We investigate the propagation and storage of a squeezed vacuum as the probe light in a collection of N four-level tripod configuration atoms under the condition of single or double electromagnetically induced transparency (EIT). The squeezing of the probe light is well preserved in both the single transparency channel and the double transparency one. On the other hand, the effects of the ground state dephasing rates on the propagation and storage of the squeezed vacuum are investigated. It is found that the maximum squeezing at the transparency points is suppressed by the dephasing rates in single or double EIT. Meanwhile, the mapping of the squeezing of the probe light onto the atomic ground coherences or onto the two atomic dark-state polaritons is also studied. In the absence of the Langevin atomic noise, the quasi-ideal squeezing transfer between the squeezed vacuum and the atomic ground coherences or the dark-state polaritons can be realized in such a system. When considering the Langevin atomic noise, the quantum characteristics of the atomic coherences at resonance are submerged by the Langevin noise, while in the scenario of the dark-state polariton, it is found that squeezing transfer onto one polariton is damaged, but the squeezing transfer onto the other polariton survives even in the presence of the Langevin noise.
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