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arXiv:quant-ph/0606145 · Physical Review A

Atom lithography with near-resonant standing waves

R. Arun, Offir Cohen, Ilya Sh. Averbukh

Published Jun 9, 2010• 4 citations
arXivHTMLPDF

Abstract

We study the optimal focusing of two-level atoms with a near-resonant standing wave light, using both classical and quantum treatments of the problem in the thin- and thick-lens regimes. It is found that the near-resonant standing wave focuses the atoms with a reduced background in comparison with far-detuned light fields. For some parameters, the quantum atomic distribution shows even better localization than the classical one. Spontaneous emission effects are included via the technique of quantum Monte Carlo wave function simulations. We investigate the extent to which nonadiabatic and spontaneous emission effects limit the achievable minimal size of the deposited structures.

DOI
10.1103/physreva.81.063809

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We studied the focusing of atoms by multiple layers of standing light waves in the context of atom lithography. In particular, atomic localization by a double-layer light mask is examined using the optimal squeezing approach. Operation of the focusing setup is analyzed both in the paraxial approximation and in the regime of nonlinear spatial squeezing for the thin-thin, as well as thin-thick, atom lens combinations. It is shown that the optimized double light mask may considerably reduce the imaging problems, improve the quality of focusing, and enhance the contrast ratio of the deposited structures.

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The focusing of atoms after interacting with both far-detuned and resonant standing wave fields in the thin-lens regime is considered. Exact quantum expressions for the Fourier components of the density (that include all spherical aberration) are used to study the focusing numerically. The following lens parameters and density profiles are calculated as functions of the pulsed field area $\ensuremath{\theta}:$ the position of the focal plane, peak atomic density, atomic density pattern at the focus, focal spot size, depth of focus, and background density. The lens parameters are compared to asymptotic, analytical results derived from a scalar diffraction theory for which spherical aberration is small but non-negligible $(\ensuremath{\theta}\ensuremath{\gg}1).$ Within the diffraction theory analytical expressions show that the focused atoms in the far-detuned case have an approximately constant background density $0.5(1\ensuremath{-}0.635{\ensuremath{\theta}}^{\ensuremath{-}1/2})$ while the peak density behaves as $3.83{\ensuremath{\theta}}^{1/2},$ the focal distance as ${\ensuremath{\theta}}^{\ensuremath{-}1}(1+1.27{\ensuremath{\theta}}^{\ensuremath{-}1/2})$ ${L}_{T}/2\ensuremath{\pi},$ the depth of focus as ${0.304L}_{T}{\ensuremath{\theta}}^{\ensuremath{-}3/2},$ and the focal spot size $0.0592\ensuremath{\lambda}{\ensuremath{\theta}}^{\ensuremath{-}3/4},$ where ${L}_{T}$ is the Talbot distance and \ensuremath{\lambda} is the wavelength of the light. Focusing by the resonant standing wave field leads to a new effect, a Rabi-like oscillation of the atom density. For the far-detuned lens, chromatic aberration is studied quantitatively with the exact Fourier results. Similarly, the degradation of the focus that results from angular divergence in beams or thermal velocity distributions in traps is studied quantitatively with the exact Fourier method and understood analytically using the asymptotic results. Overall, we show that strong thin-lens focusing is possible with modest laser powers and with currently achievable atomic beam characteristics.

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Atom lithography is a technique to structure layers of atoms during deposition, using interactions of near-resonant light fields with neutral atoms. The basic scheme uses a standing wave light field, aligned just above a substrate, while a beam of atoms impinges perpendicularly on the standing wave light field. The interaction of the light field and the atoms focuses the atoms towards the crests or troughs of the standing wave intensity, dependent on the tuning of the light field. The focused atoms are subsequently deposited on the substrate, resulting in an array of lines, whose periodicity is determined by the wavelength of the light field. The standing wave light field can therefore be seen as an array of lenses, focusing the atom beam into an array of lines. The first experiments on atom lithography were performed in the 1990s with sodium and chromium. 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We start from the intensity distribution of a standing wave (SW) laser field and deduce the classical equation of atoraic motion. The image distortion is analyzed using transfer function approach. Atomic flux density distribution as a function of propagation distance is calculated based on Monte-Carlo scheme and trajectory tracing method. Simulation results have shown that source imperfection, especially beam spread, plays an important role in broadening the feature width, and the focus depth of atom lens for real atomic source is longer than that for perfect source. The ideal focal plane can be easily determined by the variation of atomic density at the minimal potential of the laser field as a function of traveling distance.

