Fig. 14: Synthetic dimensional reduction for a \({{\mathbb{Z}}}_{2}\) chain.
From: Synthetic \({{\mathbb{Z}}}_{2}\) gauge theories based on parametric excitations of trapped ions
a We represent the transverse vibrational degrees of freedom of a trapped-ion chain in a frequency scheme, where the corresponding trap frequencies ωx < ωy can be resolved by external parametric drives. The introduction of the site-dependent shift of the frequencies in Eq. (53) leads to a two-site gradient here depicted by \(\tilde{\Delta }\). For \(| {t}_{ij}| \,\ll \,\tilde{\Delta }\), the exchange of vibrational quanta leads to alternating dimers, here depicted by green solid lines. b As a consequence of this exchange, the vibrational states inside the dimers split into center of mass (com) and zigzag (zz) modes, which can also be resolved in energies. As shown in the inset, we apply a pair of state-dependent parametric drives addressed to even-odd or odd-even dimers for the com modes, respectively, in order to induce the desired light-shift potential underlying the state-dependent tunneling of Eq. (55).
