Interference effect and Autler-Townes splitting in coherent blue light generated by four-wave mixing

An unexpected interference effect between four-wave mixing excitation routes in rubidium vapor is observed using a combination of a cw diode laser and a 1-GHz femtosecond pulse train. The generated coherent blue light is analyzed by scanning the diode frequency and the repetition rate of the frequency comb. In both cases, the cw laser induces an Autler-Townes splitting, and a large separation is observed in the doublet structure due to the configuration of copropagating fields. Remarkably, by scanning the repetition rate, a narrow peak appears as a signature of the interfering pathways. A nonperturbative treatment of the Bloch equations achieves good agreement with the experimental data and demonstrates that the interfering effect appears only when both lasers are resonant with one- and two-photon transitions for the same atomic velocity group.

Figure 1

Experimental setup with relevant energy levels of ${}^{85}\mathrm{Rb}$. BS, L, M, PBS, PMT, and SAS indicate beam splitter, lens, mirror, polarizer beam-splitter, photomultiplier, and saturation absorption spectroscopy, respectively.

Figure 2

Coherent blue light intensity as a function of (a) diode frequency detuning $\left({\delta }_d/2\pi \right)$ and (b) repetition rate variation $\left(\delta f_R\right)$ for different powers of the diode laser as indicated in each curve. In (a) $f_R$ is fixed at $\sim 987.791\mathrm{MHz}$ while in (b) the diode frequency is fixed near the closed transition, and $\delta f_R=0$ for $f_R=987.749$ 886 MHz. The upper curve in (b) is a zoom of the right structure in curve (II).

Figure 3

Comparison between experimental data [(a) and (c)] and numerical calculation [(b) and (d)] for the CBL peak intensity [(a) and (b)] and the Autler-Townes (AT) splitting [(c) and (d)] as a function of the diode laser power. ${\gamma }_{22}$ is the decay rate of the $5P_{3/2}$ state.

Figure 4

Four-level theoretical model.

Figure 5

(a) ${\left|{\rho }_{14}\right|}^2$ scanning the diode laser frequency at a fixed repetition rate for three different values of detuning of the ${\omega }_m$ mode regarding the transition $\left|2\right.〉\to \left|3\right.〉$. (b) Zoom of the bottom curve in (a) showing ${\left|{\rho }_{14}\right|}^2$ for co- and counterpropagating fields configuration. (c) Theoretical results scanning the repetition rate for a fixed diode frequency. ${\left|{\rho }_{14}^{dm}\right|}^2$ is the result for the cw-fs pathway, while ${\left|{\rho }_{14}^{nm}\right|}^2$ accounts for the fs-fs pathway considering the same repetition rate of Fig. 2. The green and dashed curves are the two possible ways of adding these coherence pathways.