Can I create squeezing with a $P^2$ interaction?

One approach to squeeze light is through the one-mode squeezing operator, which can be written as $e^{-i H t}$ with $H sim (a^2 – (a^dagger)^2)$. My question is, can I create squeezing with $H sim P^2 sim (a-a^dagger)^2$ ?

Is this described anywhere in the literature? I know it might not be easy to implement, and so of limited relevance. The term $P^2$ has also additional terms in the expansion $sim a^dagger a$, which I’m not sure how they contribute.