Nonradiative decay and absorption rates of quantum emitters embedded in metallic systems: Microscopic description and their determination from electronic transport

We investigate nonradiative decay and absorption rates of two-level quantum emitters embedded in a metal at low temperatures. We obtain the expressions for both nonradiative transition rates and identify a unique, experimentally accessible way to obtain both nonradiative transition rates via electronic transport in the host metallic system. Our findings not only provide a microscopic description of the nonradiative channels in metals, but they also allow one to identify, determine, and differentiate them from other decay channels, which is crucial to the understanding and controlling of the light-matter interactions at the nanoscale.

Figure 1

Possible relaxation mechanisms for a quantum emitter (QE) bearing an electric dipole moment (thin field lines around the QE) embedded in a metal. Besides photoemission (left) and decay into surface plasmon modes (top), electric-dipole transitions in the QE can also be induced by the inelastic scattering between electronic states (electrons and holes) close to the Fermi level (right).

Figure 2

Main panel: Black (solid) curve representing the relative difference between absorption and decay rates for nonradiative transitions for an emitter embedded in a low temperature metallic host. Inset: Red (dotted) curve representing the absorption rate, blue (dashed) curve representing the decay rate, and black (solid) curve representing the sum of absorption and decay rates. The curve shown in the main panel measures the distance between the red (dotted) and blue (dashed) curves in the inset.

Figure 3

Temperature dependence of the dc-resistivity $\rho \left(T\right)$, normalized by its zero temperature value ${\rho }_0$. Main panel: Inelastic channels, red (dotted) representing absorption $g\to e$, blue (dashed) representing decay $e\to g$, and black (solid) representing the sum of the two inelastic (decay and absorption) contributions. Inset: Elastic channels, red (dotted) representing $e\to e$ processes, blue (dashed) representing $g\to g$ processes, and black (solid) representing the sum of the two elastic contributions to transport.

Figure 4

Main panel: Amplitude of the Shubnikov–de-Haas oscillations for the case of ${\omega }_0<{\omega }_c$ for different temperatures. Solid (black) line for $k_{B}T\ll \hslash {\omega }_0$; dashed (blue) line for $k_{B}T\approx \hslash {\omega }_0$; and dotted (red) line for $k_{B}T\gg \hslash {\omega }_0$. Inset: Shubnikov–de-Haas oscillations at low magnetic fields, for the case of ${\omega }_c<{\omega }_0$.