The pulse scheme of a photon echo experiment. Three pulses with successive interpulse delays and are applied to the system. The time origin is conventionally set to the middle of the third pulse. The photon echo signal arises at times . In the 2D spectroscopy we vary the first delay to record a two-dimensional signal (in and ) for a given delay .
The time dependent three-pulse photon echo signal of a two-level system calculated for and . The relaxation and dephasing rates are and , respectively, and the duration of all three laser pulses is . Curve (a) presents the homogeneous case with all molecules having a transition frequency . Curve (b) shows the signal from an inhomogeneously broadened ensemble with the same mean frequency and a distribution width (FWHM) .
A sequence of 2D spectra for a homogeneously broadened two-level system. The population times are , 20, and ; the relaxation parameters are the same as in Fig. 2. Since the duration of the laser pulses is , the pulse overlap effects quickly disappear and the traces remain almost unaltered for , except for the absolute value of the signal which decreases for increasing . Contour lines are drawn in 10% intervals at 85%,…, 5%, 5%,…, 95% for the absorptive real parts (left column) and refractive imaginary parts (right column) of . The 100% level is determined by the highest peak value within the spectrum. Solid contour lines correspond to positive amplitudes, and dashed lines to negative amplitudes.
A sequence of 2D spectra for an inhomogeneously broadened two-level system. All other parameters are the same as in Fig. 3. The inhomogeneous broadening results in a diagonal elongation of the features.
Two-dimensional spectrum of a two-level system calculated using the stochastic scheme of Sec. VI averaging over . The comparison of the 2D traces at and reveals a considerable symmetrization of the real part of the spectrum and a change of the slope of the nodal line in the imaginary part of the spectrum caused by the loss of a system memory. The slope of the nodal line at and is represented by continuous and dashed lines, respectively.
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