Geometric phase for mixed squeezed-coherent states

In this paper, we investigate the geometric phase (GP) acquired by two-mode mixed squeezed-coherent states (SCSs) during unitary cyclic evolution, examining the influence of squeezing parameter and classical weight. We analyze the GP for three distinct mixed states, each characterized by different configurations of the SCSs. Our results reveal that increasing the squeezing parameters of individual modes compresses the GP contours in different patterns: linearly, hyperbolically, and elliptically, depending on the mixed state configuration. This behavior demonstrates the enhancement of quantum measurement precision in squeezed states through uncertainty adjustment, consistent with the established theoretical predictions.