Chinese Optics Letters•Jan 1, 2004•0 citations
We study the optimal focusing of two-level atoms with a near-resonant standing wave light, using both classical and quantum treatments of the problem in the thin- and thick-lens regimes. It is found that the near-resonant standing wave focuses the atoms with a reduced background in comparison with far-detuned light fields. For some parameters, the quantum atomic distribution shows even better localization than the classical one. Spontaneous emission effects are included via the technique of quantum Monte Carlo wave function simulations. We investigate the extent to which nonadiabatic and spontaneous emission effects limit the achievable minimal size of the deposited structures.
We studied the focusing of atoms by multiple layers of standing light waves in the context of atom lithography. In particular, atomic localization by a double-layer light mask is examined using the optimal squeezing approach. Operation of the focusing setup is analyzed both in the paraxial approximation and in the regime of nonlinear spatial squeezing for the thin-thin, as well as thin-thick, atom lens combinations. It is shown that the optimized double light mask may considerably reduce the imaging problems, improve the quality of focusing, and enhance the contrast ratio of the deposited structures.
The focusing of atoms after interacting with both far-detuned and resonant standing wave fields in the thin-lens regime is considered. Exact quantum expressions for the Fourier components of the density (that include all spherical aberration) are used to study the focusing numerically. The following lens parameters and density profiles are calculated as functions of the pulsed field area $\ensuremath{\theta}:$ the position of the focal plane, peak atomic density, atomic density pattern at the focus, focal spot size, depth of focus, and background density. The lens parameters are compared to asymptotic, analytical results derived from a scalar diffraction theory for which spherical aberration is small but non-negligible $(\ensuremath{\theta}\ensuremath{\gg}1).$ Within the diffraction theory analytical expressions show that the focused atoms in the far-detuned case have an approximately constant background density $0.5(1\ensuremath{-}0.635{\ensuremath{\theta}}^{\ensuremath{-}1/2})$ while the peak density behaves as $3.83{\ensuremath{\theta}}^{1/2},$ the focal distance as ${\ensuremath{\theta}}^{\ensuremath{-}1}(1+1.27{\ensuremath{\theta}}^{\ensuremath{-}1/2})$ ${L}_{T}/2\ensuremath{\pi},$ the depth of focus as ${0.304L}_{T}{\ensuremath{\theta}}^{\ensuremath{-}3/2},$ and the focal spot size $0.0592\ensuremath{\lambda}{\ensuremath{\theta}}^{\ensuremath{-}3/4},$ where LT{L}_{T}LT​ is the Talbot distance and \ensuremath{\lambda} is the wavelength of the light. Focusing by the resonant standing wave field leads to a new effect, a Rabi-like oscillation of the atom density. For the far-detuned lens, chromatic aberration is studied quantitatively with the exact Fourier results. Similarly, the degradation of the focus that results from angular divergence in beams or thermal velocity distributions in traps is studied quantitatively with the exact Fourier method and understood analytically using the asymptotic results. Overall, we show that strong thin-lens focusing is possible with modest laser powers and with currently achievable atomic beam characteristics.
We investigate the focusing of three-level atoms with a bichromatic standing wave laser field, using both classical and quantum treatments of the problem. We find that, for the appropriate ratio of detunings to Rabi frequencies, the atoms will experience a periodic potential which is close to harmonic across half an optical wavelength. The field thus becomes equivalent to a periodic array of microlenses, which could be utilized to deposit lines of atoms upon a substrate. We consider and compare two regimes, differentiated by the interaction time of the atoms in the optical field. The first case considered, the Raman-Nath regime, is analogous to the thin lens regime in classical optics. The second case treats the transverse atomic motion within the light field, and investigates the distribution of atoms upon a substrate placed within the field. We investigate the extent to which this case can be modeled classically. \textcopyright{} 1996 The American Physical Society.
Atom lithography is a technique to structure layers of atoms during deposition, using interactions of near-resonant light fields with neutral atoms. The basic scheme uses a standing wave light field, aligned just above a substrate, while a beam of atoms impinges perpendicularly on the standing wave light field. The interaction of the light field and the atoms focuses the atoms towards the crests or troughs of the standing wave intensity, dependent on the tuning of the light field. The focused atoms are subsequently deposited on the substrate, resulting in an array of lines, whose periodicity is determined by the wavelength of the light field. The standing wave light field can therefore be seen as an array of lenses, focusing the atom beam into an array of lines. The first experiments on atom lithography were performed in the 1990s with sodium and chromium. In this thesis experiments with iron are described, which is a magnetic element and thus allows for the creation of magnetic nanostructures. To focus atom beams into structures using atom lithography, well-colimated atom beams are required. The most common technique to create collimated atom beams is transverse laser cooling, but iron has no closed optical transition suitable for laser cooling. Fortunately Smeets and Te Sligte found that even then atom lithography of iron is possible. If the standing wave light field is considered to be an array of lenses, the focusing of the atom beam on a single lens is determined by the local collimation of the atom beam at that position. This local collimation is determined by the geometry of the beam source and the distance of the beam source to the standing wave lens. Using a small beam source (e.g. 1 mm diameter) positioned far from the standing wave (e.g. 1 m), the geometrically collimated atom beam is suitable for atom lithography. Chapter 3 shows what the implications of geometric collimation are on the structure formation in atom lithography. The geometric effects that locally collimate the atom beam on the sample also introduce local offset angles of the atom beam with respect to the focusing light field. Structure formation has been observed with