Electromagnetically induced transparency controlled by a microwave field

We have experimentally studied the propagation of two optical fields in a dense rubidium (Rb) gas in the case when an additional microwave field is coupled to the hyperfine levels of Rb atoms. The Rb energy levels form a close-$\Lambda$ three-level system coupled to the optical fields and the microwave field. It has been found that the maximum transmission of the probe field depends on the relative phase between the optical and the microwave fields. We have observed both constructive and destructive interferences in electromagnetically induced transparency. A simple theoretical model and a numerical simulation have been developed to explain the observed experimental results.

Figure 1

(Color online) Energy levels of a closed $\Lambda$ scheme three-level system. ${\Omega }_1$ and ${\Omega }_2$ are two optical fields and ${\Omega }_{\mu }$ is a microwave field.

Figure 2

(Color online) Experimental setup. EOM, electro-optic modulator; AOM, acousto-optic modulator; PD, photodiode; the oven is assembled with 1, copper tube; 2, nonmagnetic heater; 3, magnetic shield; 4, microwave cavity with antenna; 5, Rb cell. Inset (a) shows the relative frequency of the laser fields. L1 is the drive field, S1 and S2 are two sidebands generated by the EOM and S1 works as the probe field. L2 is the laser field shifted 200 MHz in frequency by the AOM. Inset (b) shows the beating signal without considering L2. Inset (c) shows the beating signals with all fields L1, L2, S1, and S2 considered.

Figure 3

(Color online) The beating signal recorded by a spectrum analyzer at the center frequency of 7.035 GHz. It represents the transmission of the probe field. (a) The enhanced transmission with the microwave field applied; (b) the transmission without the microwave field applied; (c) the suppressed transmission with the microwave field applied. The positions of the cell where (a) and (c) were taken are about 2.2 cm apart.

Figure 4

(Color online) The EIT peaks as we change the position of the cell along the propagation direction of optical fields. An EIT peak is recorded at every 3 mm we move the cell. (a) and (b) correspond to the case where the input laser fields are right and left, respectively, circularly polarized. The distance between two maxima (or minima) next to each other is about 4.4 cm.

Figure 5

(Color online) The amplitude of EIT peaks dependence on relative phase. The solid and hollow squares correspond to the cases of left and right circularly polarized input laser fields, respectively. Dash lines are fittings of the sinusoidal function.

Figure 6

(Color online) Rb level scheme. The coupling between (a) the right and (b) the left circularly polarized optical probe and drive beams and Rb levels. Near each transition, the corresponding Clebsch-Gordan factors (see Appendix ) are shown.

Figure 7

(Color online) Numerical simulation of the transmission of the probe field dependence on detuning and cell positions. In the simulation, we use ${\gamma }_{ab}=5$, ${\gamma }_{bc}={10}^{-3}$, ${\Omega }_{10}=0.1$, ${\Omega }_2=1$, ${\Omega }_{\mu }=0.02$, $\eta =0.9$, $L=2.5\text{cm}$, and $\Delta k=1.5{\text{cm}}^{-1}$.