Modeling spatiotemporal dynamics of chiral coupling of quantum emitters to light fields in nanophotonic structures

A quantum emitter placed in a nanophotonic structure can result in nonreciprocal phenomena like chiral light excitation. Here, we present a theoretical model to couple circularly polarized emitters described by the density-matrix formalism to the electromagnetic fields within a finite-difference time-domain simulation. In particular, we discuss how to implement complex electric fields in the simulation to make use of the rotating-wave approximation. By applying our model to a quantum emitter in a dielectric waveguide and an optical circulator, we show how the excitation of the quantum system depends on its position and polarization. In turn, the back-coupling can result in strongly asymmetric light excitation. Our framework and results will help better explain spatiotemporal dynamics of light fields in nanophotonic structures containing quantum emitters.

Figure 1

(a) Left: Schematic of dielectric structure. Right: Line plot of the Stokes parameters $S_0$ and $S_3$ through the cross section of the waveguide. Color plots of the Stokes parameters (b) $S_0$ and (c) $S_3$.

Figure 2

(a) Sketch of the waveguide with a quantum emitter with a V-type three-level structure as shown in the inset excited by an external source. (b) Left: Effective pulse area for two emitter polarizations as a function of the distance from the waveguide center. Included are results for the model without dephasing ($\gamma =0\text{THz}$) and with dephasing ($\gamma =4.5\text{THz}$). Right: Population dynamics of the density matrix for the two states $|L\rangle$ and $|R\rangle$ in the $C$ points without dephasing.

Figure 3

(a) Sketch of the waveguide with an excited quantum emitter. The electric field introduced by the emitter back-coupling propagating through two planes on the left (TL) and right (TR) sides of the grid is monitored. Snapshots of the electric field for the emitter placed in the center (b) for either occupation, (d) for the upper $C$ point for ${\rho }_{LL}=\frac{1}{2}$, and (f) for ${\rho }_{RR}=\frac{1}{2}$. Monitored fields in (c) the TL or TR plane for the emitter in the upper $C$ point for ${\rho }_{LL}=\frac{1}{2}$ in the TL or TR plane for $\gamma =0\text{THz}$ and (e) in the TR plane for different dephasing rates $\gamma =0,4.5$, and $23\text{THz}$.

Figure 4

(a) Schematic of the structure and light propagation of the external source field ${\mathit{E}}_{\text{src}}$ introduced on the left side of the top waveguide of the circulator. (b) $S_0$ snapshot of the source field. (c) Close-up of the $S_3$ parameter of the excited ring-resonator mode. The emitter is placed within the outer $C$ point of the ring resonator (border highlighted by white lines). (d) Schematic of the structure including emitter and propagation of the back-coupled fields induced by the emitter polarization ${\mathit{E}}_{\text{bcpl}}$. (e) Close-up of the ring-resonator region, where the emitter is placed in one of two positions. Depending on the emitter polarization, only one state of the system will be excited (indicated by color: red for $|R\rangle$, green for $|L\rangle$). Right: population dynamics for both relevant cases. (f) Snapshot of ${\mathit{E}}_{\text{bcpl}}$ of the emitter in the red case.

Figure 5

Population dynamics in the ring-resonator structure after excitation with an external source field (emitter position: green). Included are results for the model without dephasing ($\gamma =0\text{THz}$) and with dephasing ($\gamma =4.5\text{THz}$). Additionally shown is the relative electric-field strength at the emitter position $|E_x/E_{x,\text{max}}|$. A sketch of the V-type three-level structure is included in the inset on the bottom right