Phonon avalanches resonant with the optically inverted Zeeman-split $\ifmmode \bar{E}\else \={E}\fi{}{(}^{2}E)$ doublet of ${\mathrm{Cr}}^{3+}$ have been measured and analyzed in a single crystal of 500-at. ppm ruby $({\mathrm{Al}}_{2}{\mathrm{O}}_{3}:{\mathrm{Cr}}^{3+})$ with a geometry adapted to the study of coherence. A set of coherent Bloch equations governing the interacting acoustic wave and spin polarizations is found to provide an excellent description of the results, and to be far superior to incoherent rate equations for the phonon and level populations. The dephasing time conforms with the width of the inhomogeneously broadened transition connecting the $\ifmmode \bar{E}\else \={E}\fi{}{(}^{2}E)$ states, which indicates that dephasing primarily occurs by the spread in frequencies.Phonon avalanches resonant with the optically inverted Zeeman-split $\ifmmode \bar{E}\else \={E}\fi{}{(}^{2}E)$ doublet of ${\mathrm{Cr}}^{3+}$ have been measured and analyzed in a single crystal of 500-at. ppm ruby $({\mathrm{Al}}_{2}{\mathrm{O}}_{3}:{\mathrm{Cr}}^{3+})$ with a geometry adapted to the study of coherence. A set of coherent Bloch equations governing the interacting acoustic wave and spin polarizations is found to provide an excellent description of the results, and to be far superior to incoherent rate equations for the phonon and level populations. The dephasing time conforms with the width of the inhomogeneously broadened transition connecting the $\ifmmode \bar{E}\else \={E}\fi{}{(}^{2}E)$ states, which indicates that dephasing primarily occurs by the spread in frequencies.

Physical review. B, Condensed matterOct 20, 200316 citations

Avalanche instability as nonequilibrium quantum criticality

Xi Chen, Jong E. Han

A fundamental instability in the nonequilibrium conduction band under an electric field bias is proposed via the spontaneous emission of coherent phonons. Analytic theory, supported by numerical calculations, establishes that the quantum avalanche, an abrupt nonequilibrium occupation of excited bands, results from the competition between the collapse of the band minimum via the phonon emission and the dephasing of the electron with the environment. The continuous avalanche transition is a quantum phase transition with the nonequilibrium phase diagram determined by the avalanche parameter $\ensuremath{\beta}$, with peculiar reentrant avalanche domes close to the phase boundary. We further confirm the nature of the quantum avalanche with the temperature dependence.A fundamental instability in the nonequilibrium conduction band under an electric field bias is proposed via the spontaneous emission of coherent phonons. Analytic theory, supported by numerical calculations, establishes that the quantum avalanche, an abrupt nonequilibrium occupation of excited bands, results from the competition between the collapse of the band minimum via the phonon emission and the dephasing of the electron with the environment. The continuous avalanche transition is a quantum phase transition with the nonequilibrium phase diagram determined by the avalanche parameter $\ensuremath{\beta}$, with peculiar reentrant avalanche domes close to the phase boundary. We further confirm the nature of the quantum avalanche with the temperature dependence.

arXiv:2307.07612Physical review. B./Physical review. BFeb 20, 20242 citations

Phonon avalanches resonant with the optically inverted Zeeman-split $\ifmmode \bar{E}\else \={E}\fi{}{(}^{2}E)$ doublet of

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

have been measured and analyzed in a single crystal of 500-at. ppm ruby

({\mathrm{Al}}_{2}{\mathrm{O}}_{3}:{\mathrm{Cr}}^{3+})

with a geometry adapted to the study of coherence. A set of coherent Bloch equations governing the interacting acoustic wave and spin polarizations is found to provide an excellent description of the results, and to be far superior to incoherent rate equations for the phonon and level populations. The dephasing time conforms with the width of the inhomogeneously broadened transition connecting the $\ifmmode \bar{E}\else \={E}\fi{}{(}^{2}E)$ states, which indicates that dephasing primarily occurs by the spread in frequencies.