lines of up to 7 nm high on a background layer of 15 nm average height, over areas of up to 400 µm × 6 mm. This indicates that the offset angles can vary over an 8 mrad range, which is more than an order of magnitude larger than the local angle of collimation. The offset angle influence the local geometry of the deposited structures: an increasing offset angle decreases the local line height, increases the width and creates a skewness in the local line shape. The local geometry of the lines has been modelled with a Monte Carlo particle tracking model and the results were compared to experiments. It was found that the highest and narrowest lines suffer from significant broadening due to surface diffusion in experiments, limiting the achievable structure width of iron on SiOx samples to about 80 nm. We have also found that in atom lithography without laser cooling, each standing wave lens is effectively imaging the source geometry onto the substrate. We therefore propose using structured atom beam sources to image more complex patterns on sub-wavelength scales in a parallel way. The reason to use iron in atom lithography, is the option to create magnetic nanostructures. However, in previous experiments no clear magnetic signature of the atom lithographic structuring of iron was found. Therefore in Chapter 4 firstly the magnetic properties of unstructured layers of iron (Fe), nickel (Ni) and FexNi1-x are investigated. These layers are all ferromagnetic, but with a reduced magnetic moment compared to bulk values due to contaminations and crystal growth effects. As a reference for periodic atom lithography structures, periodic line structures are created with interference lithography in a polymer layer and onto these structures thin layers of FexNi1-x are shadow deposited, thereby creating a layer periodically modulated in both height and elemental composition. This periodic modulation in composition has been observed with SEM-EDX on sub-micron scales. The structures showed a clear magnetic anisotropy with an easy axis along the direction of the lines, in accordance with expectations. In Chapter 5, the magnetic properties of atom lithographic iron line structures are presented. Using MOKE microscopy, direct comparison of structured and unstructured parts of a sample is possible, which allows for the observation of clear magnetic signatures due to the atom lithographic structuring. In layers of an average thickness of about 15 nm, no anisotropy is induced by the line structures, while a magnetic easy axis along the direction of the lines is expected. The line structures introduce an isotropic increase in the coercivity of the layers, indicating that the line structures can be considered as isotropic corrugations instead of directional line structures. For layers of 30 nm average thickness and thus higher line structures, a clear magnetic anisotropy is observed for the highest line structures. This anisotropy can be seen as a magnetic easy axis along the direction of the lines, as expected for line structures. However, we also observe a sharp increase in coercivity for applied fields perpendicular to the lines. This phenomenon is intriguing and may be explained by a pinning of head-to-head domain walls along the direction of the lines. In Chapter 5, we also report on the first results of co-deposition of FexNi1-x, where the Fe is structured into lines using atom lithography, while the Ni is deposited uniformly, thereby creating an alloy of modulating composition. Magnetic analysis of these structures indicates that these structures are anisotropic, both the coercivity and the shape of domain walls is dependent on the angle of the applied field relative to the line structures. Finally in Chapter 6, we investigate the possibilities to focus a thermal beam of atoms into a single 100 nm spot using light fields, thereby creating a nanopencil suitable for deposition of nanostructures. A Monte Carlo particle tracking program was developed to model the all optical focusing or funneling of 10 µm sized atom beams to a 100 nm spot. This model included effects of initial beam divergence, magnetic substructure, laser cooling, and spontaneous as well as stimulated diffusion and it was applied to a number of promising light field configurations. The best results obtained for experimentally realistic settings are a beam focused to a full width at half maximum of FWHM = 0.55 µm in a blue detuned hollow beam where atoms are focused towards the dark center, or a FWHM = 0.31 µm in a red detuned axicon light field, where atoms are focused towards the maximum intensity at the heart line. However, in the latter case the focused beam has a flux only 25 times larger than the background flux, which is unpractical for applications. The limiting factors of all schemes are heating due to stimulated diffusion and the limited interaction time available for a thermal beam of atoms. A nanopencil could be possible if it were based on the focussing of a slow and / or monochromatic atom beam, but this would seriously complicate the practical application of such a device.
We start from the intensity distribution of a standing wave (SW) laser field and deduce the classical equation of atomic motion. The image distortion is analyzed using transfer function approach. Atomic flux density distribution as a function of propagation distance is calculated based on Monte-Carlo scheme and trajectory tracing method. Simulation results have shown that source imperfection, especially beam spread, plays an important role in broadening the feature width, and the focus depth of atom lens for real atomic source is longer than that for perfect source. The ideal focal plane can be easily determined by the variation of atomic density at the minimal potential of the laser field as a function of traveling distance.
We start from the intensity distribution of a standing wave (SW) laser field and deduce the classical equation of atoraic motion. The image distortion is analyzed using transfer function approach. Atomic flux density distribution as a function of propagation distance is calculated based on Monte-Carlo scheme and trajectory tracing method. Simulation results have shown that source imperfection, especially beam spread, plays an important role in broadening the feature width, and the focus depth of atom lens for real atomic source is longer than that for perfect source. The ideal focal plane can be easily determined by the variation of atomic density at the minimal potential of the laser field as a function of traveling distance.