Color center (NV center, F-center)

A color center is a point defect in an otherwise transparent crystal that has localized electronic states inside the bandgap, so the crystal absorbs light at photon energies far below the band edge and appears colored. The simplest is the F-center (from the German Farbe, color): an electron trapped in a vacancy where a negative ion is missing in an alkali halide. Its absorption band lies near 2.7 eV (460 nm) in NaCl and 2.2 eV (564 nm) in KCl, which is why irradiated rock salt turns yellow-brown and irradiated KCl turns violet. The same idea covers the nitrogen-vacancy (NV) center in diamond, with a zero-phonon line at 637 nm (1.95 eV), the silicon-vacancy center at 737 nm, radiation-induced defects in glasses, and dozens of other defect species.

Formation and absorption bands

Color centers form during growth, by doping, or by damaging a crystal with ionizing radiation, electrons or neutrons, sometimes followed by annealing to let vacancies migrate and combine with impurities; NV centers are made this way by implanting nitrogen or irradiating nitrogen-rich diamond and annealing near 800 °C. In alkali halides, the F-band energy decreases as the lattice spacing grows, roughly as a particle in a box whose size is set by the vacancy, so the band moves to longer wavelengths from lithium to cesium salts. Aggregates of F-centers (F₂, F₃ and their charged forms) absorb further into the red and near infrared.

Absorption bands of color centers are broad, typically tenths of an eV wide at room temperature, because the trapped electron couples strongly to lattice vibrations, a large line broadening compared with atomic transitions. Their absorption coefficient is proportional to the defect concentration, which makes the band a dose indicator in radiation dosimetry.

Zero-phonon line and phonon sideband

Strong coupling to phonons splits a color center's optical spectrum into two parts. The zero-phonon line (ZPL) is the purely electronic transition, with no phonon created or destroyed; it is narrow at low temperature. The phonon sideband contains transitions that also create one or more phonons; in emission it extends to the red of the ZPL, and in absorption to the blue. The fraction of emission in the ZPL, the Debye-Waller factor, is about $e^{-S}$ at low temperature, where $S$ is the Huang-Rhys factor (the mean number of phonons emitted per transition). For the NV center $S \approx 3.5$, so

$$e^{-3.5} \approx 0.03,$$

and only about 3% of its fluorescence lies in the 637 nm ZPL, with the rest spread from about 640 to 800 nm. The silicon-vacancy center couples weakly and puts most of its emission in the ZPL. The broad sideband provides the tuning range of color-center lasers but limits the yield of indistinguishable photons.

The NV center

The negatively charged NV center is a substitutional nitrogen next to a vacancy. It is excited efficiently with green light, commonly 532 nm, has an excited-state lifetime of about 12 ns in bulk diamond, and emits in the red. Its ground state is a spin triplet with a zero-field splitting of 2.87 GHz. Because the fluorescence rate depends on the spin state, the spin can be initialized optically and read out through the photoluminescence intensity, a technique called optically detected magnetic resonance. Magnetic fields shift the resonances by 28 GHz/T, which makes the NV center a room-temperature magnetometer; its coherence times are discussed under T2*. Single NV centers, isolated with a confocal microscope, are also single-photon sources, limited by the small ZPL fraction.

Color-center lasers

The broad emission of aggregate centers in alkali halides gave the color-center lasers of the 1970s and 1980s, tunable across roughly 0.8–3.3 µm by changing the crystal and center and pumped by other lasers. Most required cryogenic cooling and were largely displaced by Ti:sapphire, Cr-doped crystals, optical parametric oscillators and semiconductor sources. LiF with F₂⁻ centers is a room-temperature exception and remains in use as a gain medium and saturable absorber near 1.1 µm.

Unwanted color centers

In optics, color centers are more often a defect to be avoided. Ultraviolet exposure, high-energy radiation or intense laser pulses create absorbing centers in glasses and crystals: the E′ center and the nonbridging oxygen hole center in fused silica, solarization of optical glass, and photodarkening of ytterbium-doped fiber. Cerium-doped radiation-hardened glasses suppress them. These centers appear as a slow rise in absorption, which in a fiber amplifier shows as falling output power at constant pump. Distinct from these defects, rare-earth ions and transition-metal ions are deliberate dopants whose 4f or 3d transitions are not usually called color centers.

Common questions

Why is it called a color center?

Because the defects color an otherwise clear crystal. The term (Farbzentren) comes from early twentieth-century studies of colored alkali halides and now covers all optically active point defects.

What is the difference between an F-center and an NV center?

An F-center is an electron trapped at an anion vacancy, with a broad absorption band and a simple electronic structure. An NV center is a complex of a nitrogen atom and a vacancy in diamond with several electrons, a spin-triplet ground state, a sharp zero-phonon line at 637 nm and long spin coherence, which is why it is used for sensing and quantum optics.

References: C. Kittel, Introduction to Solid State Physics, 8th ed. (Wiley, 2005); B. Henderson and G. F. Imbusch, Optical Spectroscopy of Inorganic Solids (Oxford University Press, 1989); A. Gruber et al., "Scanning confocal optical microscopy and magnetic resonance on single defect centers," Science 276, 2012 (1997); L. F. Mollenauer and J. C. White, eds., Tunable Lasers (Springer, 1987).