Optical Control of the Refractive Index of a Single Atom

We experimentally demonstrate the elementary case of electromagnetically induced transparency with a single atom inside an optical cavity probed by a weak field. We observe the modification of the dispersive and absorptive properties of the atom by changing the frequency of a control light field. Moreover, a strong cooling effect has been observed at two-photon resonance, increasing the storage time of our atoms twenty-fold to about 16 seconds. Our result points towards all-optical switching with single photons.

Figure 1

Energy-level scheme of a three-level atom in free space, interacting with a strong control laser with Rabi frequency ${\Omega }_{\mathrm{con}}$ detuned by ${\Delta }_{\mathrm{con}}$ from the atomic $|g_1⟩\leftrightarrow |e⟩$ transition. The inset shows the absorption of a weak probe beam with Rabi frequency ${\Omega }_{\mathrm{p}}$ as a function of its detuning ${\Delta }_{\mathrm{p}}$ from the atomic $|g_2⟩\leftrightarrow |e⟩$ transition, highlighting the region around the state $|+⟩$, relevant for our experiment. In our measurement, we use a cavity field as a probe field.

Figure 2

(a) Schematic experimental setup. A single atom is placed between the mirrors of a high-finesse cavity and illuminated by a control laser. The transmission of a weak probe laser is detected by a single photon counting module. (b) Calculated relative cavity transmission $T/T_0$ for zero (dashed line) and one atom in state $|g_2⟩$ (coupling strength: $g/2\pi =3\mathrm{MHz}$; no EIT) inside the cavity (solid line) as a function of the detuning ${\Delta }_{\mathrm{p}\mathrm{\text{−}}\mathrm{cav}}$ of the probe laser from the resonance frequency of the empty cavity. The dispersion and absorption by the atom lead to a shift of the cavity resonance and a reduction of the maximum transmission, respectively.

Figure 3

(a) Real part (dashed line) and imaginary part (dotted line) of the linear susceptibility ${\chi }^{(1)}$ of a three-level atom inside the mode volume of a cavity as a function of the two-photon detuning $\delta$ with $({\Omega }_{\mathrm{con}},{\Delta }_{\mathrm{p}})/2\pi =(2.8,20)\mathrm{MHz}$. The dotted line corresponds to the absorption inside the highlighted region in Fig. 1. The solid line shows the relative probe laser transmission for a single atom in the weak probing limit without dephasing, obtained from a numerical solution of the master equation with $g/2\pi =3\mathrm{MHz}$. The small insets (i–vi) are calculated cavity transmission functions as in Fig. 2b for a series of fixed values of $\delta$, i.e., fixed values of ${\chi }^{(1)}(\delta )$, with $-50\mathrm{kHz}\le \delta /2\pi \le 200\mathrm{kHz}$. (b) Relative transmission of the probe laser through the cavity as a function of the two-photon detuning $\delta$, for $N=1$, 2, 3 atoms. The experimental data are shown as open circles with statistical error. The solid lines show numerical solutions of the master equation, taking AC-Stark shifts, dephasing, and the nonvanishing probe laser power into account.

Figure 4

(a) Probability of one atom to remain trapped inside the cavity (survival probability) as a function of the two-photon detuning $\delta$ for a holding time of 20 ms (squares) and 300 ms (circles). The shaded regions indicate the corresponding probabilities (top to bottom) for large two-photon detunings. (b) Survival probability of single atoms inside the cavity as a function of time. The circles show the survival probability with the control laser at two-photon resonance and the squares show the survival with the far-detuned trapping lasers switched on only. The error bars in both graphs are statistical.