Resonant control of polar molecules in individual sites of an optical lattice

We study the resonant control of two nonreactive polar molecules in an optical lattice site, focusing on the example of RbCs. Collisional control can be achieved by tuning bound states of the intermolecular dipolar potential by varying the applied electric field or trap frequency. We consider a wide range of electric fields and trapping geometries, showing that a three-dimensional optical lattice allows significantly wider avoided crossings than free space or quasi-two dimensional geometries. Furthermore, we find that dipolar confinement-induced resonances can be created with reasonable trapping frequencies and electric fields, and have widths that will enable useful control in forthcoming experiments.

Figure 1

(a) Eigenenergies for two RbCs molecules in an optical lattice site with $f_z=f_{\rho }=25$ kHz. Trap states are adiabatically converted to bound states as the dipolar interaction is increased. Points marked ‘b’ and ‘c’ correspond to the wave functions shown in the lower panels, which illustrate the head-to-tail configuration at two different dipole moments. For the three lowest energy trap states, the partial wave at $\mu =0$ is indicated. We also give the partial waves into which these states have a significant projection after being converted to bound states as $\mu$ is increased. Red crosses indicate the noninteracting trap-state energies. In (b) and (c), we plot ${\rho \left|\psi \right|}^2$, and scale all lengths by the confinement length in the $z$ direction, ${\ell }_{\mathrm{ho}}^z$.

Figure 2

Elastic collision rate as a function of $\mu$ for a trapping frequency of $f_z=50$ kHz and collision energy of $k_{\mathrm{B}}\times 200$ nK, showing the contributions of the $m=0$, $\pm 2$, and $\pm 4$ partial waves (upper panel), and the corresponding $m=0$ bound-state calculation with $f_z=50$ kHz and $f_{\rho }=1$ kHz (lower panel). The $z$ trap states with a substantial admixture are indicated for each bound state not concentrated solely in $n_z=0$.

Figure 3

Confinement-induced resonances for a quasi-2D trap as function of $f_z$. The top panel shows the elastic collision rate, where we have summed the contributions of partial waves from $m=0$ to $\left|m\right|=4$. Solid lines correspond to $\mu =0.3048$ D and collision energies of $k_{\mathrm{B}}\times 1$ nK, $k_{\mathrm{B}}\times 100$ nK, and $k_{\mathrm{B}}\times 200$ nK, as labeled. The dashed line ($\mu =0.3058$ D) shows the sensitivity of the resonance location to electric field variation. The bottom panel shows the eigenenergies of the Schrödinger equation with the potential of Eq. (1), using $\mu =0.3048$ D and trapping frequencies of $f_z=50$ kHz and $f_{\rho }=1$ kHz. The dashed green line shows the perturbative result of Eq. (2). Dotted red lines correspond to the energy of a noninteracting pair of molecules in the ground trap state with $k_{\mathrm{B}}\times 1$ nK and $k_{\mathrm{B}}\times 200$ nK of relative kinetic energy. Arrows show the intersections of this calculation with scattering states of the given kinetic energies. These intersections agree well with the calculated resonance locations of the upper panel.