Higher-order exceptional points and enhanced quantum squeezing in a pseudo-Hermitian semiconductor optomechanical system

We investigate higher-order exceptional points and quantum squeezing of exciton polaritons in a pseudo-Hermitian semiconductor optomechanical system. We show that a third-order exceptional point (EP3) can emerge from the tripartite coupling among photons, excitons, and phonons under pseudo-Hermitian conditions. A pronounced two-mode quantum squeezing of exciton polaritons is revealed, and we demonstrate that this squeezing is significantly enhanced in the vicinity of the EP3. Furthermore, we find that in the PT-symmetric phase, the squeezing dynamics produce a frequency comb of exciton polaritons, whereas the squeezing remains constant over time in the PT-symmetry broken phase and exactly at the EP3. The sudden change in quantum squeezing dynamics can be used to probe the phase transition and the EP3. Our work opens a pathway to manipulate quantum squeezing in semiconductor optomechanical platforms, offering potential advantages for quantum sensing and metrology.