Abstract:
We observe the electron spin resonance of conduction electrons in boron doped (6400 ppm) superconducting diamond (Tc =3.8 K). We clearly identify the benchmarks of conduction electron spin resonance (CESR): the nearly temperature independent ESR signal intensity and its magnitude which is in good agreement with that expected from the density of states through the Pauli spin-susceptibility. The temperature dependent CESR linewidth weakly increases with increasing temperature which can be understood in the framework of the Elliott-Yafet theory of spin-relaxation. An anomalous and yet unexplained relation is observed between the g-factor, CESR linewidth, and the resistivity using the empirical Elliott-Yafet relation.

Abstract:
A collapse and revival shape of Rabi oscillations of a single Nitrogen-Vacancy (NV) center electron spin has been observed in diamond at room temperature. Because of hyperfine interaction between the host 14N nuclear spin and NV center electron spin, different orientation of the 14N nuclear spin leads to a triplet splitting of the transition between the ground ms=0 and excited states ms=1. Microwave can excite the three transitions equally to induce three independent nutations and the shape of Rabi oscillations is a combination of the three nutations. This result provides an innovative view of electron spin oscillations in diamond.

Abstract:
Following the recent successful experimental manipulation of entangled 13C atoms on the surface of Diamond, we calculate the decoherence of the electron spin in Nitrogen Vacancy NV centers of Diamond via a nonperturbative treatment of the time-dependent Greens function of a Central-Spin model in order to identify the Replica Symmetry Breaking mechanism associated with intersystem mixing between the ms = 0 sublevel of the 3 A 2 and 1 A 1 states of the NV？ centers, which we identify as mediated via the meta-stability of 13C nuclei bath processes in our calculations. Rather than the standard exciton-based calculation scheme used for quantum dots, we argue that a new scheme is needed to formally treat the Replica Symmetry Breaking of the 3 A 2 → 3 E excitations of the NV？ centers, which we define by extending the existing Generalized Master Equation formalism via the use of fractional time derivatives. Our calculations allow us to accurately quantify the dangerously irrelevant scaling associated with the Replica Symmetry Breaking and provide an explanation for the experimentally observed room temperature stability of Diamond for Quantum Computing applications.

Abstract:
We present a theoretical analysis of the electron spin decoherence in single Nitrogen-Vacancy defects in ultra-pure diamond. The electron spin decoherence is due to the interactions with Carbon-13 nuclear spins in the diamond lattice. Our approach takes advantage of the low concentration (1.1%) of Carbon-13 and their random distribution in the diamond lattice by an algorithmic aggregation of spins into small, strongly interacting groups. By making use of this \emph{disjoint cluster} approach, we demonstrate a possibility of non-trival dynamics of the electron spin that can not be described by a single time constant. This dependance is caused by a strong coupling between the electron and few nuclei and results, in particular, in a substantial echo signal even at microsecond time scales. Our results are in good agreement with recent experimental observations.

Abstract:
The protocols for the control and readout of Nitrogen Vacancy (NV) centres electron spins in diamond offer an advanced platform for quantum computation, metrology and sensing. These protocols are based on the optical readout of photons emitted from NV centres, which process is limited by the yield of photons collection. Here we report on a novel principle for the detection of NV centres magnetic resonance in diamond by directly monitoring spin-preserving electron transitions through measurement of NV centre related photocurrent. The demonstrated direct detection technique offers a sensitive way for the readout of diamond NV sensors and diamond quantum devices on diamond chips. The Photocurrent Detection of Magnetic Resonance (PDMR) scheme is based on the detection of charge carriers promoted to the conduction band of diamond by the two-photon ionization of NV- centres. Optical detection of magnetic resonance (ODMR) and PDMR are compared, by performing both measurements simultaneously. The minima detected in the measured photocurrent at resonant microwave frequencies are attributed to the spin-dependent occupation probability of the NV- ground state, originating from spin-selective non-radiative transitions.

Abstract:
The mixed diamond chain is a frustrated Heisenberg chain composed of successive diamond-shaped units with two kinds of spins of magnitudes S and S/2 (S: integer). Ratio $lambda$ of two exchange parameters controls the strength of frustration. With varying $lambda$, the Haldane state and several spin cluster states appear as the ground state. A spin cluster state is a tensor product of exact local eigenstates of cluster spins. We prove that a spin cluster state is the ground state in a finite interval of $lambda$. For S=1, we numerically determine the total phase diagram consisting of five phases.

Abstract:
Exact ground states of interacting electrons on the diamond Hubbard chain in a magnetic field are constructed which exhibit a wide range of properties such as flat-band ferromagnetism and correlation induced metallic, half-metallic or insulating behavior. The properties of these ground states can be tuned by changing the magnetic flux, local potentials, or electron density.

Abstract:
We construct exact ground states of interacting electrons on triangle and diamond Hubbard chains. The construction requires (i) a rewriting of the Hamiltonian into positive semidefinite form, (ii) the construction of a many-electron ground state of this Hamiltonian, and (iii) the proof of the uniqueness of the ground state. This approach works in any dimension, requires no integrability of the model, and only demands sufficiently many microscopic parameters in the Hamiltonian which have to fulfill certain relations. The scheme is first employed to construct exact ground state for the diamond Hubbard chain in a magnetic field. These ground states are found to exhibit a wide range of properties such as flat-band ferromagnetism and correlation induced metallic, half-metallic or insulating behavior, which can be tuned by changing the magnetic flux, local potentials, or electron density. Detailed proofs of the uniqueness of the ground states are presented. By the same technique exact ground states are constructed for triangle Hubbard chains and a one-dimensional periodic Anderson model with nearest-neighbor hybridization. They permit direct comparison with results obtained by variational techniques for f-electron ferromagnetism due to a flat band in CeRh3B2.

Abstract:
The novel aspect of the centre (NV-) in diamond is the high degree of spin polarisation achieved through optical illumination. In this paper it is shown that the spin polarisation occurs as a consequence of an electron-vibration interaction combined with spin-orbit interaction, and an electronic model involving these interactions is developed to account for the observed polarisation.

Abstract:
We report on imaging of microwave (MW) magnetic fields using a magnetometer based on the electron spin of a nitrogen vacancy center in diamond. We quantitatively image the magnetic field generated by high frequency (GHz) MW current with nanoscale resolution using a scanning probe technique. We demonstrate a MW magnetic field sensitivity in the range of a few nT/$\sqrt{\text{Hz}}$, polarization selection and broadband capabilities under ambient conditions and thereby establish the nitrogen vacancy center a versatile and high performance tool for the detection of MW fields. As a first application of this scanning MW detector, we determine the MW current density in a stripline and demonstrate a MW current sensitivity of a few nA/$\sqrt{\text{Hz}}$