The operation threshold of a double barrier phonon laser

Abstract

We make an adaptation of laser modelling equations to describe the behavior of a phonon laser (saser). Our saser consists of an AlGaAs/GaAs double barrier heterostructure designed to generate an intense beam of transversal acoustic (T A) phonons. To study our system, we begin with a Hamiltonian that describes the decay of primary longitudinal optical phonons (LO 1 ) into secondary (LO 2 ) and T A (LO 1 → LO 2 + T A) and its inverse process (recombination). Using this Hamiltonian, a set of coupled equations of motion for the phonons is obtained. We also consider the interaction between the phonons and its reservoirs. These interactions are introduced in the equations of motion leading to a set of coupled Langevin equations. In order to obtain an expression to describe our saser we apply, in the Langevin equations, an adiabatic elimination of some variables of the subsystem. Following the method above we obtain the value of the injection threshold for the operation of our phonon laser. At this threshold occurs a phase transition from a disordered to a coherent state. It is shown that it is not necessary a big "optical" pumping to get a sasing region.

Realization of phonon laser with femtosecond technology

“…With a below threshold photo-excited carrier density of l.3x10'2cm2, the measured transient transmission change is dominated by carrier dynamics. However with an above-threshold carrier density of 14.4x10'2crn2, a clear coherent acoustic oscillation corresponding to the lased phonon mode can be observed 0 5 10 15 20 0 5 10 15 20 on top of the already large background carrier dynamics. It is interesting to notice that the phonon laser pulse has a pulse width of 8 p5, determined by its cavity lifetime.…”

Phonon amplification in two coupled cavities containing one mechanical resonator

“…It well known that lasing can be generated when the stimulated emission is coherently amplified by a gain medium inside a cavity. Similar to the lasing, several theoretical proposals were put forward to generate phonon coherent amplification of stimulated emission in different systems, e.g., the quantum dot [19], ultra-cold atomic gas [20], nanomagnets [21], acoustical cavities [22], and double barrier systems [23]. The amplification of mechanical oscillations was also theoretically studied by coupling a nanomechanical resonator to polarized paramagnetic nuclei [24].…”

An ultrasound emitter based on assisted tunneling

“…The expectation that the secondary TA phonons can form a coherent beam inspired a proposal for the generation of a coherent sound beam (in the region of 2 THz) which justifies the name of SASER in analogy with LASER [12,13] for such device. The critical intensities required for stimulated decay of the primary phonons were recently discussed [14]. Although definitive rates would be those provided by experiments, it is clear that operation in the 'sasing' regime would require an important source of primary optical phonons.…”