We study the environmental dependence of ultralight scalar dark matter (DM) with linear interactions to the standard model particles. The solution to the DM field turns out to be a sum of the cosmic harmonic oscillation term and the local exponential fluctuation term. The amplitude of the first term depends on the local DM density and the mass of the DM field. The second term is induced by the local distribution of matter, such as the Earth. And it depends not only on the mass of the Earth, but also the density of the Earth. Then, we compute the phase shift induced by the DM field in atom interferometers (AIs), through solving the trajectories of atoms. Especially, the AI signal for the violation of weak equivalence principle (WEP) caused by the DM field is calculated. Depending on the values of the DM coupling parameters, contributions to the WEP violation from the first and second terms of the DM field can be either comparable or one larger than the other. Finally, we give some constraints to DM coupling parameters using results from the terrestrial atomic WEP tests.

我们研究了具有线性相互作用的超轻标量暗物质 (DM) 对标准模型粒子的环境依赖性。DM 场的解原来是宇宙谐波振荡项和局部指数波动项的总和。第一项的幅度取决于局部 DM 密度和 DM 场的质量。第二项是由物质的局部分布引起的，例如地球。而且它不仅取决于地球的质量，还取决于地球的密度。然后，我们通过求解原子的轨迹来计算由原子干涉仪 (AI) 中的 DM 场引起的相移。特别是计算了由DM场引起的违反弱等价原则（WEP）的AI信号。根据 DM 耦合参数的值，DM 字段的第一项和第二项对 WEP 违规的贡献可以是可比的，也可以比另一个大。最后，我们使用地面原子 WEP 测试的结果对 DM 耦合参数进行了一些限制。