Phonon-assisted transitions from quantum dot excitons to cavity photons

For a single semiconductor quantum dot embedded in a microcavity, we theoretically and experimentally investigate phonon-assisted transitions between excitons and the cavity mode. Within the framework of the independent boson model we find that such transitions can be very efficient, even for relatively large exciton-cavity detunings of several millielectron volts. Furthermore, we predict a strong detuning asymmetry for the exciton lifetime that vanishes for elevated lattice temperature. Our findings are corroborated by experiment, which turns out to be in good quantitative and qualitative agreement with theory.

Figure 1

(Color online) (a) Phonon-assisted scattering rate from exciton to cavity as a function of exciton-cavity detuning, and for different temperatures. We use material parameters for GaAs and consider deformation potential and piezo electric interactions with acoustic phonons. For the electron and hole wave functions we assume Gaussians, with full width of half maxima of 6 and 3.5 nm along the transversal and growth directions, respectively. For details of our model see Ref. 25. (b) Full lines: spontaneous emission lifetime for the QD exciton as a function of temperature. We use $Q=10000$, $\hslash /\gamma =5\text{ns}$, and $g=60\mu \text{eV}$. The symbols show results of our quantum-kinetic simulations, in good agreement with the rate-equation model for the range of parameters investigated. The inset shows the calculated decay transients for detunings of 0.2, 0.5, and 1 meV in order of decreasing decay constant and for $T=2\text{K}$.

Figure 2

(Color online) (a) Photoluminescence spectra of QD-cavity system I, with $Q=2900$ and $T=15\text{K}$. The mode was spectrally tuned away from the QD s-shell to lower energies by adsorption of molecular nitrogen. (b) Decay transients of the indicated QD state for three different dot-cavity detunings. (c) Photoluminescence spectra of QD-cavity system II, with $Q=3200$ and $T=18\text{K}$. The mode was spectrally tuned through a QD transition to lower energies by adsorption of molecular nitrogen. (d) Decay transients of the QD transition for three different quantum dot-cavity detunings.

Figure 3

(Color online) (a) Extracted decay times of QD-cavity system I as a function of detuning. The squares correspond to the $1X_1$ state. The black dotted line and the cyan solid line are theoretical decay times obtained from calculations with the phonon coupling turned off and a phonon bath at 15 K temperature, respectively. (b) Extracted decay times of QD-cavity system II as a function of detuning. The squares and circles correspond to the fast and the slow decay component, respectively. The gray traces are shown for better comparison, and display the data for negative detunings mirrored on the positive axis. The lines are calculations of the system without phonon coupling and for different temperatures (10, 20, and 30 K). Note that the measured lifetimes in resonance are limited by the temporal resolution of the detection system of $\sim 150\text{ps}$ after deconvolution.