Entanglement Dynamics of a Strongly Driven Trapped Atom

We study the entanglement between the internal electronic and the external vibrational degrees of freedom of a trapped atom which is driven by two lasers into electromagnetically induced transparency. It is shown that basic features of the intricate entanglement dynamics can be traced to Landau-Zener splittings (avoided crossings) in the spectrum of the atom-laser field Hamiltonian. We further construct an effective Hamiltonian that describes the behavior of entanglement under dissipation induced by spontaneous emission processes. The proposed approach is applicable to a broad range of scenarios for the control of entanglement between electronic and translational degrees of freedom of trapped atoms through suitable laser fields.

Figure 1

Dynamics of the negativity during the cooling process for the initial vibrational level $n_i=10$ for three values of the excited state width $\Gamma$ and $\eta =0.1$. The top scale gives the mean vibrational quantum number for the 6 MHz result. The dotted line represents a power law decay, $\mathcal{N}\propto t^{-3/2}$.

Figure 2

(a) Trapped three-level atom and (b) energies of dressed vibronic states as a function of the normalized ac-Stark shift.

Figure 3

Time dependence of the negativity obtained from the Schrödinger equation (6) for initial vibrational levels $n_i=3$ and 30. Parameters: $\eta =0.1$, $\omega =0.03$, $\Delta =15$, $g_1=1.34$, $g_1/g_2=10$ (all frequencies are given in units of $2\pi \mathrm{MHz}$). The broken lines represent the prediction according to Eq. (13).

Figure 4

The negativity obtained from the quantum master equation (2) for various $\Gamma$, as also shown in Fig. 1. Fits of Eq. (20) are shown by the broken lines. Conditions as given in Fig. 3.