  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 long-time 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.
