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The decoherence of mixed electron-nuclear spin qubits is a topic of great current importance, but understanding is still lacking: while important decoherence mechanisms for spin qubits arise from quantum spin bath environments with slow decay of correlations, the only analytical framework for explaining observed sharp variations of decoherence times with magnetic field is based on the suppression of classical noise. Here we obtain a general expression for decoherence times of the central spin system which exposes significant differences between quantum-bath decoherence and decoherence by classical field noise. We perform measurements of decoherence times of bismuth donors in natural silicon using both electron spin resonance (ESR) and nuclear magnetic resonance (NMR) transitions, and in both cases find excellent agreement with our theory across a wide parameter range. The universality of our expression is also tested by quantitative comparisons with previous measurements of decoherence around `optimal working points or `clock transitions where decoherence is strongly suppressed. We further validate our results by comparison to cluster expansion simulations.
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In this paper, we study the electron spin decoherence of single defects in silicon carbide (SiC) nuclear spin bath. We find that, although the natural abundance of $^{29}rm{Si}$ ($p_{rm{Si}}=4.7%$) is about 4 times larger than that of $^{13}{rm C}$ ($p_{rm{C}}=1.1%$), the electron spin coherence time of defect centers in SiC nuclear spin bath in strong magnetic field ($B>300~rm{Gauss}$) is longer than that of nitrogen-vacancy (NV) centers in $^{13}{rm C}$ nuclear spin bath in diamond. The reason for this counter-intuitive result is the suppression of heteronuclear-spin flip-flop process in finite magnetic field. Our results show that electron spin of defect centers in SiC are excellent candidates for solid state spin qubit in quantum information processing.
The interplay of optical driving and hyperfine interaction between an electron confined in a quantum dot and its surrounding nuclear spin environment produces a range of interesting physics such as mode-locking. In this work, we go beyond the ubiquitous spin 1/2 approximation for nuclear spins and present a comprehensive theoretical framework for an optically driven electron spin in a self-assembled quantum dot coupled to a nuclear spin bath of arbitrary spin. Using a dynamical mean-field approach, we compute the nuclear spin polarization distribution with and without the quadrupolar coupling. We find that while hyperfine interactions drive dynamic nuclear polarization and mode-locking, quadrupolar couplings counteract these effects. The tension between these mechanisms is imprinted on the steady-state electron spin evolution, providing a way to measure the importance of quadrupolar interactions in a quantum dot. Our results show that higher-spin effects such as quadrupolar interactions can have a significant impact on the generation of dynamic nuclear polarization and how it influences the electron spin evolution.
We derive a master equation for a driven double-dot damped by an unstructured phonon bath, and calculate the spectral density. We find that bath mediated photon absorption is important at relatively strong driving, and may even dominate the dynamics, inducing population inversion of the double dot system. This phenomenon is consistent with recent experimental observations.
The quantum coherence and gate fidelity of electron spin qubits in semiconductors is often limited by noise arising from coupling to a bath of nuclear spins. Isotopic enrichment of spin-zero nuclei such as $^{28}$Si has led to spectacular improvements of the dephasing time $T_2^*$ which, surprisingly, can extend two orders of magnitude beyond theoretical expectations. Using a single-atom $^{31}$P qubit in enriched $^{28}$Si, we show that the abnormally long $T_2^*$ is due to the controllable freezing of the dynamics of the residual $^{29}$Si nuclei close to the donor. Our conclusions are supported by a nearly parameter-free modeling of the $^{29}$Si nuclear spin dynamics, which reveals the degree of back-action provided by the electron spin as it interacts with the nuclear bath. This study clarifies the limits of ergodic assumptions in analyzing many-body spin-problems under conditions of strong, frequent measurement, and provides novel strategies for maximizing coherence and gate fidelity of spin qubits in semiconductors.
Different approaches in quantifying environmentally-induced decoherence are considered. We identify a measure of decoherence, derived from the density matrix of the system of interest, that quantifies the environmentally induced error, i.e., deviation from the ideal isolated-system dynamics. This measure can be shown to have several useful features. Its behavior as a function of time has no dependence on the initial conditions, and is expected to be insensitive to the internal dynamical time scales of the system, thus only probing the decoherence-related time dependence. For a spin-boson model - a prototype of a qubit interacting with environment - we also demonstrate the property of additivity: in the regime of the onset of decoherence, the sum of the individual qubit error measures provides an estimate of the error for a several-qubit system, even if the qubits are entangled, as expected in quantum-computing applications. This makes it possible to estimate decoherence for several-qubits quantum computer gate designs for which explicit calculations are exceedingly difficult.
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