Abstract:　Superradiant　phase　transition　and　entanglement　entropy　in　the　Dicke　model　with　a　squeezed　light　are　investigated.　We　find　a　special　rotation　coordinate　system　mapping　the　original　Hamiltonian　into　an　effective　dual-oscillator　Hamiltonian　in　the　thermodynamic　limit.　We　analytically　derive　the　eigenenergy　and　eigenstate　of　the　ground　state.　The　ground　state　is　demonstrated　to　undergo　superradiant　phase　transition　at　a　nonlinear　critical　boundary　collectively　induced　by　the　squeezed　driving　and　qubit-field　coupling.　This　phase　boundary　requires　neither　large　qubit-field　detuning　nor　strong　squeezed　driving.　An　exact　expression　of　the　ground-state　entropy　is　obtained.　We　demonstrate　that　the　squeezed　light　enhances　the　qubit-field　entanglement　entropy　linearly.　Graphical　abstract:　(Figure　presented.)　©　The　Author(s),　under　exclusive　licence　to　EDP　Sciences,　SIF　and　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature　2024.