Dynamic Sensitivity Based On The Coherent Properties Of Atomic Ensembles

The quantum phase transition (QPT) occurs at zero temperature when the external parameters of some interacting many-body systems change to reach the critical values. Generally, it is associated with the ground state with energy level crossing and symmetry breaking at the critical points. Recently, it was discovered that, near the quantum critical point the QPT system possesses the ultra-sensitivity in its dynamical evolution. This theoretical prediction has been demonstrated by an NMR experiment.In this paper, we study the dynamic sensitivity of an atomic ensemble in a cavity with a single-mode electromagnetic field (called a photon-dressed atomic ensemble), which is described by the Dicke model. We assume the atoms in the Dicke model are resonant with the cavity field. When an extra two-level atom in large detuning goes through the cavity field, the frequency of cavity field will be shifted effectively according to the Stark effect so that the photon-dressed atomic ensemble near the QPT will be forced into its critical point. In this situation the dynamic evolution of the Dicke model becomes too sensitive in response to the passage of the extra atom.This dynamic sensitivity is characterized by the Loschmidt echo, which is intrinsically defined by the structure of the photon-dressed atomic ensemble. For a short time approximation, we prove that the LE is just an exponential function of the photon number variance in the photon-dressed atomic ensemble. This finding means that the LE can be experimentally measured by detect-ing the photon correlation. Its sudden change may imply the passage of an extra atom through the cavity. With this reorganization we will demonstrate that such quantum sensitivity in the Dicke model is very similar to the clas-sical sensitivity of the cloud chamber for detecting a flying particle, which is characterized by the macroscopically-observable trajectories enhanced by the classical phase transitions.