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X iv :2 10 5. 13 69 0v 1 [ qu an tph ] 2 8 M ay 2 02 1 Optimal three-state field-free molecular orientation with terahertz pulses Qian-Qian Hong, Li-Bao Fan, Chuan-Cun Shu, ∗ and Niels E. Henriksen Hunan Key Laboratory of Super-Microstructure and Ultrafast Process, School of Physics and Electronics, Central South University, Changsha 410083, China Department of Chemistry, Technical University of Denmark, Building 207, DK-2800 Kgs. Lyngby, Denmark Abstract We present a combined analytical and numerical investigation to show how an optimal control field can be designed to generate maximum field-free orientation of molecules for three populated rotational states. Based on a model involving pure rotational ladder-climbing excitation between rotational states, a set of optimal amplitude and phase conditions are analytically derived for the applied control fields. The maximum degree of orientation can be achieved when the field satisfies amplitude and phase conditions at the two transition frequencies. Multiple optimal solutions exist and to examine these conditions, we devise a quantum coherent control scheme using two terahertz pulses and successfully apply it to the linear polar molecule HCN at ultracold temperature. The sensitivity of both populations and phases of rotational states to control field parameters, i.e., the detuning, bandwidth, and time delay, is analyzed for understanding the optimal orientation mechanism. This work thus examines the frequency domain landscape belonging to optimal pulses.