Pure and Mixed State Entanglement Dynamics in Tavis-Cummings Model with Squeezed Coherent Thermal States

TL;DR

The paper addresses how entanglement between two atoms and between the atoms and a single-mode cavity field evolves in the Tavis–Cummings model when the field is prepared in a squeezed coherent thermal state and the atoms start in either pure Bell or mixed Werner states. The authors derive the exact time evolution under the collective atom–field interaction, compute reduced density matrices, and quantify entanglement with concurrence and negativity while exploring Ising-type, dipole–dipole, detuning, and Kerr nonlinearities; Wigner functions are used to assess field nonclassicality. Key findings show that thermal photons generally suppress entanglement and prolong ESD, whereas squeezing enhances entanglement and mitigates ESD, with the purity of the initial atomic state playing a crucial role in the observed dynamics. Detuning and nonlinearities yield state-dependent control: detuning can protect Bell-state entanglement but suppress Werner-state entanglement, dipole–dipole coupling can enhance Bell-state entanglement while reducing Werner-state correlations, and Kerr nonlinearity redistributes entanglement between subsystems in a manner that depends on the initial state. These results offer guidance for managing quantum correlations in realistic light–matter platforms where noise, detuning, and nonlinear effects are unavoidable.

Abstract

We investigate the entanglement dynamics of two atoms interacting with a single-mode cavity field within the Tavis-Cummings model in the presence of noise. The atoms are initially prepared in either pure Bell states or mixed Werner states, allowing a direct comparison of pure- and mixed-state entanglement. The cavity field is described by generalized single-mode squeezed coherent thermal states, incorporating both thermal and quantum noise effects. Atom-atom and atom-field entanglement are quantified using concurrence and negativity, respectively. We analyze entanglement sudden death and revival, and examine how Ising-type coupling, dipole-dipole interaction, Kerr nonlinearity, and detuning modify the entanglement dynamics. Our results show that thermal photons generally suppress entanglement and enhance sudden death, while squeezing counteracts these effects. The influence of nonlinearities and interatomic interactions depends sensitively on the purity of the initial atomic state, leading to qualitatively different behaviors for Bell and Werner states.

Figures (17)

• Figure 1: Schematic of two entangled atoms interacting with a single-mode cavity field.
• Figure 2: Effects of squeezed photons and thermal photons on entanglement dynamics with atoms in Bell state. Here, (a) blue curve $\Rightarrow \bar{n}_c = 5, \bar{n}_s = 0, \bar{n}_{th} = 0$, (b) green curve $\Rightarrow \bar{n}_c = 5, \bar{n}_s = 0, \bar{n}_{th} = 1$, (c) red curve $\Rightarrow \bar{n}_c = 5, \bar{n}_s = 1, \bar{n}_{th} = 0$ and (d) black curve $\Rightarrow \bar{n}_c = 5, \bar{n}_s = 1, \bar{n}_{th} = 1$.
• Figure 3: (a), (b) represent 3D plots for $C(t), N(t)$ vs $\bar{n}_{th}$ and $\lambda t$; (c), (d) represent 3D plots for $C(t), N(t)$ vs $\bar{n}_{s}$ and $\lambda t$ for the atoms in Bell state. Here, in Fig. 2(a), 2(b) $\bar{n}_c = 2, \bar{n}_s = 0$ and $\bar{n}_{th}$ is varied; in Figs. 3(c), 3(d) $\bar{n}_c = 2, \bar{n}_{th} = 0$ and $\bar{n}_{s}$ is varied.
• Figure 4: Effects of squeezed photons and thermal photons on entanglement dynamics with atoms in Werner state. Here, (a) blue curve $\Rightarrow \bar{n}_c = 5, \bar{n}_s = 0, \bar{n}_{th} = 0$, (b) green curve $\Rightarrow \bar{n}_c = 5, \bar{n}_s = 0, \bar{n}_{th} = 1$, (c) red curve $\Rightarrow \bar{n}_c = 5, \bar{n}_s = 1, \bar{n}_{th} = 0$ and (d) black curve $\Rightarrow \bar{n}_c = 5, \bar{n}_s = 1, \bar{n}_{th} = 1$.
• Figure 5: (a), (b) represent 3D plots for $C(t), N(t)$ vs $\bar{n}_{th}$ and $\lambda t$; (c), (d) represent 3D plots for $C(t), N(t)$ vs $\bar{n}_{s}$ and $\lambda t$ for the atoms in Werner state ($\eta = 0.5$). Here, in Fig. 4(a), 4(b) $\bar{n}_c = 2, \bar{n}_s = 0$ and $\bar{n}_{th}$ is varied; in Fig. 4(c), 4(d) $\bar{n}_c = 2, \bar{n}_{th} = 1$ and $\bar{n}_{s}$ is varied.