Two-dimensional spectroscopy is performed on a terahertz (THz) frequency quantum cascade laser (QCL) with two broadband THz pulses. Gain switching is used to amplify the first THz pulse and the second THz pulse is used to probe the system. Fourier transforms are taken with respect to the delay time between the two THz pulses and the sampling time of the THz probe pulse. The two-dimensional spectrum consists of three peaks at (ωτ = 0, ωt = ω0), (ωτ = ω0, ωt = ω0), and (ωτ = 2ω0, ωt = ω0) where ω0 denotes the lasing frequency. The peak at ωτ = 0 represents the response of the probe to the zero-frequency (rectified) component of the instantaneous intensity and can be used to measure the gain recovery.
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