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.

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-

The spin fluctuations of electron and hole doped self-assembled quantum dot ensembles are measured optically in the low-intensity limit of a probe laser in absence and presence of longitudinal or transverse static magnetic fields. The experimental results are modeled by two complementary approaches based either on semiclassical or quantum mechanical descriptions. This allows us to characterize the hyperfine interaction of electron and hole spins with the surrounding bath of nuclei on time scales covering several orders of magnitude. Our results demonstrate (i) the intrinsic precession of the electron spin fluctuations around the effective nuclear Overhauser field caused by the host lattice nuclear spins, (ii) the comparably long time scales for electron and hole spin decoherence, as well as (iii) the dramatic enhancement of the spin lifetimes induced by a longitudinal magnetic field due to the decoupling of nuclear and charge carrier spins.

Mazur's inequality renders statements about persistent correlations possible. We generalize it in a convenient form applicable to any set of linearly independent constants of motion. This approach is used to show rigorously that a fraction of the initial spin correlations persists indefinitely in the isotropic central spin model unless the average coupling vanishes. The central spin model describes a major mechanism of decoherence in a large class of potential realizations of quantum bits. Thus the derived results contribute significantly to the understanding of the preservation of coherence. We will show that persisting quantum correlations are not linked to the integrability of the model, but caused by a finite operator overlap with a finite set of constants of motion. PACS numbers: 78.67.Hc, 72.25.Rb, 03.65.Yz, 02.30.Ik a. Introduction. The two-time correlation function of two observables reveals important information about the dynamics of a system in and out of equilibrium: The noise spectra are obtained from symmetric combinations of correlation functions, while the causal, antisymmetric combination determines the susceptibilities required for the theory of linear response.The two-time correlation function only depends on the time difference if at t = 0 the system of interest is prepared in a stationary state whose density operator commutes with the time-independent Hamiltonian. This is what will be considered in this work. Since correlations generically decay for t → ∞, important information about the system dynamics is gained if a non-decaying fraction of correlations prevails at infinite times. Such non-decaying correlations are clearly connected to a limited dynamics in certain subspaces of the Hilbert space. The question arises if such a restricted dynamics is always linked to the integrability of the Hamiltonian. Here integrability means that the Hamiltonian can be diagonalized by Bethe ansatz which implies that there is an extensive number of constants of motion. Identifying and understanding those non-decaying correlations can be potentially exploited in applications for persistent storage of (quantum) information.In this Letter we first prove that persisting correlations are not restricted to integrable systems by using a generalized form of Mazur's inequality 1,2 . This is in contrast to the behavior of the Drude weight in the frequency-dependent conductivity of one-dimensional systems which appears to vanish abruptly once the integrability is lost, even if only by including an arbitrarily small perturbation. So far, the Drude weight has been the most common application of Mazur's inequality, see for instance Refs. 3-6 and references therein. Second, we apply this approach to the central spin model (CSM) 7 describing the interaction of a single spin, e.g., an electronic spin in a quantum dot 8,9 , an effective two-level model in a NV center in diamond 10 , or a 13 C nuclear spin 11 , coupled to a bath of surrounding nuclear spins inducing decoherence.Persisting spin correlations have been found in ...

Decoherence of a central spin coupled to an interacting spin bath via inhomogeneous Heisenberg coupling is studied by two different approaches, namely an exact equations of motion (EOMs) method and a Chebyshev expansion technique (CET). By assuming a wheel topology of the bath spins with uniform nearest-neighbor XX-type intrabath coupling, we examine the central spin dynamics with the bath prepared in two different types of bath initial conditions. For fully polarized baths in strong magnetic fields, the polarization dynamics of the central spin exhibits a collapserevival behavior in the intermediate-time regime. Under an antiferromagnetic bath initial condition, the two methods give excellently consistent central spin decoherence dynamics for finite-size baths of N ≤ 14 bath spins. The decoherence factor is found to drop off abruptly on a short time scale and approach a finite plateau value which depends on the intrabath coupling strength non-monotonically. In the ultrastrong intrabath coupling regime, the plateau values show an oscillatory behavior depending on whether N/2 is even or odd. The observed results are interpreted qualitatively within the framework of the EOM and perturbation analysis. The effects of anisotropic spin-bath coupling and inhomogeneous intrabath bath couplings are briefly discussed. Possible experimental realization of the model in a modified quantum corral setup is suggested.