signal-to-noise of the latter technique has led to direct observations of the lifetime-limited Lorentzian homogeneous profile of a single pentacene impurity3 as well as the surprising observation of spontaneous spectral diffusion4. Spectral diffusion, or changes in the resonance frequency of an impurity molecule with time as a result of low-energy excitations (two-level system transitions (TLS)),5 is generally expected in amorphous hosts. Indeed, the presence of TLSs in amorphous solids is intimately connected with nonphotochemical mechanisms for persistent spectral hole-burning (PSHB) in amorphous materials6-8. Using perylene impurity molecules in poly(ethylene), we have observed the optical spectra of single molecules in a polymeric host for the first time. At 1.5K, individual perylene molecules show the expected spectral diffusion; moreover, we observe light-induced changes in resonance frequency, i.e., persistent spectral hole-burning, which allows one to envision optical storage on the single-molecule level.

Spectral Hole-Burning and Related Spectroscopies: Science and ApplicationsJan 1, 19910 citations

Spectral and Laser Characteristics of Activated Crystals

Alexander A. Kaminskii

Springer series in optical sciences/SPringer series in optical sciencesJan 1, 19812 citations

Dynamics of phonons in submicrometer zones generated by an optical waveguide

Robert Jan van Wijk, J. I. Dijkhuis, H. W. de Wijn

We introduce a technique utilizing the evanescent field of an optical waveguide to examine the dynamics of nonequilibrium high-frequency phonons resonant with optically excited centers in zones of submicrometer dimension. The technique is used to create a nearly saturated zone of excited ${\mathrm{Cr}}^{3+}$ ions at the surface of a 700-at. ppm ruby crystal at 1.5 K by optical pumping through the broad bands. At the same time, the optical pumping serves to generate resonant 29-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ phonons. The decay of the combined spin-phonon system, measured via the ${\mathit{R}}_{2}$ luminescence following interruption of the optical pumping, is explained by elastic spatial diffusion in parallel with spectral wipeout. The time constant for loss by spatial diffusion is derived rigorously from rate equations. Spectral wipeout is treated according to the model developed by Goossens et al. based on one-site inelastic scattering by weakly exchange-coupled ${\mathrm{Cr}}^{3+}$ pairs, but modified to include the appreciable elastic diffusion remaining after wipeout under the present extreme conditions. Spectral wipeout turns out to predominate at high excited-state concentration. The optical feeding into 2A\ifmmode\bar\else\textasciimacron\fi{} ${(}^{2}$ E) is found to result mainly from excited-state absorption starting from E\ifmmode\bar\else\textasciimacron\fi{} ${(}^{2}$ E), despite the low probability of the latter at the light wavelength used (514.5 nm).We introduce a technique utilizing the evanescent field of an optical waveguide to examine the dynamics of nonequilibrium high-frequency phonons resonant with optically excited centers in zones of submicrometer dimension. The technique is used to create a nearly saturated zone of excited ${\mathrm{Cr}}^{3+}$ ions at the surface of a 700-at. ppm ruby crystal at 1.5 K by optical pumping through the broad bands. At the same time, the optical pumping serves to generate resonant 29-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ phonons. The decay of the combined spin-phonon system, measured via the ${\mathit{R}}_{2}$ luminescence following interruption of the optical pumping, is explained by elastic spatial diffusion in parallel with spectral wipeout. The time constant for loss by spatial diffusion is derived rigorously from rate equations. Spectral wipeout is treated according to the model developed by Goossens et al. based on one-site inelastic scattering by weakly exchange-coupled ${\mathrm{Cr}}^{3+}$ pairs, but modified to include the appreciable elastic diffusion remaining after wipeout under the present extreme conditions. Spectral wipeout turns out to predominate at high excited-state concentration. The optical feeding into 2A\ifmmode\bar\else\textasciimacron\fi{}${(}^{2}$E) is found to result mainly from excited-state absorption starting from E\ifmmode\bar\else\textasciimacron\fi{}${(}^{2}$E), despite the low probability of the latter at the light wavelength used (514.5 nm).

Physical review. B, Condensed matterJun 1, 19910 citations

0.3%

risk that a qubit has an ISD error larger than the error from other sources. In those cases, the qubit can be discarded and its frequency channel can be reused by another qubit. However, in most cases the ISD errors are significantly smaller than other errors, thus opening up the possibility to perform noisy intermediate-scale quantum (NISQ) algorithms despite ISD being present.

{\mathrm{Cr}}^{3+}

ions at the surface of a 700-at. ppm ruby crystal at 1.5 K by optical pumping through the broad bands. At the same time, the optical pumping serves to generate resonant 29-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ phonons. The decay of the combined spin-phonon system, measured via the

{\mathit{R}}_{2}

luminescence following interruption of the optical pumping, is explained by elastic spatial diffusion in parallel with spectral wipeout. The time constant for loss by spatial diffusion is derived rigorously from rate equations. Spectral wipeout is treated according to the model developed by Goossens et al. based on one-site inelastic scattering by weakly exchange-coupled

{\mathrm{Cr}}^{3+}

pairs, but modified to include the appreciable elastic diffusion remaining after wipeout under the present extreme conditions. Spectral wipeout turns out to predominate at high excited-state concentration. The optical feeding into 2A\ifmmode\bar\else\textasciimacron\fi{}

{(}^{2}

E) is found to result mainly from excited-state absorption starting from E\ifmmode\bar\else\textasciimacron\fi{}

{(}^{2}

E), despite the low probability of the latter at the light wavelength used (514.5 nm).