Compensating loss via non-Hermiticity in optically trapped and bounded particles

The non-Hermiticity in the optical trapping and binding originates from their open nature. Once the non-Hermiticity is sufficiently large such that it pushes the system across the exceptional point, the non-Hermitian force will provide an effective gain to the systems. In this scenario, the trapped particles acquire additional energies as a consequence of the non-Hermitian force field, which effectively serve as a gain. Conversely, these trapped or bound particles can also dissipate energy as a result of the damping effect experienced during oscillation within optical trapping or binding. People usually employ vacuum extraction to extend the lifetime of particles' vibrational modes. However, low-pressure environments can induce instability in the systems. Here, we propose using the "non-Hermitian gain" to compensate for damping loss and enhance the quality factor (lifetime, Q-factor) of vibrational modes. Our study also takes into account the Brownian motion in optical trapping. Nevertheless, even after taking the Brownian motion into account, the Q-factors remained high. We further unveil the physical mechanism that can enhance or diminish non-Hermitian forces, such as increasing particle radius and refractive index and utilizing propagating or standing waves.