  This paper explores the Bogoliubov transformation's extension to two-mode
squeezed states, building on our previous work with Virasoro-squeezing. We
establish the Virasoro-Bogoliubov transformation as a non-linear extension of
the traditional Bogoliubov transformation, creating non-linear two-mode
squeezed states. This research unveils novel quantum states with the potential
for innovative insights in various fields of quantum physics.
