Enhancement of near-resonant degenerate four-wave-mixing signals by excitation of a coupled transition

It is shown that intense collisionless Rayleigh-type extraresonant signals in degenerate four-wave mixing (DFWM) can be obtained when the $| a 〉\to | b 〉$ transition which produces the DFWM signal is coupled to another transition ($| a 〉\to | d 〉$) which is excited near-resonantly by an additional laser beam. Two effects contribute to the Rayleigh-type extraresonant signal at ${\omega }_2={\omega }_1$. The first effect is resonance-enhanced three-photon scattering (TPS), which leads to the population of state $| b 〉$ and consequently contributes a term in ${\rho }_{\mathrm{ba}}$, the off-diagonal density-matrix element, which is characterized by the linewidth ${\left(\frac{1}{T_1}\right)}_{\mathrm{ba}}$, the inverse lifetime of the state $| b 〉$. The second effect derives from the effective lifetime acquired by the ground state $| a 〉$ due to its strong coupling to state $| d 〉$. This leads to a term in ${\rho }_{\mathrm{ba}}$ characterized by a linewidth $\frac{1}{2}{\left(\frac{1}{T_1}\right)}_{\mathrm{da}}$, which is half the inverse lifetime of the state $| d 〉$. When ${\left(\frac{1}{T_1}\right)}_{\mathrm{da}}\gg {\left(\frac{1}{T_1}\right)}_{\mathrm{ba}}$, the TPS effect dominates and the extraresonant DFWM signal is narrow and intense. When ${\left(\frac{1}{T_1}\right)}_{\mathrm{da}}\simeq {\left(\frac{1}{T_1}\right)}_{\mathrm{ba}}$, the signal is less intense and interference between the two effects is evident.