Observation of atomic localization using electromagnetically induced transparency

We present a proof-of-principle experiment in which the population of an atomic level is spatially localized using the technique of electromagnetically induced transparency (EIT). The key idea is to utilize the sensitive dependence of the dark state of EIT on the intensity of the coupling laser beam. By using a sinusoidal intensity variation (standing wave), we demonstrate that the population of a specific hyperfine level can be localized much more tightly than the spatial period.

Figure 1

(a) The schematic of our experiment. The experiment is performed in a magneto-optical trap (MOT) of ultracold ${}^{87}\mathrm{Rb}$ atoms. With atoms starting in the $|F=1\rangle$ hyperfine level, we drive the atoms to the dark state with a probe laser beam and a spatially varying coupling laser beam. The spatial profile for the coupling laser is obtained by combining two identical beams at the MOT at an angle of 3 mrad, producing a vertical standing wave. The atomic localization is measured by taking fluorescence images with a CCD camera. (b) The relevant energy level diagram, with probe laser ${\mathrm{E}}_P$ and coupling laser ${\mathrm{E}}_C$. The experiment works with three parallel $m_F$ channels. (c) Transmission of a weak probe beam ($~$100 nW power) through the cloud as a function of frequency with (squares) and without (triangles) the coupling laser beam. The lines are weak-probe electromagnetically induced transparency (EIT) line-shape (solid blue) and Lorentzian (dashed red) fits to the data. We perform this measurement with Coupling Beam 1 at an intensity of 120 mW/cm${}^2$ and do not use the standing wave. The on-resonance transmission is about 70%, demonstrating reasonably good EIT.

Figure 2

Fluorescence images of the atomic cloud for (a) $I_{C_0}\simeq 22\times I_P$ and (b) $I_{C_0}\simeq 418\times I_P$. The images are obtained by fluorescing the $|F=2\rangle$ level via the cycling transition after the EIT beams are turned off. The fringes are confined to the intensity nodes of the coupling beam and become more localized as the intensity of the coupling laser increases. Panel (c) shows horizontally averaged line profiles of each fluorescence image for more direct comparison. The solid line is for the image in panel (a), and the dashed line is for the image in panel (b). The lower right diagram shows the experimental timing cycle.

Figure 3

The width of the fringes as a function of peak coupling-beam intensity for $I_P=3.9$ mW/cm${}^2$ and $I_P=15.6$ mW/cm${}^2$. The vertical scale is normalized such that one unit corresponds to a fringe width that equals half the spatial period (a sine wave). The population of $|F=2\rangle$ becomes more tightly localized to the standing wave nodes with increasing coupling-laser beam intensity. The data points are experimental observations, and the solid lines are the results of numerical simulations. See the text for a discussion of the discrepancy between the experimental data and the numerical results. The insets show the integrated probe transmission through the cloud as the intensity of the coupling beam is increased. We observe increased transmission with increasing coupling-beam intensity, demonstrating the presence of EIT.

Figure 4

Demonstration of stimulated Raman adiabatic passage (STIRAP). For this test, we initialize the atoms to level $|F=1\rangle$ and probe the population of $|F=2\rangle$ as the overlap between the EIT pulses is varied. We observe maximal population transfer to $|F=2\rangle$ when the coupling and probe pulses completely overlap. The solid line shows the result of a density matrix calculation with only one adjustable parameter.