The fourth-order squeezing and amplitude-squared squeezing of cotangent states produced in one-atom micromasers are investigated. It is found that optimal squeezing in the cotangent state can be achieved by properly choosing the relative amplitudes of the atomic coherent state. From our study of the dynamic process of the generation of steady-state fourth-order squeezing and amplitude-squared squeezing in one-atom micromasers, it is also shown that for sufficiently large atomic flux, the cavity loss, and finite temperature in the cavity have very little influence on the generation of these higher-order squeezings in practice.
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