Dynamic sensitivity of photon-dressed atomic ensemble with quantum criticality

We study the dynamic sensitivity of an atomic ensemble dressed by a single-mode cavity field (called a photon-dressed atomic ensemble), which is described by the Dicke model near the quantum critical point. It is shown that when an extra atom in a pure initial state passes through the cavity, the photon-dressed atomic ensemble will experience a quantum phase transition showing an explicit sudden change in its dynamics characterized by the Loschmidt echo of this quantum critical system. With such dynamic sensitivity, the Dicke model can resemble the cloud chamber for detecting a flying particle by the enhanced trajectory due to the classical phase transition.

Figure 1

(Color online) Schematic of a cavity field coupled with an atomic gas consisting of $N$ two-level atoms. An extra detected two-level atom $S$ is injected into cavity field.

Figure 2

(Color online) 3D diagram of the LE plotted as a function of the time $t$ and the coupling strength $g$ both in the normal phase (the left panel) and in the super-radiant phase (the right panel). Here, in unit of $\omega$, ${\omega }_0=1.44\omega$, $\tilde{\delta }=g_s^2/{\Delta }_s=0.001\omega \left({\Delta }_s=0.1\omega ,g_s=0.01\omega \right)$, the critical point $g_c=\sqrt{\omega {\omega }_0}/2=0.6\omega$, the number of atoms $N=100$.

Figure 3

(Color online) The cross section of the 3D surface of the LE in Fig. 2 at $\omega t=100$. For other parameters see Fig. 2.

Figure 4

(Color online) The LE of the systems for different $N$ at $\omega t=100$. In normal phase, the LE is independent of $N$. In super-radiant phase, $N=100$ (solid line), 1000 (dashed line), and $10000$ (dotted line), respectively, from up to bottom. For other parameters see Fig. 2.