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We theoretically study the quantum speed limit of a single atom trapped in aFabry-Perot microresonator. The cavity mode will be squeezed when a drivinglaser is applied to the second-order nonlinear medium, and the effectiveHamiltonian can be obtained under the Bogoliubov squeezing transformation. Theanalytical expression of evolved atom state can be obtained by using thenon-Hermitian Schr\"{o}dinger equation for the initial excited state, and thequantum speed limit time coincides very well for both the analytical expressionand the master equation method. From the perspective of quantum speed limit, itis more conducive to accelerate the evolution of the quantum state for thelarge detuning, strong driving and coupling strength. For the initialsuperposition state case, the form of initial state has more influence on theevolution speed. The quantum speed limit time is not only dependent on thesystem parameters but also determined by the initial state.

Quantum speed limit of a single atom in a squeezed optical cavity mode