Figure 1

(Color online) (a) Four-level system. ${\gamma }_3\left({\gamma }_4\right)$ is the spontaneous decay rate $({\gamma }_3\approx {\gamma }_4=2\pi \times 5.4\times {10}^6{\mathrm{s}}^{-1})$. Interference occurs between (b) three-photon excitation ∣1⟩-∣3⟩-∣2⟩-∣4⟩ and (c) one-photon excitation ∣1⟩-∣4⟩. The interference between three-photon excitation ∣1⟩-∣4⟩-∣2⟩-∣3⟩ and one-photon excitation ∣1⟩-∣3⟩ is not drawn here.Reuse & Permissions

Figure 2

(Color online) (a) Calculated probe transmission vs ${\Delta }_p$ without the control laser. (b) Calculated probe transmission vs ${\Delta }_p={\Delta }_c$ with ${\Omega }_c\left(0\right)={\Omega }_p\left(0\right)$. The absorption is suppressed by destructive interference at ${\Delta }_p=0$ and enhanced by constructive interference at ${\Delta }_p=\pm \Omega$. (c) Calculated probe absorption vs ${\Delta }_p={\Delta }_c$ with ${\Omega }_c\left(0\right)=-{\Omega }_p\left(0\right)$. The absorption is enhanced by constructive interference at ${\Delta }_p=0$ and suppressed by destructive interference at ${\Delta }_p=\pm \Omega$. The parameters are ${\Omega }_1={\Omega }_2={\gamma }_3,{\gamma }_3={\gamma }_4,{\gamma }_2=0.02{\gamma }_3,{\Delta }_1={\Delta }_2=0$, and $K_{13}\ell ∕{\gamma }_3=K_{14}\ell ∕{\gamma }_4=1$.Reuse & Permissions

Figure 3

(Color online) (a) Simplified diagram of the experimental setup with two frequency modulated lasers and the coupled four-level ${}^{85}\mathrm{Rb}$ system. (b) Simplified diagram of the experimental setup used for measurements of the light transmission vs the phase variation of the control field. AOM: acousto-optic modulator; EOM: electro-optic modulator; PMF: polarization maintaining fiber; $\lambda ∕4$: quarter-wave plate; DL: extended-cavity diode laser; M: mirror; D: photodetector.Reuse & Permissions

Figure 4

(Color online) Measured probe transmission [(a) and (c)] and measured fluorescence intensity [(b) and (d)] vs the detuning ${\Delta }_c={\Delta }_p$. The solid (dashed) lines are experimental data (calculations). In (a) and (b), the weak laser is not frequency modulated (no control field component). In (c) and (d), the weak laser is frequency modulated to produce two sidebands used as the probe and control fields, and the absorption peaks at ${\Delta }_p=0$ in (a) and (b) are suppressed by the destructive interference. The experimental parameters are ${\Omega }_1∕\left(2\pi \right)\approx {\Omega }_2∕\left(2\pi \right)\approx 4\mathrm{MHz},{\Omega }_p∕\left(2\pi \right)\approx {\Omega }_c∕\left(2\pi \right)\approx 0.2\mathrm{MHz}$, and ${\Delta }_1={\Delta }_2=0$. The fitting parameters are ${\gamma }_2\approx 0.02{\gamma }_3,K_{13}\ell ∕{\gamma }_3=K_{14}\ell ∕{\gamma }_4=0.8$.Reuse & Permissions

Figure 5

(Color online) Transmission of the control and the probe fields vs the phase variation of the control field. The dots are experimental data and the solid lines are calculations with the adiabatic phase change. Left panel: ${\Phi }_c=\pi \cos \left(2\pi ft\right)+{\phi }_0$ ($f=2.3\mathrm{KHz}$ and ${\phi }_0$ is set by the dc offset voltage). Right panel: square-wave shift of ${\Phi }_c$ (between 0 and $\pi$) at $f=2.3\mathrm{KHz}$. (a) and $\left({\mathrm{a}}^{\prime }\right)$: the light transmission at ${\Delta }_c={\Delta }_p\approx 0$; (b) and $\left({\mathrm{b}}^{\prime }\right)$: the light transmission at ${\Delta }_c={\Delta }_p\approx \Omega$; (c) and $\left({\mathrm{c}}^{\prime }\right)$: the control-laser phase ${\varphi }_c$ vs time. ${\Omega }_1∕\left(2\pi \right)\approx {\Omega }_2∕\left(2\pi \right)\approx 4.5\mathrm{MHz}$, and the other parameters are the same as those in Fig. 4.Reuse & Permissions