Line-shape analysis of double-quantum multidimensional coherent spectra

Double-quantum two-dimensional (2D) coherent spectroscopy (MDCS) is a powerful optical method that is used to study the optical properties of atomic and complex molecular systems and semiconductor materials. Double-quantum 2D spectra and particularly the peak line shapes on the spectra can also provide information about many-body interactions. We model 2D spectra by solving the optical Bloch equations and show the effects of correlation between coupled resonances, which also explains the discrepancies between the experimental results reported by multiple groups.

Figure 1

(a) Schematic diagram of multidimensional coherent spectroscopy. In the figure the photon echo excitation sequence is displayed. Pulse $A^{*}$ creates a coherence between the ground and excited states. Pulse $B$ converts the coherence into the population state and then pulse $C$ converts it back to the coherence between the ground and excited states which emits a four-wave-mixing (FWM) signal. The signal is detected with a local oscillator pulse. $\left|g\right.〉$ and $\left|e\right.〉$ correspond to ground and excited states, respectively. (b) Magnitude of a single-quantum two-dimensional spectrum. The evolution frequency is negative to reflect the negative phase evolution during the evolution period in the photon echo excitation sequence. The black dotted line shows the diagonal line. White and red arrows indicate homogeneous and inhomogeneous linewidths. (c) Magnitude of a double-quantum two-dimensional spectrum. The peak is elongated along the diagonal line (black dotted line). ${\omega }_{\text{ref}}$ is the arbitrary optical frequency.

Figure 2

(a) Double-quantum excitation scheme. (b) Energy-level diagram of two combined two-level systems without interaction. (c) Double-sided Feynman diagrams contributing to the generation of the FWM signal. (d) Energy-level diagram of two combined two-level systems with interaction. ${\mathrm{\Delta }}_1$ and ${\mathrm{\Delta }}_2$ energy shifts due to interaction. Dotted lines show the shifted energy states. (e) Energy-level diagram of two combined V-type systems which is also represented as a superposition of states created by two-level systems (1)–(4). $\left|g\right.〉, \left|e\right.〉$, and $\left|f\right.〉$ correspond to ground, excited, and doubly excited states, respectively.

Figure 3

Simulation results. (a) $\rho =-0.9$, (b) $\rho =-0.6$, (c) $\rho =0.0$, (d) $\rho =0.6$, (e) $\rho =0.9$, (f) $\rho =0.75$, and increased decay rate. ${\omega }_{\text{ref}}$ is the arbitrary optical frequency. The color scale shows the normalized signal magnitude.