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

Abstract

We present an investigation of the electron spin dynamics in an ensemble of singly-charged quantum dots subject to an external magnetic field and laser pumping with circularly polarized light. The spectral laser width is tailored such that different groups 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 the counterbalancing effect of the total dephasing time when increasing the spectral laser width. On one hand, the deviations of the electron g-factors increase. On the other hand, an increasing number of coherently pumped electron spins synchronize due to the spin-spin interaction. 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 J ≈ 0.26 µeV.

Cross-correlation spectra in interacting quantum dot systems

“…Its microscopic origin is still unclear, but an optical RKKY interaction 33 can be ruled out due to its time dependency. Potential candidates that are currently discussed are either a direct exchange interaction for spatially adjacent QDs 34 or a long-range RKKY-like interaction mediated by a weak carrier doping of the conduction bands as a side effect of charging the QD with a single electron that was found for selfassembled semiconductor QD ensembles 32,33 .…”

“…While these two papers focused on the propagation of a well defined central spin state in time, our approach extends the SCA to general correlation functions. Variations of this approach have already already been used in previous publications 21,30,32 .…”

“…While the power or noise spectrum in QDs is well established 1,25,54,55 , the inter-QD interactions enter just as an additional small noise source into the autocorrelation function, which makes them hardly distinguishable from the other central spin interactions 32 . However, a non-vanishing cross-correlation function is explicitly generated by the inter-QD interactions and can reveal the true origin of these interactions.…”

“…32,33 . Therefore, we perform configuration averaging over individual realizations of A (i) k as well as the effective coupling constant J between two QDs 32 .…”

“…Our numerical data suggests that a genuine interacting QD ensemble can be mapped onto a coupled two-QD model augmented by a distribution function of the effective coupling constants when targeting two-color spinnoise spectroscopy. This is backed by the analytic structure of the equation of motion where the total effect of all other electron spins of the ensemble onto the dynamics of the electron spin in an individual QD is included into a single additional effective noise field in addition to the Overhauser field 32 . The mapping is constructed such that the first two momenta of this fluctuating field are reproduced.…”