Quantum Entanglement of Matter and Light

A peculiar phenomenon called the entanglement is responsible for those features of quantum mechanics which Albert Einstein called ``the spooky action at a distance.'' Indeed, quantum systems in an entangled state seem to violate either the locality, or physical reality, or even both. Local measurements performed on one part of an entangled system \textit{instantly} influence the outcome of local measurements on the other part. I will describe experiments in which quantum states of matter (in the form of trapped atomic ions) and light (in the form of single photons) are entangled. The matter-light system offers many advantages for fundamental studies of quantum mechanics, as well as applications in quantum computation and quantum information.