Fig. 2
Time evolution of the geometric phase for several different values of γ. The value of ω used in the graphics is 0.3 for a, 0.99 for b, and 5 for c. The squeezing parameters chosen here are \(\mu =\sqrt {2}\) and ν=1; this choice gives q-squeezed state at initial time. Other quantities that we have used are m=1, ω0=1, A0=1, fd=1, \(\hbar =1\), φ=0, and γG(0)=0. We confirm that the geometric phase is large when the damping factor γ is large in most cases, but not all. The frequency of the case b is near to the resonant frequency, whereas those of a and c are far from the resonant one. The geometric phase for the resonant case (b) increases very rapidly over time