Squeezed Phonon Lasing via Floquet-Controlled Solid-State Defects

We propose a general Floquet-engineered scheme for phonon lasing that enables a continuous transition from conventional lasing to phase-locked squeezed phonon lasing. Focusing on a solid-state platform based on color centers embedded in a circular hexagonal boron nitride (hBN) membrane, we demonstrate that a mechanical oscillator coupled to principal and ancilla spins, and controlled via effective Floquet driving simultaneously exhibits squeezed-state amplification and cooling dynamics, leading to the emergence of a stable squeezed phonon laser. We analyse the steady-state properties of the system, including the lasing threshold, mechanical occupation, emission spectrum and second-order correlations. Furthermore, we show that Floquet engineering can realize phase-locked lasing while enabling controlled quadrature squeezing, thereby providing a simple yet effective route toward squeezed lasing in quantum mechanical systems. Our results offer new insights into the generation of squeezed phonon lasers in solid-state platforms, with potential applications in quantum metrology.