Spin noise in the anisotropic central spin model

Abstract

Spin-noise measurements can serve as direct probe for the microscopic decoherence mechanism of an electronic spin in semiconductor quantum dots (QD). We have calculated the spin-noise spectrum in the anisotropic central spin model using a Chebyshev expansion technique which exactly accounts for the dynamics up to an arbitrary long but fixed time in a finite size system. In the isotropic case, describing QD charge with a single electron, the short-time dynamics is in good agreement with a quasi-static approximations for the thermodynamic limit. The spin-noise spectrum, however, shows strong deviations at low frequencies with a power-law behavior of ω −3/4 corresponding to a t −1/4 decay at intermediate and long times. In the Ising limit, applicable to QDs with heavy-hole spins, the spin-noise spectrum exhibits a threshold behavior of (ω − ωL) −1/2 above the Larmor frequency ωL = gµBB. In the generic anisotropic central spin model we have found a crossover from a Gaussian type of spin-noise spectrum to a more Ising-type spectrum with increasing anisotropy in a finite magnetic field. In order to make contact with experiments, we present ensemble averaged spin-noise spectra for QD ensembles charged with single electrons or holes. The Gaussian-type noise spectrum evolves to a more Lorentzian shape spectrum with increasing spread of characteristic time-scales and g-factors of the individual QDs.

Erratum: Quantum model for mode locking in pulsed semiconductor quantum dots [Phys. Rev. B 94 , 245308 (2016)]

“…In particular, it has been suggested that the nuclear Zeeman effect, absent in our model, leads to a significant decrease in the mode-locking rate [53,57]. Further interactions that affect the nuclear dynamics are the quadrupolar interaction of the nuclei (in case they are considered as spin-3 2 particles) [39][40][41][42], the dipoledipole interaction between nuclei [43], and anisotropy of the dipolar hyperfine interaction or of the g factors (in case of a hole central spin rather than an electron) [40,47,[61][62][63][64][65]. The present framework of perturbation theory could be extended with these additional interactions with relatively small effort.…”

Nonequilibrium nuclear spin distribution function in quantum dots subject to periodic pulses

“…For the last step, one could remain within a fully quantum mechanical description [10,17] but is limited to a relative small number of nuclear spins [17,19], or to short-time dynamics [10] using a TD-DMRG approach [22]. Alternatively, one can map the dynamics onto a set of classical equations of motion [5,12,23] which shows remarkably good agreement with the full quantum mechanical treatment [10] but is easily extendable to a large number of spins.…”

“…We are either restricted to small nuclear system sizes [17,19] or we employ the frozen nuclear approximation [5], and arrive at independent Lindblad equationṡ…”

“…Several different distributions have been used for the CSM [6,7,10,17,28], ranging from the simple box model [18] which assumes equal coupling constants a k = a = 1/ √ N , ∀k, to the more elaborate distributions of coupling constants p(a k ) [4,6,7,17].…”

“…It has been shown, that the accuracy of the FOA approximation [5] increases with increasing magnetic field [9,11,17]. Only in the theory of higher order correlation functions additional processes have to be included in order to make connection to the experiment [32].…”