Autler–Townes spectroscopy of high-lying state by phase conjugate six-wave mixing**Project supported by the National Basic Research Program of China (Grant No. 2013CB922002), the National Natural Science Foundation of China (Grant Nos. 11274376 and 61308011), and the National High Technology Research and Development Program of China (Grant No. 2011AA120102).

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An Autler–Townes (AT) spectroscopy based on phase conjugate six-wave mixing (SWM) is proposed to detect AT doublet of high-lying state in a Doppler-broadened cascade four-level system. It is found that the SWM spectrum is dependent strongly on the ratios between the magnitudes of the wave vectors. We discuss how the Doppler broadening affects the SWM spectrum from a time-domain viewpoint and find that, due the atomic motion, the atomic polarizations acquire different phases for atoms with different velocities as time evolves. The Doppler free SWM spectrum can be obtained only when the atomic polarization can be rephasing again at certain time after the interactions of all the incident fields.