Probing Electric and Magnetic Vacuum Fluctuations with Quantum Dots

The electromagnetic-vacuum-field fluctuations are intimately linked to the process of spontaneous emission of light. Atomic emitters cannot probe electric- and magnetic-field fluctuations simultaneously because electric and magnetic transitions correspond to different selection rules. In this Letter we show that semiconductor quantum dots are fundamentally different and are capable of mediating electric-dipole, magnetic-dipole, and electric-quadrupole transitions on a single electronic resonance. As a consequence, quantum dots can probe electric and magnetic fields simultaneously and can thus be applied for sensing the electromagnetic environment of complex photonic nanostructures. Our study opens the prospect of interfacing quantum dots with optical metamaterials for tailoring the electric and magnetic light-matter interaction at the single-emitter level.

Figure 1

Decay dynamics of mesoscopic QDs beyond the dipole approximation. (a) Schematic of the QD decay channels in the proximity of a metal interface. The electron (blue) and hole (red) wave functions illustrate the built-in asymmetry. (b) Light-matter interaction processes governing ${\mathrm{\Gamma }}^{(0)}$, where the ED interacts with the radiation modes (RAD) of the electric vacuum $E_x^{\mathrm{RAD}}$ and the guided surface plasmon (PL) modes $E_x$. (c) Processes governing the ED-MD interference. The light emitted by the ED ${\mu }_x$ interacts with the MD $m_y$ and creates a magnetic field. The physical picture of ${\mathrm{\Gamma }}^{(1Q)}$ is conceptually analogous. (d) Processes governing ${\mathrm{\Gamma }}^{(2)}$ with pure MD and EQ contributions. The EQ $Q_{xz}$ couples to the gradient of the electric vacuum.

Figure 2

Decay dynamics of QDs near a silver interface. All the rates are normalized to the decay rate in homogeneous GaAs. (a) Decay rate for the direct (inverted) QD orientation marked by blue (orange) lines. The black dashed line denotes the dipole theory. (b) Decomposition of the decay rates according to the expansion order. The Ohmic losses are indicated by the dotted black line. (c) The ED-MD and ED-EQ Green’s tensor probed by mesoscopic QDs and normalized to $\text{Im}{\{G}_{xx}(0,0)\}$ in homogeneous GaAs.

Figure 3

Probing field gradients with mesoscopic QDs. (a) For an axially oriented dipole, ${\mathrm{\Gamma }}^{(1)}$ enhances (suppresses) the light-matter interaction for the configuration marked by orange (blue). The dashed line is the prediction of the dipole theory. (b) Vector plot of the plasmonic field generated by the ED of the QD situated 20 nm away from the nanowire. Both the length of the arrows and the color scale denote the field magnitude. (c) The field projections probed by the QD can be extracted by subtracting the decay curves in (a). The gray-shaded area is the region where nonradiative losses are dominant. (d) For a radially oriented dipole, ${\mathrm{\Gamma }}^{(1)}=0$ and the QD behaves as an electric dipole.