We study the dynamical Casimir-Polder force on a two-level atom with different initial states in the one-dimensional dielectric cavity with output coupling, and obtain the analytical expression of the expectation value of dynamical Casimir-Polder force. Results show that the expectation values of dynamical Casimir-Polder force may be affected by the initial states of the atom. Moreover, the expectation value of Casimir-Polder force may vanish at some special atomic positions by properly selecting the initial state of the system. The effects of different relative dielectric constants and the cavity size on the expectation value of Casimir-Polder force are also discussed. The existence of electromagnetic vacuum fluctuations has caused many quantum effects, such as Casimir-Polder force 1,2. The Casimir-Polder force is the long-range interaction between neutral polarizable particles and macroscopic objects, which is successfully observed in experiments 3 and has received considerable attentions 4-7 due to its potential application in basic physics and designing of quantum devices 6,8-11. For instance, the Casimir-Polder force has covered various configurations such as trapping cold atoms near surfaces 12-16 , quantum reflection 17-20 , graphene 21 , Bose-Einstein condensates 17,22 , and carbon nanotubes 23-25. At finite temperatures, the key correlations between these interactions and the topological and magnetoelectric properties of interacting objects are highlighted 26,27. In recent years, many studies have focused on the Casimir-Polder force on atoms when they start from ground or excited states 28-31. In Ref. 31 and 4 , the authors investigate the dynamcial Casimir-Polder force on a two level atom placed before a ideal metal plate starting from the ground state and the excited state, respectively. Results show that the static Casimir-Polder force is always attractive for the ground state condition, while the static Casimir-Polder force is either attractive or repulsive for the excited condition. At some special atom-wall distances, the static Casimir-Polder force can vanish for the excited condition. Besides, the static Casimir-Polder force for the excited-atom condition is much greater than that of the ground-atom condition. In this paper, we will investigate the effect of initial states on the dynamical Casimir-Polder force acting on a two-level atom in a caivity with output coupling 32. The analytical expression of the expectation value of dynamical Casimir-Polder force on atom starting from the superposition state will be obtained. And the effects of the dielectric and cavity size will be discussed. The paper is organized as follows: in "Model and Hamiltonian" section, we describe the model and the Hamiltonian of the system. In "Calculation of the expectation value of dynamical Casimir-Polder force" section we will calculate the expectation value of dynamical Casimir-Polder force. In "Dynamical Casimir-Polder force on an initially general superposition state atom" section we will discuss the dynamical Casimi...

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In this paper, a model of interaction between a two-level atom and a dissipative cavity is considered. The dynamical Casimir-Polder forces between the atom and the cavity wall in different initial states are discussed and analyzed. The quasimode theory is used to describe the electromagnetic field. The results show that the magnitude and properties of the dynamical Casimir-Polder force are different in different initial states of atoms. By adjusting the initial state of the atom properly, the dynamical Casimir-Polder force can also reach zero. This conclusion has important reference significance for the application of quantum information.