Abstract

In a sequence of single spins interacting longitudinally with a mechanical oscillator, and using the micromaser model with random injection, we show that after an appropriate postselection of each spin, a phonon laser analog with Poisson statistics is created with nearly perfect coherence, evidenced by the second order coherence function that goes asymptotically to one. The nonlinear gain of the system depends crucially on the properly postselected spin state as well as the pump. Our model and results suggest that the mechanism of interaction followed by a postselected state or partial trace (common in laser and maser theory) of the spins may create the coherent vibrational radiation. However, for situations where the mechanical losses are high and it is impossible to decrease these, then the heralded postselection can be the only resource to get phonon lasing if compared to the partial trace operation. These ideas and results may be useful for further theoretical and technical developments.