Subwavelength Localization of Atomic Excitation Using Electromagnetically Induced Transparency

We report an experiment in which an atomic excitation is localized to a spatial width that is a factor of 8 smaller than the wavelength of the incident light. The experiment utilizes the sensitivity of the dark state of electromagnetically induced transparency (EIT) to the intensity of the coupling laser beam. A standing-wave coupling laser with a sinusoidally varying intensity yields tightly confined Raman excitations during the EIT process. The excitations, located near the nodes of the intensity profile, have a width of 100 nm. The experiment is performed using ultracold ${}^{87}\mathrm{Rb}$ atoms trapped in an optical dipole trap, and atomic localization is achieved with EIT pulses that are approximately 100 ns long. To probe subwavelength atom localization, we have developed a technique that can measure the width of the atomic excitations with nanometer spatial resolution.

Popular Summary

Focusing light of a particular wavelength onto a spot smaller than half of the wavelength is fundamentally impossible because of the wave nature of light. This limit is called “the diffraction limit.” Using the light to “address” an atomic cloud of a size smaller than the diffraction limit would then be impossible for the same reason. In this experimental paper, we demonstrate that it is actually possible to overcome this limit to manipulate the internal states of atoms in a cloud smaller than the diffraction limit.

Our technique takes advantage of the structure of the internal states of our atoms, which are rubidium atoms. When unexcited, rubidium atoms stay in two ground states that differ only slightly in their energies. A laser beam of correct color can excite the atoms from one of the ground states to another state of much higher energy and thus becomes “absorbed” by the atoms. A very interesting phenomenon, the so-called electromagnetically induced transparency, is known to occur: When a second laser of a slightly different color (corresponding to the transition from the second ground state to the excited state) is added, the absorption of the first light is suppressed and a population transfer of the atoms from the first ground state to the second results.

The new physical insight behind our experiment is this: By manipulating when each laser is turned on and how powerful it is, we can control the population transfer of atoms between the two ground states, and how well this transfer is controlled spatially depends very sensitively on the ratio of the intensities of the two lasers—a quantity not subject to the diffraction limit. By appropriately engineering the ratio of the intensities, we have been able to achieve population transfer of atoms in “clouds” about one-eighth of the wavelength of the light used. Moreover, as direct “imaging” of such a subwavelength phenomenon is still prevented by the diffraction limit, we have devised a technique that can accurately determine the subwavelength size of the atomic cloud within which the population transfer takes place.

Our technique could lead to progress toward atomic manipulation and imaging with better spatial resolutions.

Figure 1

(a) Three-level $\Lambda$ scheme for driving the atoms to a dark state and observing EIT. With atoms starting in the ground state $|1⟩$, the dark state can be prepared using a counterintuitive pulse sequence; i.e., ${\Omega }_C$ should be turned on before ${\Omega }_P$. (b) Spatial localization of excitation using the dark state. Because of the sinusoidal intensity profile of the coupling laser (standing wave), the population transfer to state $|2⟩$ is localized to regions near the intensity nodes. The width of the localized regions is controlled by the ratio of the intensities of the probe and coupling laser beams.

Figure 2

(a) The top view of our ultrahigh vacuum chamber. The probe and the coupling laser beams propagate at a slight angle to the dipole-trapping beam direction. The coupling laser standing wave is formed using a counterpropagating beam pair. The blow-away beam, ${\Omega }_{\mathrm{blow}\mathrm{\text{−}}\mathrm{away}}$, removes from the trap the atoms that have been transferred to the $F=2$ level. This beam is required for the localization measurement protocol as described in the text. (b) A photograph of the atoms trapped in the MOT. (c) The fluorescence image of the atoms trapped in the dipole trap.

Figure 3

(a) Energy-level schematic. We set up an EIT $\Lambda$ scheme in ${}^{87}\mathrm{Rb}$ using $F=1\to F^{\prime }=2$ and $F=2\to F^{\prime }=2$ transitions in the ${\mathrm{D}}_2$ line, and we address these transitions with the probe and coupling laser beams, respectively. We start the experiment by pumping atoms to the $F=1$ level, and the experiment works in three parallel $m_F$ channels. (b) The transmission of a weak focused probe laser through the atoms in the dipole trap as a function of frequency. We observe good EIT, with a transparency width of 0.5 MHz.

Figure 4

The population transfer to the $F=2$ level (i.e., $|⟨\psi |F=2⟩{|}^2$) as a function of the time delay between the probe and the coupling laser beams. The zero time delay point corresponds to overlapping the probe and coupling lasers, with both beams turning off simultaneously. The solid line is a numerical simulation of the density matrix with a single adjustable parameter. See text for details.

Figure 5

The timing protocol for the localization experiment. In order to resolve nanometer spatial scales, we use two EIT pulses separated by $\tau$. The standing wave for the coupling laser is shifted to a different location between the two pulses. This shift is accomplished by setting the frequencies of the two counterpropagating beams to be slightly different. We obtain localization information through correlation measurements by scanning the spatial shift and recording the number of atoms that remain in the trap.

Figure 6

The normalized number of atoms that remain in the trap as a function of the scanning distance of the standing wave. For these data, the power of the probe beam is held at a constant value of 5 mW. The coupling laser power changes from 3 mW to 14 mW for part (a), and 3 mW to 30 mW for part (b). The solid lines are the results of numerical simulations, where we solve the density matrix equations at each point along the spatial profile of the standing wave. The simulations also take into account the diffusion of the atoms due to their finite temperature.

Figure 7

The inferred population transfer from $F=1$ to $F=2$ along two cycles of the standing wave for the conditions of the experiment of Fig. 6b. This transfer curve is the result of the same simulation that produces good agreement with the experimental data of Fig. 6b. The inferred width of the transfer is 100 nm, which is a factor of 8 smaller than the wavelength of the EIT laser beams.