Tunable Holstein model with cold polar molecules

We show that an ensemble of polar molecules trapped in an optical lattice can be considered as a controllable open quantum system. The coupling between collective rotational excitations and the motion of the molecules in the lattice potential can be controlled by varying the strength and orientation of an external dc electric field as well as the intensity of the trapping laser. The system can be described by a generalized Holstein Hamiltonian with tunable parameters and can be used as a quantum simulator of excitation energy transfer and polaron phenomena. We show that the character of excitation energy transfer can be modified by tuning experimental parameters.

Figure 1

Nearest-neighbor couplings $J_{12}$ (solid line), $D_{12}$ (dashed line), and $V_{12}^{gg}$ (dot-dashed line). (a) Dependence on the dc field strength parameter $\lambda =dE/B_e$ for a dc field $\mathbf{E}=E\widehat{\mathbf{z}}$ perpendicular to the one-dimensional array. (b) Dependence on the angle $\theta$ between the electric field and the array, for $\lambda =1$. Energy in units of $V_{dd}=d^2/a_L^3$, where $d$ is the permanent dipole moment and $a_L$ is the lattice constant. $B_e$ is the rotational constant of the molecule.

Figure 2

Polaron shift $\Delta E_g$ as a function of the trapping frequency ${\omega }_0$ for an array of 10 LiCs molecules separated by 400 nm. Curves are shown for electric fields of 9 kV/cm (solid line), 2 kV/cm (dashed line), and 0.6 kV/cm (dotted line). Panels (a) and (b) correspond to a field perpendicular and parallel to the array, respectively. In panel (a) we have $|\Delta E_g|>J_{12}=6.73$ kHz, for $E=9$ kV/cm and ${\omega }_0/2\pi <20$ kHz, which is a signature of strong exciton-phonon coupling.

Figure 3

Excitation energy transfer in an array of five LiCs molecules in a dc electric field perpendicular to the array. (a) Evolution of the excitation probability $p_1\left(t\right)$, when no phonons are present. (b) The same as in (a), but with phonons in an optical lattice with trapping frequency ${\nu }_0={\omega }_0/2\pi$ varying in time as indicated in the inset. The field strength is 0.5 kV/cm.