A definition a bogoliubov transformation is defined as b=ua+va† , b†=u∗a†+v∗a But, using squeeze operator S=exp[12(z(a†)2−z∗a2)] we can claim that b=SaS† is also a bogoliubov transform. Using S, how do we find the value of u and v corresponding to the first set of expressions? I have tried applying BCH formula to b=SaS† but didn't get anything helpful.
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