Abstract
This review article focuses on biphoton sources based on the double-Lambda spontaneous four-wave mixing (SFWM) process in laser-cooled as well as room-temperature or hot atomic ensembles. These biphoton sources have the advantage of providing stable frequencies, ultranarrow linewidths, and a tunability of the temporal biphoton width of more than one order of magnitude for high-bandwidth applications. Therefore, the generated photons can be efficiently interfaced to, e.g., atomic quantum memories. In contrast, solid-state biphoton sources typically require assistance by an optical cavity to operate at narrow linewidth that limits the tunability of the temporal width of the biphotons. Present state-of-the-art double-Lambda SFWM biphoton sources can achieve one of the following results: a spectral linewidth of 50 kHz (290 kHz) or a temporal width of 13 mu s (580 ns) with cold (hot) atoms, a detection rate of about 7x10(3) cps, and a generation rate of 10(7) cps at a duty cycle of 0.4% or of 10(5) cps in the steady state. The theoretical background of these biphoton sources, experimental implementations with cold and hot atoms, and progress over the years, will be illustrated.