Signatures of long-range spin-spin interactions in an (In,Ga)As quantum dot ensemble

We present an investigation of the electron spin dynamics in an ensemble of singly charged semiconductor quantum dots subject to an external magnetic field and laser pumping with circularly polarized light. The spectral laser width is tailored such that ensembles with an increasing number of quantum dots are coherently pumped. Surprisingly, the dephasing time ${T}^{*}$ of the electron spin polarization depends only weakly on the laser spectral width. These findings can be consistently explained by a cluster theory of coupled quantum dots with a long-range electronic spin-spin interaction. We present a numerical simulation of the spin dynamics based on the central spin model that includes a quantum mechanical description of the laser pulses as well as a time-independent Heisenberg interaction between each pair of electron spins. We discuss the individual dephasing contributions stemming from the Overhauser field, the distribution of the electron $g$ factors, and the electronic spin-spin interaction as well as the spectral width of the laser pulse. This analysis reveals counterbalancing effects on the total dephasing time when increasing the spectral laser width. On one hand, the increasing deviations of the electron $g$ factors reduce the dephasing time. On the other hand, more electron spins are coherently pumped and synchronize due to the electronic spin-spin interaction which extends the dephasing time. We find an excellent agreement between the experimental data and the dephasing time in the simulation using an exponential distribution of Heisenberg couplings with a mean value $\overline{J}\ensuremath{\approx}0.26\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{eV}$.