Quantum Features in Atomic Nanofabrication using Exactly Resonant Standing Waves

We report on the first fabrication of nanostructures with exactly resonant light revealing the quantum character of the atom-light interaction. Classically the formation of nanostructures is not expected; thus, the observed formation of complex periodic line patterns can be explained only by treating atom-light interaction and propagation of the atoms quantum mechanically. Our numerical quantum calculations are in quantitative agreement with this experimental finding. Moreover, the theory predicts that for small detunings nanostructures with $\lambda /4$ period can be produced, which beats the standard nanofabrication limit of $\lambda /2$. Our experiments confirm this prediction.

Figure 1

Experimental setup and results. (a) A collimated chromium beam impinges on a resonant standing light wave and subsequently hits a substrate. After deposition the substrate topography is analyzed with an atomic force microscope (AFM). (b) The Rabi frequency shows a spatial dependence due to the Gaussian laser beam profile along the $y$ direction. Thus each individual substrate contains the whole intensity dependence of the atom-light interaction. (c) The AFM image and (d) cross sections reveal the light intensity dependence of the formed structures. For low intensity, peculiar periodic structures with feature spacings below $\lambda /2$ are observed.

Figure 2

Dressed states description of on resonant atom-light interaction: (a) The standing light wave is formed by retroreflecting a laser beam from a mirror with reflectivity $R=94\%$ as shown in the inset. This leads to a periodic intensity distribution that is not fully modulated (depicted not to scale). Hence, the Rabi frequency is complex. The change in phase proves to be dramatic at the standing wave node, where the phase jumps by $\pi$ within few nanometers. (b) Where the phase is constant, the ground state wave packet is decomposed into two resting dressed state wave packets, whereas near the nodes this decomposition leads to two moving dressed state wave packets. Their motion is deduced from the dressed state eigenenergies, therefore a $|+⟩$-state wave packet is attracted to the node and a $|-⟩$-state wave packet to the antinode of the standing wave. As illustrated at position $x=0.75$, the motion of wave packets near the node is influenced less by the potentials and more by the phase gradient of the Rabi frequency.

Figure 3

(a) Cross sections of the calculated atomic flux at a distance of $35\mu \mathrm{m}$ behind the center of the standing wave for the indicated Rabi frequencies. For large Rabi frequencies, $\lambda /2$ period nanostructures are formed, whereas low Rabi frequencies lead to peculiar patterns with feature spacings smaller than $\lambda /2$. (b) AFM cross sections taken at different positions as indicated with solid circles in Fig. 1b corresponding to equivalent Rabi frequencies as used in the quantum simulation. The experimental findings are in excellent quantitative agreement with the simulation.

Figure 4

Comparison between nanostructures fabricated with different detunings: For $\Delta =0$, $\lambda /2$ structures are shown to illustrate the shift of $12\pm 3\mathrm{n}\mathrm{m}$ of the new feature in between. The nanostructures obtained by detuning the laser frequency $\Delta =1\Gamma$ exhibit a much smaller shift of $1\pm 4\mathrm{n}\mathrm{m}$. The observed behavior confirms the prediction of our quantum simulation and demonstrate the periodicity doubling for very near resonant standing light waves.