Resonances in Fock Space : Optimization of a SASER device

We model the Fock space for the electronic resonant tunneling through a double barrier including the coherent effects of the electron-phonon interaction. The geometry is optimized to achieve the maximal optical phonon emission required by a SASER (ultrasound emitter) device. The possibility of generating coherent phonons in a double barrier semiconductor heterostructure was first proposed[1] a few years ago. This is the basis of a SASER device[2] which transforms the electric potential energy in a single vibrational mode of the lattice. This is facilitated by the electronic confinement in a double barrier structure. The phonon emission appears when the energy of the resonant state is one quantum ¯ hω 0 (LO phonon energy) bellow the energy of the incoming electrons. As in laser devices this is enhanced if the first excited state of the well lies bellow the Fermi energy and becomes overpopulated. According to ref.[3] the emitted LO phonons decay coherently into a pair of LO and TA phonons the last the useful ones in a SASER device. In this paper we want to explore the case in which well's ground state mediates the decay of the emitter states into the collector's ones plus a phonon. This feature represents a resonance in the electron-phonon Fock space and is observed as a satellite peak in the current[4]. This resonant condition is tuned directly by the applied voltage and we expect that its optimization could also provide enough emission of primary phonons to allow for SASER operation. We carry out the modeling of the electronic structure and the electron-phonon interaction to get a minimal structure in the Fock space. Thus, the optimization of the phonon emission for different geometries of the device (height and width of the barriers, field intensity) can be discussed in simple terms. We consider a one-dimensional model for a double barrier including the inter