Fourth-order spin correlation function in the extended central spin model

Abstract

Spin noise spectroscopy has developed into a very powerful tool to access the electron spin dynamics. While the spin-noise power spectrum in an ensemble of quantum dots in a magnetic field is essentially understood, we argue that the investigation of the higher order cumulants promises to provide additional information not accessible by the conventional power noise spectrum. We present a quantum mechanical approach to the correlation function of the spin-noise power operators at two different frequencies for small spin bath sizes and compare the results with a simulation obtained from the classical spin dynamics for large number of nuclear spins. This bispectrum is defined as a two-dimensional frequency cut in the parameter space of the fourth-order spin correlation function. It reveals information on the influence of the nuclear-electric quadrupolar interactions on the longtime electron spin dynamics dominated by a magnetic field. For large bath sizes and spin lengths the quantum mechanical spectra converge to those of the classical simulations. The broadening of the bispectrum across the diagonal in the frequency space is a direct measure of the quadrupolar interaction strength. A narrowing is found with increasing magnetic field indicating a suppression of the influence of quadrupolar interactions in favor of the nuclear Zeeman effect.

Cross-correlation spectra in interacting quantum dot systems

“…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 .…”

“…The spectrum also reveals the importance of the nuclear-electric quadrupolar interaction for qubit decoherence 13,16,17 . Recently, higher-order spin correlators attracted attention, because they contain additional information that is absent in the standard spinnoise power-spectra [18][19][20][21][22][23] .…”

Interplay of spin mode locking and nuclei-induced frequency focusing in quantum dots

“…This Hamiltonian, often referred to as the central spin or Gaudin model [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51], is extremely hard to solve for a non-uniform distribution of the couplings A k so that one is typically restricted by either the bath size N or the maximum simulation time in spite of the existence of a Bethe ansatz solution [33][34][35][36][37][38].…”

Theory of optically detected spin noise in nanosystems

“…For electrons localized in quantum dots, the measurement of the fourth order spin correlators allows one to obtain the parameters of the nuclear spin dynamics caused by the precession in the external magnetic field, in the Knight field or by the interaction of the nuclear quadrupole moment with the elastic strain in the quantum dot [159,160].…”