Influence of squeezing on the weak-to-strong measurement transition

Abstract

In this work, we study the measurement transition for a coherent squeezed pointer state through a transition factor $\mathrm{\ensuremath{\Gamma}}$ that involves a system-pointer coupling by using an arbitrary measured observable $A$. In addition, we show that the shift in the pointer's position and momentum establishes a relationship with a new value defined as the transition value, which generalizes the weak value as well as the conditional expectation value. Furthermore, a strategy is introduced to achieve different measurement regimes by just adjusting the $r$ and ${\ensuremath{\phi}}_{\ensuremath{\xi}}$ parameters of the coherent squeezed pointer state, opening an interesting way to test quantum mechanics foundations. Our scheme has been theoretically applied in a trapped ion illuminated by a bichromatic laser beam, with a high potential to be implemented in future experimental setups.