  We consider the dephasing of two internal states |0> and |1> of a trapped
impurity atom, a so-called atomic quantum dot (AQD), where only state |1>
couples to a Bose-Einstein condensate (BEC). A direct relation between the
dephasing of the internal states of the AQD and the temporal phase fluctuations
of the BEC is established. Based on this relation we suggest a scheme to probe
BEC phase fluctuations nondestructively via dephasing measurements of the AQD.
In particular, the scheme allows to trace the dependence of the phase
fluctuations on the trapping geometry of the BEC.
