A Weak Value Amplification Scheme Based on Single-Particle Multi-Levels

Weak measurements have many applications in the field of quantum information due to the peculiar properties of weak values. Quantum weak measurement can be performed by two particles or two degree of freedom of single particle. The former needs complex operations, the latter require the reconstruction of the motion state wavepacket, which consumes substantial quantum resources. This paper presents a novel weak measurement scheme that encodes multiple internal energy levels of a single particle into the measured system and the measuring pointer, while defining a finite-coupling postselected pointer ratio (FCPR). The FCPR obtained from this scheme enables both weak value amplification and rapid experimental results. To verify these advantages, we measured the FCPR using a trapped ⁴⁰Ca⁺ experimental setup and monitored fluctuations of the laser power within the experimental system. The results show that our scheme can detect weaker laser power fluctuations, thus providing higher precision for laser power locking.