applications in magnetic resonance, quantum computing, quantum optics, and broadband magnetometry., we apply a magnetic field 2 New J. Phys. 16 (2014) 093022 J Scheuer et al 7 New J. Phys. 16 (2014) 093022 J Scheuer et al

Here we report the size reduction and effects on nitrogen-vacancy centres in nanodiamonds by air oxidation using a combined atomic force and confocal microscope. The average height reduction of individual crystals as measured by atomic force microscopy was 10.6 nm/h at 600 °C air oxidation at atmospheric pressure. The oxidation process modified the surface including removal of non-diamond carbon and organic material which also led to a decrease in background fluorescence. During the course of the nanodiamond size reduction, we observed the annihilation of nitrogen-vacancy centres which provided important insight into the formation of colour centres in small crystals. In these unirradiated samples, the smallest nanodiamond still hosting a stable nitrogen-vacancy centre observed was 8 nm.

Fluorescent nanodiamonds contain nitrogen-vacancy (NV) centers as quantum defects. When exposed to a continuous-wave 325 nm laser or a femtosecond 344 nm laser, the particles emit red fluorescence from NV0 centers at ∼620 nm. Power dependence measurements of the emission strength revealed a predominantly linear behavior at the laser peak intensity lower than 1 GW·cm–2, contributed mainly by photoexcitation of electrons from the valence band of diamond to the NV0 centers, followed by relaxation via electron–hole recombination. In the higher power regions, however, nonresonant two-photon interband excitation of the diamond matrix dominates the photoluminescence processes. Best fits of the experimental data to semiempirical models revealed an ionization coefficient of ∼1 cm–1 for the one-photon valence-to-defect excitation and a saturation intensity of 180 ± 60 GW·cm–2 for the two-photon interband excitation. The study provides new insight into the photoionization of NV0 centers and the interband excitation properties of diamond in the UV region.

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Fixed-pammeter tractability and approximabilityof NP-hard optimization problems are studied based on a model GC(s(n),IIt). Our main results are (1) a class of NP-hard optimization problems, including Dominating-Set and Zero-One Integer-Progmm m ing, a re jixed-pam me te r tractable if and only if GC(s(n),IIk) C P for some s(n) E w(1ogn); (2) Most approximable NP-hard optimization problems are jixedparameter tmctable. In particular, the class MAX N P is jixed-parameter tmctable; (8) a class of optimization problems do not have fully polynomial time approximation scheme unless GC(s(n), T I : ) C P for some s(n) E o(1ogn) and for some k > 1; and (4) every jixed-parameter tmctable optimization problem can be approximated in polynomial time to a non-trivial ratio. 0-8186-3630-0193 $3.00 0 1993 IEEE