Diatomic molecule in the polar trap

We discuss the trapping of heteronuclear diatomic molecules prepared in their electronic and vibrational ground states. We tune and shape the trapping potential for bosonic polar molecules in superpositions of rotational states by dressing rotational excitations with a static sextupole electric field. The translational motion of a molecule is treated classically. We examine the Hamiltonian which governs the center of mass dynamics. The effective potential has a global minimum that provides the trapping ability of this trap. The first term of its Taylor series expansion, corresponding to the quadratic Stark shifts, results in the integrable potential. In terms of cylindrical coordinates the center of mass Hamiltonian splits into axial and radial parts. Corresponding trajectories are parameterized by elliptic functions. At low electric fields, the non-approximated Hamiltonian is treated as a small perturbation of the mentioned integrable system described by Kolmogorov-Arnold-Moser theory. The applicability of this approximation is discussed and illustrated using the Poincar & eacute; cross-section method. We present results of numerical simulations illustrating the trapping and confinement of a polar molecule in the trap.