Perfect higher-order squeezing via strong nonlinearity in microwave-modified electromagnetically induced transparency

We show that it is possible to obtain perfect higher-order squeezing via strong nonlinearities in the microwave-modified electromagnetically induced transparency (EIT). In a typical $\mathrm{\ensuremath{\Lambda}}$ three-level system coupled to a control field and a microwave field, the strong nonlinearity is existent under the full-resonant conditions and can be effectively controlled by the relative intensity of the optical and microwave fields. Via dressed-state and Bogoliubov mode transformation, we explore that the internal nonlinearity is closely related to the squeezing parameter and dissipative rate for two cavity modes. As a result, it is found that the two-mode higher-order squeezing is nearly close to $100%$ under ideal conditions, which is verified by our numerical and analytical results. In addition, we reveal that the higher-order squeezing in the present scheme is robust against the dephasing rate between two lower levels. This may find potential applications in high-precision measurement and provide a convenient way for experimental implementation.