Ramp Dynamics of Phonons in an Ion Trap: Entanglement Generation and Cooling

We show that the ramp dynamics of phonons in a one-dimensional ion trap can be used for both generating multiparticle entangled states and motional state cooling of a string of trapped ions. We study such ramp dynamics using an effective Bose-Hubbard model which describes these phonons at low energies and show that specific protocols, involving site-specific dynamical tuning of the on-site potential of the model, can be used to generate entangled states and to achieve motional state cooling without involving electronic states of the ions. We compare and contrast our schemes for these to the earlier suggested ones and discuss specific experiments to realize the suggested protocols.

Figure 1

A schematic of the experimental setup for the implementation of the ramp protocol. The blue standing wave laser phase is controlled by micromirrors placed on piezo stages.

Figure 2

(left) Plot of $C_{14}$ as a function of elapsed time and $\tau |U^{(1)}|/\hslash =100$ (solid line), 200 (dash-dotted line), and 500 (dashed line) for $L=6$ ions with a total of $N=2$ phonons and $J/U^{(0)}=0.2$. The ramp continues till $t=\tau$; see text for details. (right) Plot of $C_{14}^{\max }$ as a function of $J/U^{(0)}$ for $\tau |U^{(1)}|/\hslash =100$ (blue square), 200 (red circles), and 500 (black triangles).

Figure 3

(left) Plot of $N_2(t=\tau )/N$ as a function of ramp time $\tau$ in ms for $U^{(1)}=-1.1\mathrm{kHz}$, $J/U^{(0)}=0.5$, and $N=3..6$. (right) Optimization of the cooling: Plot of $N_2/N$ as a function of ramp time for $J/U^{(0)}=0.05$, 0.2, 0.3, 0.5, 0.7, and 0.9 (from left to right) for $N=3$.