# Phonon maser stimulated by spin post-selection

## TL;DR

This paper demonstrates that a phonon laser with high coherence can be generated through spin post-selection in a micromaser-like system, offering a new method to achieve phonon lasing especially under high mechanical losses.

## Contribution

The study introduces a novel phonon maser model utilizing spin post-selection, showing how it enhances coherence and enables phonon lasing under conditions of high mechanical loss.

## Key findings

- Phonon laser with Poisson statistics and high coherence is achieved.
- Post-selection of spins is crucial for the non-linear gain and coherence.
- Heralded post-selection can enable phonon lasing when mechanical losses are high.

## 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 post-selection 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 non-linear gain of the system depends crucially on the properly post-selected spin state as well as the pump. Our model and results suggest that the mechanism of interaction followed by a post-selected state or partial trace (common in laser/maser theory) of the spins may create the coherent vibrational radiation. However, for situations where the mechanical losses are high and it is imposible to decrease these, then the heralded post-selection 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.