Light Scattering from Solid-State Quantum Emitters: Beyond the Atomic Picture

Coherent scattering of light by a single quantum emitter is a fundamental process at the heart of many proposed quantum technologies. Unlike atomic systems, solid-state emitters couple to their host lattice by phonons. Using a quantum dot in an optical nanocavity, we resolve these interactions in both time and frequency domains, going beyond the atomic picture to develop a comprehensive model of light scattering from solid-state emitters. We find that even in the presence of a low-$Q$ cavity with high Purcell enhancement, phonon coupling leads to a sideband that is completely insensitive to excitation conditions and to a nonmonotonic relationship between laser detuning and coherent fraction, both of which are major deviations from atomlike behavior.

Figure 1

(a) Schematic of the experiment: BS, beam splitter; CCD, charge-coupled device (camera); FPI, Fabry-Perot interferometer; LP, linear polarizer; SM, single mode fiber; SPAD, single photon avalanche diode; $\mathrm{\Delta }\varphi$, phase shift; $\tau$ path length difference. (b) Measurement of the first-order correlation function [$g^{(1)}(\tau )$] at $\mathcal{S}=0.25$ with ${\mathrm{\Delta }}_{\mathrm{LX}}=0$. The emission contains a phonon sideband (${\mathcal{F}}_{\mathrm{PSB}}$), incoherent resonance fluorescence (${\mathcal{F}}_{\mathrm{inc}}$), and coherently scattered (${\mathcal{F}}_{\mathrm{CS}}$) fractions. Experimental measurements of fringe contrast (red circles) agree well with a calculation using the polaron master equation (solid red line) where the phonon coupling strength $\alpha$ and cutoff frequency ${\nu }_c$ are the only free parameters. A pure dephasing model (dashed red line) decays monoexponentially and cannot capture phonon dynamics. Inset: An experimental spectrum (blue triangles) measured simultaneously is also well reproduced by the polaron model (blue line) with the same parameters. The calculated spectrum is convolved with the spectrometer instrument response in order to reproduce the observed ZPL width.

Figure 2

Components of the resonant scattering spectrum. (a) Semilog spectrum at low resolution ($\mathcal{S}=10$, ${\mathrm{\Delta }}_{\mathrm{LX}}=0$): gray circles, experiment; yellow, fit to ZPL; red, fit to PSB; black line, total fit. Inset: High resolution spectrum. Gray circles, experiment; green, fit to coherent scattering; blue, fit to incoherent resonance fluorescence; yellow, total fitted profile. (b) Evolution with increasing $\mathrm{\Omega }$: red diamonds, PSB; green circles, coherent scattering; blue triangles, incoherent resonance fluorescence; dashed lines, polaron model. (c) Coherent scattering occurs when laser photons scatter directly from the bare transition (solid black lines) with probability given by the square of the Franck-Condon factor ($B^2$). (d) Inelastic scattering occurs when the system scatters [with probability $(1-B^2)$] into a different vibrational state within the ground-state manifold (gray shading). A LA phonon (purple) is emitted or absorbed for the Stokes and anti-Stokes cases, respectively.

Figure 3

Phonon influences in detuned (${\mathrm{\Delta }}_{\mathrm{LX}}\ne 0$) coherent scattering. (a) Semilog spectra (normalized by integrated intensity) for ${\mathrm{\Delta }}_{\mathrm{LX}}=\pm 0.27\mathrm{meV}$ (blue/red) at constant $\hslash \mathrm{\Omega }=5.7\mu \mathrm{eV}$. Inset: Theoretical spectrum. (b) ${\mathcal{F}}_{\mathrm{CS}}$ vs ${\mathrm{\Delta }}_{\mathrm{LX}}$ at constant $\hslash \mathrm{\Omega }=25.6\mu \mathrm{eV}$: gray circles, experimental ${\mathcal{F}}_{\mathrm{CS}}$ extracted as in Fig. 1; red lines, polaron master equation; green lines, atomic model, both models include additional pure dephasing and spectral wandering [39] and have upper and lower bounds from uncertainty in $\mathrm{\Omega }$. (c) For ${\mathrm{\Delta }}_{\mathrm{LX}}>0$, emission of a LA phonon can populate $|X⟩$, allowing incoherent relaxation. (d) For ${\mathrm{\Delta }}_{\mathrm{LX}}<0$, populating $|X⟩$ requires LA phonon absorption which is weak at $T=4.2\mathrm{K}$.