Quantum Simulation of Small-Polaron Formation with Trapped Ions

We propose an analog quantum simulation of small-polaron physics using a one-dimensional system of trapped ions acted upon by off-resonant standing waves. This system, envisioned as an array of microtraps, in the single-excitation case allows the realization of the antiadiabatic regime of the Holstein model. We show that the strong excitation-phonon coupling regime, characterized by the formation of small polarons, can be reached using realistic values of the relevant system parameters. Finally, we propose measurements of the quasiparticle residue and the average number of phonons in the ground state, experimental probes validating the polaronic character of the phonon-dressed excitation.

Figure 1

System schematic: Trapped-ion chain subject to three pairs of counterpropagating laser beams giving rise to three standing waves. The standing wave with the polarization ${\sigma }^{+}$ in the direction $\alpha$ induces the transition from $|\uparrow {⟩}_{\alpha }$ to $|e_{\downarrow }{⟩}_{\alpha }$, where $|\uparrow ,\downarrow {⟩}_x=(|\uparrow {⟩}_z\pm |\downarrow {⟩}_z)/\sqrt{2}$ and $|\uparrow ,\downarrow {⟩}_y=(|\uparrow {⟩}_z\pm i|\downarrow {⟩}_z)/\sqrt{2}$.

Figure 2

Calculated quasiparticle residue at $k=0$ for different values of the renormalized longitudinal-phonon frequency ${\tilde{\omega }}_z$. All three curves correspond to the hopping amplitude $J=25\mathrm{kHz}$.

Figure 3

Average number of phonons in the single-excitation ground state. All three curves correspond to $J=25\mathrm{kHz}$.