Influence of the Nuclear Electric Quadrupolar Interaction on the Coherence Time of Hole and Electron Spins Confined in Semiconductor Quantum Dots

Abstract

The real-time spin dynamics and the spin noise spectra are calculated for p and n-charged quantum dots within an anisotropic central spin model extended by additional nuclear electric quadrupolar interactions (QC) and augmented by experimental data studied using identical excitation conditions. Using realistic estimates for the distribution of coupling constants including an anisotropy parameter, we show that the characteristic long time scale is of the same order for electron and hole spins strongly determined by the QC even though the analytical form of the spin decay differs significantly consistent with our measurements. The low frequency part of the electron spin noise spectrum is approximately 1/3 smaller than those for hole spins as a consequence of the spectral sum rule and the different spectral shapes. This is confirmed by our experimental spectra measured on both types of quantum dot ensembles in the low power limit of the probe laser.PACS numbers: 78.67. Hc, Introduction: The promising perspective of combining traditional electronics with novel spintronics devices lead to intensive studies of the spin dynamics of a single electron (n) or hole (p) confined in a semiconductor quantum dot (QD) [1][2][3][4]. In contrast to defects in diamonds [5,6], such QDs may be integrated into conventional semiconductor devices. While the strong confinement of the electronic wave function in QDs reduces the interaction with the environment and suppresses electronic decoherence mechanisms, it simultaneously enhances the hyperfine interaction between the confined electronic spin and the nuclear spin bath formed by the underlying lattice.Generally it is believed [3,4,7,8] that the hyperfine interaction dominates the spin relaxation in QDs. The s-wave character of the electron-wave function at the nuclei leads to an isotropic central spin model (CSM) [9] for describing the electron-nuclear hyperfine coupling, while for p-charged QDs, the couplings to the nuclear spins can be mapped onto an anisotropic CSM [4,10]. Since the coupling constants for p-charged QDs are reduced compared to the n-charged QDs [4,10], and additionally a large anisotropy factor Λ > 1 suppresses the spin decay of the S z component [4,10], p-charged QDs have been considered as prime candidates for long lived spin excitations in spintronics applications.Experimentally, however, there is evidence for comparable spin-decay times of the S z components [11][12][13][14][15] in p-and n-charged QDs: hence the anisotropic CSM provides only an incomplete description of the relevant spin-relaxation processes in such systems.In this paper, we resolve this puzzle by investigating the effect of an additional realistic nuclear electric quadrupolar interaction term (QC) [16] onto the spin decoherence. Most of the Ga and As isotopes have a nuclear spin I = 3/2 which is subject to a quadrupolar split-

Quantum Effects in Higher-Order Correlators of a Quantum-Dot Spin Qubit

“…The slowly oscillatory behavior is contrary to predictions of the model with only two lifetimes, but comparable to features observed in spin echo measurements [5,20,31].…”

“…This confirms that the oscillations of g 3 (t, t) at magnetic fields below 4 T can be explained by the presence of quadrupole interactions in the nuclear spin bath, in agreement with Refs. [5,20,31].…”

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

“…N ≫ the spin lengths can be absorbed into the definition of T * or ω fluc [5,26]. For S = I the change of the classical spin length leads to a modified coupling constant a ′ k = a k /2 in Eq.…”

“…Additional interactions such as the electric quadrupolar interaction [11,26,35] as well nuclear dipole-dipole interactions [4] neglected in the simulations are also expected to lead to a broadening of the peaks in the Overhauser distributions, therefore, to a reduction in the steady state revival amplitude. While the experiments clearly reach the steady-state, the theoretical revival amplitude has not been converged even after 20 000 pulses, as can be seen from Fig.…”

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

“…The coupling strengths are encoded through the energies A j . For the sake of simplicity, we neglect the effect of the external magnetic field on the nuclear spins, and omit any additional couplings that are relevant only at time scales much longer than the pulse repetition period, such as the quadrupolar coupling term between the electron and the nuclei [39][40][41][42] or the hyperfine interaction among the nuclear spins [43].…”