Upper bound for permanent orientation of symmetric-top molecule induced by linearly polarized electric fields

Many symmetric top molecules are among the most important polyatomic molecules. The orientation of a polyatomic molecule is a challenging task, which is at the heart of its quantum control and crucial for many subsequent applications in various fields. Most recent studies focus on the temporary orientation achieved via the quantum revivals. In this study, we reveal the underlying mechanism behind the observed permanent orientation and discuss strategies for a higher degree of permanent orientation. By a careful analysis of symmetry and unitary, it is possible to estimate an upper bound of ⟨⟨cosθ⟩⟩<(2-2)/4≈0.1464 for a molecule in its thermal equilibrium states using a linear field. We show that this bound can be reached for an oblate symmetric-top molecule in the high temperature limit. To demonstrate different possible schemes, we take CHCl₃ as an example. Simply with designed microwave fields, one can permanently orient CHCl₃ with a degree of ⟨cos θ⟩ ≈ 0.045. We show that this value can be significantly increased by adding one or more pump pulses.