Physical Realization of an Anti- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> </mml:math> -Pseudo-Hermitian Mechanical System

The anti-P-pseudo-Hermitian system has recently been recognized as a new avenue in non-Hermitian physics, exhibiting symmetry-related phenomena without the need for time-reversal symmetry. However, its physical realization remains challenging due to the difficulty of integrating tunable media while simultaneously enabling nonreciprocal coupling. In this Letter, we introduce a novel framework for constructing an anti-P-pseudo-Hermitian mechanical system by incorporating piezoelectric actuators and sensors with nonreciprocal coupling into mechanical beams. We theoretically demonstrate that this system can exhibit programmable exceptional points (EPs) and validate our approach numerically and experimentally. Precise tuning of EPs is crucial for optimizing the system's sensitivity under operational conditions. As a key demonstration, we show that this system excels in detecting minute mass variations, making it highly effective for ultrasensitive sensing applications. This Letter not only advances the understanding of non-Hermitian physics, but also lays the groundwork for the next generation of mechanical sensors based on EP physics.