Sound amplification by stimulated emission of radiation implies that lasers should be as feasible with sound as they are with light. In the 21st century, it is easy to produce low frequency sound in the range that humans can hear (~20 kHz), in either a random or orderly form. However, at the terahertz frequencies in the regime of phonon laser applications, more difficulties arise. The problem stems from the fact that sound travels much slower than light. This means that the wavelength of sound is much shorter than light at a given frequency. Instead of resulting in orderly, coherent phonon laser structures that can produce terahertz sound,
Sound amplification by stimulated emission of radiation electrons become localized in the quantum wells and vertical electron transport takes place via hopping between neighboring quantum wells, which may be phonon assisted. As it had been shown previously, under these conditions stimulated phonon emission can become the dominant phonon-assisted hoping process for phonons of an energy value close to the Stark splitting. Thus, coherent phonon amplification is theoretically possible in this type of system. Together with the increase in amplitude, the spectrum of the bias-induced oscillations is narrower than the spectrum of the coherent phonons at zero bias. This shows that coherent amplification of phonons due to stimulated