The coherence of the AlGaAs–GaAs phonon laser

Abstract

To study the emission properties of an AlGaAs–GaAs phonon laser we develop a formalism similar to that used to describe a laser. The device studied here consist of a double-barrier resonant tunneling diode tailored to generate an intense rate of primary LO 1 phonons. These phonons are confined in the well and they decay into a pair of secondary LO 2 and TA phonons. The TA phonons are generated by stimulated emission and they are partially reflected in the well walls. A combination of these two processes leads, for injection rates greater than the threshold, to the selection of a single phonon mode. Finally, the TA phonons escape through the barriers forming an intense coherent phonon beam. We start with a Hamiltonian that takes into account the electrons, the three phonon branches, the electron–phonon interaction and the phonon–phonon interaction. The last one is responsible for the TA phonon generation. From this Hamiltonian we get a set of five coupled Heisenberg–Langevin equations that are solved making an expansion in coherent states and doing the usual adiabatic approximation. The threshold for phonon lasing is calculated. The results show that it is not necessary to have a big pumping to get a single mode operation. This confirm our previous results obtained using rougher approximations. The phonon laser studied here has a very short wavelength. The mean free path of TA phonons is of the order of 2 mm. Therefore, it could be useful to perform acoustic nanoscopy and other applications.