Controllable three-dimensional electrostatic lattices for manipulation of cold polar molecules

Engineering many-body systems of particles in lattices has attracted intense interest in the last few decades, thanks to their promising applications such as in quantum computation or topological matter. While lattices of different dimensions have been demonstrated with magnetic and/or optical fields, little work has been done upon three-dimensional (3D) electrostatic lattices to tame polar molecules. Here, we propose a 3D electrostatic lattice consisting of periodically distributed square-patterned electrodes in space, whose potentials reach tens of millikelvin and can be controlled easily. Detailed analysis and Monte Carlo simulations indicate that ${\mathrm{ND}}_3$ molecules in its $|J,KM\rangle =|1,-1\rangle$ state can be effectively trapped and evaporatively cooled. In addition, replacing the electrodes with different patterns enables realizing 3D electric lattices with new topological geometry (e.g., honeycomb or kagome). As a natural extension of the 3D optical and magnetic lattices, the 3D electrostatic lattice offers intriguing perspectives for cold chemistry, quantum simulation, and precision metrology.

Figure 1

(a) Schematic view of the 3D electrostatic lattice for trapping a Stark-decelerated cold polar molecular beam. The 3D electrostatic lattice is formed by a series of periodically spaced electrode plates. (b) Zoom-in view of one piece of plate of the 3D electric lattice, together with the pattern parameters.

Figure 2

Four slices of the electric field distributions of the 3D electrostatic lattice at different positions through the electric field minima of the sites (a), together with the potential-well distribution along the longitudinal (b) and the lateral (c) directions for ${\mathrm{ND}}_3$ molecules.

Figure 3

Loading and trapping polar molecules into the 3D electric lattice employing only one electric field configuration (a) and two different electric field configurations in succession (b). The dashed red line and dotted blue line represent the Stark potential energy of the molecules in the lattice, and the solid green lines indicate the molecular potential energy gained in the loading processes.

Figure 4

The calculated longitudinal phase-space distribution of ${\mathrm{ND}}_3$ molecules at $t=2\mathrm{ms}$ for the loading methods I (a) and II (b), respectively. (c) The loading efficiency of ${\mathrm{ND}}_3$ molecules as a function of the forward velocity using two different loading schemes. (d) The dependence of the molecular number density upon a time in the lattice sites for different loading methods.

Figure 5

Space-periodic $\mathrm{N}{\mathrm{D}}_3$ molecular packets in the 3D electrostatic lattice at voltages of 100 V (a) and 40 V (b).

Figure 6

The dependence of the filling ratio and the average number of molecules per lattice site on applied electrode voltage, respectively.

Figure 7

The design of hexagonal honeycomb (a) and kagome (d) 3D electric lattices and the pattern in the electrodes. Electric field distribution of the honeycomb (b) and the kagome lattices (e) along the $z$ direction. The two-dimensional transverse electric field distributions through the lattice site minima of the honeycomb (c) and the kagome (f) 3D lattices, together with the electric field strength bar.

Figure 8

Transverse space distribution of ${\mathrm{ND}}_3$ molecules in the honeycomb (a) and the kagome (c) lattices after $2\mathrm{ms}$ of confinement. Molecular phase-space distribution in the $z$ direction in the honeycomb (b) and the kagome (d) lattice sites.