We present a quantum solution to the electron spin decoherence by a nuclear pair-correlation method for the electron-nuclear spin dynamics under a strong magnetic field and a temperature high for the nuclear spins but low for the electron. The theory incorporates the hyperfine interaction, the intrinsic (both direct and indirect) nuclear interactions, and the extrinsic nuclear coupling mediated by the hyperfine interaction with the single electron in question. The last is shown to be important in free-induction decay (FID) of the single electron spin coherence. The spin echo eliminates the hyperfine-mediated decoherence but only reduces the decoherence by the intrinsic nuclear interactions. Thus, the decoherence times for single spin FID and ensemble spin echo are significantly different. The decoherence is explained in terms of quantum entanglement, which involves more than the spectral diffusion.

To exploit the quantum coherence of electron spins in solids in future technologies such as quantum computing, it is first vital to overcome the problem of spin decoherence due to their coupling to the noisy environment. Dynamical decoupling, which uses stroboscopic spin flips to give an average coupling to the environment that is effectively zero, is a particularly promising strategy for combating decoherence because it can be naturally integrated with other desired functionalities, such as quantum gates. Errors are inevitably introduced in each spin flip, so it is desirable to minimize the number of control pulses used to realize dynamical decoupling having a given level of precision. Such optimal dynamical decoupling sequences have recently been explored. The experimental realization of optimal dynamical decoupling in solid-state systems, however, remains elusive. Here we use pulsed electron paramagnetic resonance to demonstrate experimentally optimal dynamical decoupling for preserving electron spin coherence in irradiated malonic acid crystals at temperatures from 50 K to room temperature. Using a seven-pulse optimal dynamical decoupling sequence, we prolonged the spin coherence time to about 30 mus; it would otherwise be about 0.04 mus without control or 6.2 mus under one-pulse control. By comparing experiments with microscopic theories, we have identified the relevant electron spin decoherence mechanisms in the solid. Optimal dynamical decoupling may be applied to other solid-state systems, such as diamonds with nitrogen-vacancy centres, and so lay the foundation for quantum coherence control of spins in solids at room temperature.

The detection of single nuclear spins would be useful for fields ranging from basic science to quantum information technology. However, although sensing based on diamond defects and other methods have shown high sensitivity, they have not been capable of detecting single nuclear spins, and defect-based techniques further require strong defect-spin coupling. Here, we present the detection and identification of single and remote (13)C nuclear spins embedded in nuclear spin baths surrounding a single electron spin of a nitrogen-vacancy centre in diamond. We are able to amplify and detect the weak magnetic field noise (∼10 nT) from a single nuclear spin located ∼3 nm from the centre using dynamical decoupling control, and achieve a detectable hyperfine coupling strength as weak as ∼300 Hz. We also confirm the quantum nature of the coupling, and measure the spin-defect distance and the vector components of the nuclear field. The technique marks a step towards imaging, detecting and controlling nuclear spins in single molecules.

Control of electron spin decoherence in contact with a mesoscopic bath of many interacting nuclear spins in an InAs quantum dot is studied by solving the coupled quantum dynamics. The nuclear spin bath, because of its bifurcated evolution predicated on the electron spin up or down state, measures the which-state information of the electron spin and hence diminishes its coherence. The many-body dynamics of nuclear spin bath is solved with a pair-correlation approximation. In the relevant timescale, nuclear pair-wise flip-flops, as elementary excitations in the mesoscopic bath, can be mapped into the precession of non-interacting pseudo-spins. Such mapping provides a geometrical picture for understanding the decoherence and for devising control schemes. A close examination of nuclear bath dynamics reveals a wealth of phenomena and new possibilities of controlling the electron spin decoherence. For example, when the electron spin is flipped by a π-pulse at τ , its coherence will partially recover at √ 2τ as a consequence of quantum disentanglement from the mesoscopic bath. In contrast to the re-focusing of inhomogeneously broadened phases by conventional spin-echoes, the disentanglement is realized through shepherding quantum evolution of the bath state via control of the quantum object. A concatenated construction of pulse sequences can eliminate the decoherence with arbitrary accuracy, with the nuclear-nuclear spin interaction strength acting as the controlling small parameter.