We present systematic measurements of longitudinal relaxation rates (1/T 1 ) of spin polarization in the ground state of the nitrogen-vacancy (NV − ) color center in synthetic diamond as a function of NV − concentration and magnetic field B. NV − centers were created by irradiating a Type 1b single-crystal diamond along the [100] axis with 200 keV electrons from a transmission electron microscope with varying doses to achieve spots of different NV − center concentrations. Values of (1/T 1 ) were measured for each spot as a function of B. and small ensembles 8-12 and single nuclear spins 13 , study magnetic resonance on a molecular scale, measure electric fields, strain and temperature, detect low concentrations of paramagnetic molecules and ions, and image magnetic field distributions of physical or biological systems. These applications are made possible by the unique properties of the NV − center level structure, shown in Fig. 1, which allows manipulation of the ground-state spin state by optical fields and microwaves and measurement of the interactions of the ground-state spin with the local environment by monitoring the fluorescence intensity. Understanding spin relaxation processes is important in optimizing these techniques. Previous measurements of the dependence of longitudinal relaxation rate (1/T 1 ) of magnetic field have shown enhanced rates near B = 0 G, B = 595 G (Refs.14-17 ), and B = 514 G (Refs. ( 15,18 ). The enhancements at zero field and B = 595 G have been linked to interactions with NV centers whose orientation makes their energies degenerate at these fields, while the enhancement at B = 514 G is related to interactions with substitutional nitrogen (P1 centers). Previous work has also shown that the 1/T 1 rate depends on NV concentration 17 . In this paper we describe systematic measurements of the longitudinal relaxation rates of ensembles of NV − centers created with different, controlled radiation doses on a single diamond crystal, achieved through irradiation with a transmission electron microscope (TEM). This method of preparing NV − centers is more convenient for many laboratories than irradiation in accelerators and also could facilitate

Nonlinear magneto-optical resonances on the hyperfine transitions belonging to the D2 line of rubidium were changed from bright to dark resonances by changing the laser power density of the single exciting laser field or by changing the vapor temperature in the cell. In one set of experiments atoms were excited by linearly polarized light from an extended cavity diode laser with polarization vector perpendicular to the light's propagation direction and magnetic field, and laser induced fluorescence (LIF) was observed along the direction of the magnetic field, which was scanned. A low-contrast bright resonance was observed at low laser power densities when the laser was tuned to the Fg = 2 −→ Fe = 3 transition of 87 Rb and near to the Fg = 3 −→ Fe = 4 transition of 85 Rb. The bright resonance became dark as the laser power density was increased above 0.6mW/cm 2 or 0.8 mW/cm 2 , respectively. When the Fg = 2 −→ Fe = 3 transition of 87 Rb was excited with circularly polarized light in a second set of experiments, a bright resonance was observed, which became dark when the temperature was increased to around 50 o C. The experimental observations at room temperature could be reproduced with good agreement by calculations based on a theoretical model, although the theoretical model was not able to describe measurements at elevated temperatures, where reabsorption was thought to play a decisive role. The model was derived from the optical Bloch equations and included all nearby hyperfine components, averaging over the Doppler profile, mixing of magnetic sublevels in the external magnetic field, and a treatment of the coherence properties of the exciting radiation field.

Energy levels of nitrogen-vacancy centers in diamond were investigated using optically detected magnetic-resonance spectroscopy near the electronic ground-state level anticrossing (GSLAC) at an axial magnetic field around 102.4 mT in a diamond sample with a nitrogen concentration of 1 ppm. By applying radiowaves in the frequency ranges from 0 to 40 MHz and from 5.6 to 5.9 GHz, we observed transitions that involve energy levels mixed by the hyperfine interaction. We developed a theoretical model that describes the level mixing, transition energies, and transition strengths between the ground-state sublevels, including the coupling to the nuclear spin of the NV center's 14 N and 13 C atoms. The calculations were combined with the experimental results by fitting the ODMR spectral lines based on a theoretical model, which yielded information about the polarization of nuclear spins. This study is important for the optimization of experimental conditions in GSLAC-based applications, e.g., microwave-free magnetometry and microwave-free nuclear-magnetic-resonance probes.

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