Theoretical study of atom collision by two-nondegenerate four-wave mixing
Authors: Sun Jiang  , Chang Xiao-Yang  , Zhang Su-Heng  , Xiong Zhi-Qiang  ,   College of Physical Science and Technology, Hebei University, Baoding 071002, China
Published: December 2020

In recent years, the collisional redistribution of radiation and collision-induced broadening of Rydberg atomic spectral lines by buffer gas perturbation have aroused the renewed interest. Rydberg atoms having a large dipole moment and long lifetime can interact with each other coherently for relatively long time, which makes them a potential candidate for quantum information processing. Besides, collisional redistribution has an important potential application in laser cooling and trapping.
Based on previous experimental data, in this paper, two-nondegenerate four-wave mixing (NFWM) for studying atom collision, composed of two-photon resonant NFWM and collisional redistribution NFWM, is reported. The spectrum variation of the two-NFWM affected by the pressure, temperature, detuning and collision-broadening rate coefficient is analyzed.
The principle of two-NFWM involving three incident beams is explained as follows. Consider two-NFWM in a |0-|1-|2 cascade three-level system, where states between |0 and |1 and between |1 and |2 ightangle are coupled by resonant frequencies 1 and 2 , respectively. Beam 1 with frequency 1 propagates along the direction opposite to the direction of beam 2, beams 2 and 2' have the same frequency 2, and between their directions there exists a small angle. Assuming that 1 1 and 2 2 so that 1 drives the transition from |0 to |1 while 2 drives the transition from |1 to |2, the simultaneous interactions of atoms with beams 1 and 2 will induce atomic coherence between |0 and |2 through two-photon excitation. This coherence is probed by beam 2', and as a result a two-photon resonant NFWM signal of frequency 1 is generated in the direction almost opposite to the direction of beam 2'. To avoid strong absorption at the resonant frequency of transition from |0 to |1, here the wavelength of beam1 is detuned from the exact resonance. An atom population of level |1 caused by collisional redistribution can be induced when a certain buffer gas pressure is imposed. The collisional redistribution NFWM process also exists in this case. Beam 2 drives the transition from |1 to |2 to induce an atomic coherence which is probed by beam 2' for giving rise to an atomic population grating. A collisional redistribution NFWM signal propagating along the same direction as the two-photon resonant NFWM signal is generated when beam 1 is scattered by the grating. Much information about atomic collisions can be obtained by analyzing the two NFWM signals.
In a cascade three-level system composed of ground state, intermediate state and Rydberg state, and the two-NFWM can be used to investigate not only the broadening and shifting of the Rydberg level but also the collisional redistribution of the intermediate state. Unlike other experiments studying the pressure dependence of the longitudinal relaxation rate of atom states, this technique is a purely optical coherent means, and can measure the transverse relaxation rate 20 between Rydberg state and ground state as well as the pressure dependence of the transverse relaxation rate 21 between Rydberg state and intermediate state.