Total and net photon number pathways to optimize molecular orientation by an ultra-short THz pulse

Molecules oriented in the laboratory frame offer many benefits for experiments to understand their complex interaction with strong laser light. One method to orient molecules under field-free conditions is to apply a short, impulsive THz pulse. There have been various proposals, such as using a pulse sequence, to enhance the degree of orientation. Yet, basic questions---such as at which time after the pulse is the orientation degree maximized and what is the optimal carrier-envelope phase (CEP)---have been addressed largely by numerical computation so that a general analytical understanding is still lacking. We attempt to address this lack by analyzing the orientation dynamics of a linear rigid molecule in terms of the interference of transition pathways labeled by the total and net numbers of THz photons absorbed and emitted. The amplitudes of these pathways are unambiguously obtained by expanding the rotational state as a perturbation series in the THz field strength and a Fourier series in the CEP. The perturbation order and the Fourier index correspond to the total and net photon numbers, respectively. We derive an expression for the optimal free-propagation time and CEP to maximize the orientation degree at the weak-field limit and predict how this optimal condition changes as the THz intensity is increased.