Casimir-like Force Between Contaminants In Ideal Bose-einstein Condensates At Squeezed Vacuum State

Casimir indicated that system's free energy (or zero point energy) will change when the zero of quantum electromagnetic field floats so that mutual effects practically occur between boundaries. The phenomenon is called Casimir effect and the floating zero induce a force, the force named Casimir Force, which plays a very important role in the development of condensed matter physics, field theory,quantum mechanics, molecular physics, atomic physics and cosmography.Eighty years ago, Indian physical scientist Bose treated photon as unconservation of number of particle in his researches and conducted the law of Planck blackbody radiation, he also presented successfully a statistical way to described the behavior of photon. Einstein generalized the Bose's theory to the other particle with mass, considered that phase transition will happen at the very low temperature which all boson condense at the lowest energy state. It is the Bose-Einstein Condensation that the particle system composed by the boson condenses to the lowest energy state in momentum space at the very low temperature, when the particle's quantum number of self-spinning angle momentum is integer.In this paper we calculate the Casimir-Like force between contaminants in ideal Bose-Einstein condensates at vacuum state and squeezed vacuum state respectively. We obtain that the Casimir force at the squeezed vacuum state is larger than that of the vacuum state. It is significant to measure the force between contaminants in Bose-Einstein condensates in experiments.