Figure 1

(a) Experimental setup. PBS: polarizing beam-splitter, $\lambda /2$: half-wave plate. (b) Four-level tripod system with perpendicularly polarized probe (blue dashed line) and coupling (red continuous line) beams. $\theta$ is the angle between the probe polarization and the $Z$ axis. The $Z$ axis is fixed by the direction of the magnetic field $B$ so that $\theta =0$ gives a $\pi$ probe and a $\sigma$ coupling. ${\Delta }_{\mathrm{Z}}$ is the Zeeman splitting.Reuse & Permissions

Figure 2

(a) Experimental result of transmission versus probe-coupling detuning obtained for $\theta ={30}^{\circ }$, with magnetic field $=$ 30 mG, and coupling power $=$ 4 mW. The Zeeman shift ${\Delta }_{\mathrm{Z}}$ is 84 kHz. Four peaks can be attributed to EIT as shown in subfigures (1), (2), and (3), where the coupling beam (red continuous line) has a frequency equal to the atomic transition $m=0\to m=0$ frequency. The small peak labeled 1 on the left is given by the $\Lambda$ system drawn in subfigure (1) below, the second peak labeled 2 is due to two different $\Lambda$ systems drawn in subfigure (2). The two peaks on the right are due to symmetrical $\Lambda$ systems. As shown in subfigure (3), the central resonance happens for coupling and probe beams of the same frequency, which does not correspond to any Raman resonance in the $\Lambda$ subsystems of the tripod. (b) Amplitudes of the oscillating parts of the populations (at a fixed time) versus $\delta$, with the same Zeeman shift, a coupling Rabi frequency of ${\Omega }_{\mathrm{C}}/2\pi =6$ MHz (corresponding to a coupling power of 4 mW), and a Raman coherence decay rate of ${\Gamma }_{\mathrm{R}}/2\pi =3$ kHz. $\Delta {\rho }_{g_{+}{g}_{+}}\equiv 2\text{Re}{\left({\mathbf{R}}_{+1}\right)}_{31}{e}^{-i\delta t}$ and $\Delta {\rho }_{g_{-}{g}_{-}}\equiv 2\text{Re}{\left({\mathbf{R}}_{+1}\right)}_{11}{e}^{-i\delta t}$ (blue and green dashed lines) are in phase and oscillate in antiphase with $\Delta {\rho }_{g_0{g}_0}\equiv 2\text{Re}{\left({\mathbf{R}}_{+1}\right)}_{21}{e}^{-i\delta t}$ (black dotted line), while the excited-state population $\Delta {\rho }_{ee}$ (red continuous line) does not exhibit any variation.Reuse & Permissions

Figure 3

Numerically calculated transmission profiles versus probe-coupling detuning with (a) $\theta ={30}^{\circ }$ and (b) $\theta ={60}^{\circ }$ for ${\overline{\Gamma }}_{\mathrm{R}}\equiv {\Gamma }_{\mathrm{R}}/2\pi =3$ kHz (black squares) and ${\Gamma }_{\mathrm{R}}/2\pi =12$ kHz (red dots). Other parameters used are Zeeman splitting ${\Delta }_{\mathrm{Z}}/2\pi =84$ kHz (corresponding to a magnetic field, $B=30$ mG) and coupling Rabi frequency ${\overline{\Omega }}_{\mathrm{C}}\equiv {\Omega }_{\mathrm{C}}/2\pi =6$ MHz (corresponding to a coupling power of 4 mW).Reuse & Permissions

Figure 4

Transmission profiles versus probe-coupling detuning for the double tripod system. (a)–(d) Experimentally measured with magnetic fields at 0 mG (black squares), 10 mG (red dots), and 30 mG (blue triangles), at coupling power $=$ 4 mW. (e)–(h) Numerically calculated with Zeeman splitting ${\overline{\Delta }}_{\mathrm{Z}}\equiv {\Delta }_{\mathrm{Z}}/2\pi =0$ kHz (black squares), ${\Delta }_{\mathrm{Z}}/2\pi =28$ kHz (red dots), and ${\Delta }_{\mathrm{Z}}/2\pi =84$ kHz (blue triangles), at coupling Rabi frequency ${\Omega }_{\mathrm{C}}/2\pi =6$ MHz with the Raman coherence decay rate ${\Gamma }_{\mathrm{R}}/2\pi =3$ kHz.Reuse & Permissions

Figure 5

Variation of populations, ${\rho }_{ee}$ (black squares), ${\rho }_{g_{-}{g}_{-}}$ (red dots), ${\rho }_{g_0{g}_0}$ (blue triangles), and ${\rho }_{g_{+}{g}_{+}}$ (green rhombuses), with rotation angle $\theta$ for (a) ${\overline{\Delta }}_{\mathrm{Z}}\equiv {\Delta }_{\mathrm{Z}}/2\pi =0$ ($B=0$) and (b) ${\Delta }_{\mathrm{Z}}/2\pi =84$ kHz ($B=30$ mG), with coupling Rabi frequency ${\overline{\Omega }}_{\mathrm{C}}\equiv {\Omega }_{\mathrm{C}}/2\pi =6$ MHz (corresponding to a coupling power of 4 mW) and Raman coherence decay rate ${\Gamma }_{\mathrm{R}}/2\pi =3$ kHz.Reuse & Permissions