Probing Electron-Phonon Interaction through Two-Photon Interference in Resonantly Driven Semiconductor Quantum Dots

We investigate the temperature dependence of photon coherence properties through two-photon interference (TPI) measurements from a single quantum dot (QD) under resonant excitation. We show that the loss of indistinguishability is related only to the electron-phonon coupling and is not affected by spectral diffusion. Through these measurements and a complementary microscopic theory, we identify two independent separate decoherence processes, both of which are associated with phonons. Below 10 K, we find that the relaxation of the vibrational lattice is the dominant contribution to the loss of TPI visibility. This process is non-Markovian in nature and corresponds to real phonon transitions resulting in a broad phonon sideband in the QD emission spectra. Above 10 K, virtual phonon transitions to higher lying excited states in the QD become the dominant dephasing mechanism, this leads to a broadening of the zero phonon line, and a corresponding rapid decay in the visibility. The microscopic theory we develop provides analytic expressions for the dephasing rates for both virtual phonon scattering and non-Markovian lattice relaxation.

Figure 1

(a) Scheme of the experimental setup. A tunable Ti:sapphire (82-MHz) laser delivers 3-ps pulses and, for HOM experiments, pairs of pulses separated by 3 ns. The laser is focused by a microscope objective on the cleaved edge of one ridge, and the RF is collected from the top surface by a second microscope objective. The sample and the two objectives are inside a closed-cycle He temperature-variable cryostat. The signal is coupled to a fibered setup (FBS denotes the fibered beam splitters) for either standard spectroscopy or Michelson interferometry ($g^{(1)}$) or TPI experiments ($g^{(2)}$) using a 3-ns unbalanced Mach-Zehnder interferometer. Single-photon avalanche diodes (SPAD1 and SPAD2) collect the signal. (b) Scanning electron microscopy image of one ridge, with the dots schematically drawn in the layer.

Figure 2

Second-order correlation measurements for QD1 at 4 K for a 1-hr acquisition time. (a) Coincidences histogram for the HBT experiment. We extract $g_{\mathrm{HBT}}^{(2)}=0.12\pm 0.02$. (b) Coincidences histogram for the TPI experiment. After correction by the remaining laser background, we obtain $V_{\mathrm{TPI}}=0.79\pm 0.03$.

Figure 3

Plot showing the visibility of the measured TPI for QD1 as a function of temperature (the black points). The data are fitted with Eq. (2); the full expression is used to produced the solid red curve, which fits accurately over the full temperature range. The dashed purple curve shows only the effect of the phonon sideband on the TPI visibility.

Figure 4

(Left panel) Schematic of real and virtual transition in a QD. (a),(b) The impact of these transitions on the QD spectra. Virtual transitions give a broadening of the ZPL as in (a). Real transitions lead to the broad phonon sideband illustrated in (b).