Probing the Combined Electromagnetic Local Density of Optical States with Quantum Emitters Supporting Strong Electric and Magnetic Transitions

We experimentally demonstrate that the radiative decay rate of a quantum emitter is determined by the combined electric and magnetic local density of optical states (LDOS). A Drexhage-style experiment was performed for two distinct quantum emitters, divalent nickel ions in magnesium oxide and trivalent erbium ions in yttrium oxide, which both support nearly equal mixtures of isotropic electric dipole and magnetic dipole transitions. The disappearance of lifetime oscillations as a function of emitter-interface separation distance confirms that the electromagnetic LDOS refers to the total mode density, and thus similar to thermal emission, these unique electronic emitters effectively excite all polarizations and orientations of the electromagnetic field.

Figure 1

(a) Normalized electric (${\tilde{\rho }}^{\mathrm{E}}$, red) and magnetic (${\tilde{\rho }}^{\mathrm{M}}$, blue) LDOS together with their summation (${\tilde{\rho }}^{\mathrm{E}}+{\tilde{\rho }}^{\mathrm{M}}$, black). Inset is the sample schematic. (b) Normalized lifetimes for purely ED (red), MD (blue), and strongly mixed ED-MD emitters (black) with varied quantum efficiencies $q$. The dielectric constants for the emitter’s host and metal are $\epsilon =2.25$ and $-97+11.5i$.

Figure 2

(a) Schematic of experimental setup. BL: Bertrand lens, DM: Dichroic mirror, LP: Long pass filter, Pol: Linear polarizer, SP: Short pass filter. Flip mirror (FM) switches between the energy-momentum spectroscopy setup (left) and the lifetime measurement setup (right). Inset depicts the MgO steps separating the ${\mathrm{Ni}}^{2+}:\mathrm{MgO}$ emitter layer from either gold mirror or air interface for the lifetime studies. (b) Spectrally-resolved emission rates, ${\mathrm{A}}_{\mathrm{ED}}$ (red line) and ${\mathrm{A}}_{\mathrm{MD}}$ (blue line), deduced from fitting analysis together with 95% confidence intervals (shaded regions). (c) Examples of time-resolved photoluminescence data and fits used to determine the excited state lifetime.

Figure 3

Lifetime data acquired for ${}^3{T}_2$ state of ${\mathrm{Ni}}^{2+}:\mathrm{MgO}$ near (a) a gold mirror and (b) an air interface together with fits to the purely electric LDOS (red solid line) and combined electromagnetic LDOS (black line). For completeness, we also plot the electric (red dashed) and magnetic (blue dashed) contributions to the electromagnetic LDOS, i.e., the variations expected for ED and MD transitions which are then averaged according to the fit percentages to obtain the black curve. Error bars associated with measured lifetimes are not shown here, because they are smaller than the data point symbols.

Figure 4

Fits of the lifetime data by the mixed ED-MD model (black line), the purely ED model (red line) and the purely MD model (blue line) for both cases: with the gold mirror (a) and with an air interface (b). The shaded gray area represents the 95% confidence intervals of fitting result in the ED and MD model. The insets show the lifetime data together with a purely ED model fit of the ${{}^{4}S}_{3/2}\to {{}^{4}I}_{15/2}$ transition at wavelength $\sim 560\mathrm{nm}$ measured on the same sample, which yields ${\tau }_0=89\pm 0.7\mu \mathrm{s}$ and $q=35.9\pm 5.2\%$.