Addressing the correlation of Stokes-shifted photons emitted from two quantum emitters

Abstract

In resonance fluorescence excitation experiments, light emitted from solid-state quantum emitters is typically filtered to eliminate the laser photons, ensuring that only red-shifted Stokes photons are detected. However, theoretical analyses of the fluorescence intensity correlation often model emitters as two-level systems, focusing on light emitted exclusively from the purely electronic transition (the zero-phonon line), or they rely on statistical approaches based on conditional probabilities that neglect the quantum coherence between the emitters and the coherence between the electric fields they generate. Here, we propose a model to characterize the correlation of either zero-phonon line photons or Stokes-shifted photons. This model successfully reproduces the experimental correlation of Stokes-shifted photons emitted from two interacting molecules and predicts that this correlation is affected by quantum coherence. Besides, we analyze the role of quantum coherence in the Stokes-shifted emission from two distant emitters, showing a sharp peak at zero time delay due to the Hanbury Brown--Twiss effect.

Figures (3)

• Figure 1: (a) Schematic representation of light emitted from two interacting emitters, the filtering of this light and the measurement of the intensity correlation $g^{(2)}(\tau)$. A laser beam at frequency $\omega_L$ (in blue) excites resonantly the pure electronic excited state of the quantum emitters, which then can emit a photon at the same frequency (blue circles) or a Stokes-shifted photon (red circles). A filter selects either the ZPL or Stokes-shifted light (gray circles represent these filtered photons). (b,c) Energy levels and relaxation processes of two noninteracting emitters represented in the uncoupled local basis, using the single-emitter representation in (b) and the two-emitter representation in (c). Blue arrows correspond to ZPL transitions, and red arrows to Stokes-shifted transitions.
• Figure 2: Comparison of the correlation of ZPL photons and Stokes-shifted photons emitted from two strongly interacting dibenzanthanthrene (DBATT) molecules. The molecules are in a J-aggregate configuration, as depicted in the inset in (a), and have $1/\gamma_0 =7.4$ ns. The laser is tuned resonantly to the (a) superradiant state $\ket{\Lambda_-}$ ($\omega_L = \omega_0 - \Lambda$), (b) subradiant state $\ket{\Lambda_+}$ ($\omega_L = \omega_0 + \Lambda$) and (c) two-photon resonance ($\omega_L = \omega_0$). The simulated intensity correlation $g^{(2)}(\tau)$ of (solid blue line) ZPL and (dashed red line) Stokes-shifted light are plotted as a function of time delay $\tau$. Solid gray line corresponds to the experimental results reported in Ref. Trebbia_NatComms_2022. All the parameters are specified in Supplemental Material Note1.
• Figure 3: Impact of quantum coherence in the correlation of Stokes-shifted photons emitted from two DBATT molecules. The molecules are in an H-aggregate configuration, as depicted in the inset in (b), and have $1/\gamma_0 =7.4$ ns. We consider $r_{12}=27$ nm in (a, b) and $r_{12}=400$ nm in (c, d). The laser is tuned to the two-photon resonance $\Delta_0 = 0$ in all panels (with $\Delta_0 = \omega_0 - \omega_L$), except in (b) where $\Delta_0 = 0.93 \gamma_0$. Red lines correspond to the simulation using the full model including quantum coherence in the emission, whereas green lines correspond to the simulation neglecting this coherence. Gray lines in (a,b) correspond to experimental measurements. The rest of the parameters are specified in Supplemental Material Note1.