<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">PT</mml:mi></mml:math> symmetry, induced mechanical lasing, and tunable force sensing in a coupled-mode optically levitated nanoparticle

We theoretically investigate $\mathcal{PT}$ symmetry, induced mechanical lasing, and force sensing in an optically levitated nanoparticle with coupled oscillation modes. The coupling the system is created by modulation of asymmetric optical potential plane transverse to beam trapping nanoparticle. show that such a can lead $\mathcal{PT}$-symmetric behavior for experimentally realistic parameters. Further, examining phonon dynamics second-order coherence modes, we determine lasing also possible. Finally, demonstrate tunable ultrasensitive ($\ensuremath{\sim}zN/\sqrt{Hz}$) be engineered system. Our studies represent advance fields coherent manipulation degrees freedom oscillators their application sensing.