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arXiv:0811.3409 · Physical Review A

Coherent patterning of matter waves with subwavelength localization

J. Mompart, V. Ahufinger, G. Birkl

Published May 28, 2009• 65 citations
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Abstract

We propose the subwavelength localization via adiabatic passage (SLAP) technique to coherently achieve state-selective patterning of matter waves well beyond the diffraction limit. The SLAP technique consists in coupling two partially overlapping and spatially structured laser fields to three internal levels of the matter wave yielding state-selective localization at those positions where the adiabatic passage process does not occur. We show that by means of this technique matter wave localization down to the single nanometer scale can be achieved. We analyze in detail the potential implementation of the SLAP technique for nanolithography with an atomic beam of metastable ${\text{Ne}}^{\ensuremath{\ast}}$ and for coherent patterning of a two-component $^{87}\text{R}\text{b}$ Bose-Einstein condensate.

DOI
10.1103/physreva.79.053638

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We propose the subwavelength localization via adiabatic passage (SLAP) technique to coherently achieve state-selective patterning of matter waves well beyond the diffraction limit. The SLAP technique consists in coupling two partially overlapping and spatially structured laser fields to three internal levels of the matter wave yielding state-selective localization at those positions where the adiabatic passage process does not occur. We show that by means of this technique matter wave localization down to the single nanometer scale can be achieved. We analyze in detail the potential implementation of the SLAP technique for nanolithography with an atomic beam of metastable Ne\ensuremath∗{\text{Ne}}^{\ensuremath{\ast}}Ne\ensuremath∗ and for coherent patterning of a two-component 87Rb^{87}\text{R}\text{b}87Rb Bose-Einstein condensate.
In this work, the authors proposed a novel state selective atom localization and patterning scheme named subwavelength localization via adiabatic passage (SLAP) that consists in coupling two partially overlapping and spatially structured laser fields to three internal levels of the matter wave yielding state-selective localization at those positions where the adiabatic passage process does not occur. Compared to the coherent population trapping (CPT) based techniques, the SLAP technique presents several important advantages. The paper describes the SLAP technique to coherently achieve state-selective patterning and addressing of matter waves and analyze its potential implementation for nanolithography with an atomic beam of metastable Ne and for coherent patterning of a two-component87Rb BEC.
We propose a single-site addressing implementation based on the subwavelength localization via adiabatic passage (SLAP) technique. We consider a sample of ultracold neutral atoms loaded into a two-dimensional optical lattice with one atom per site. Each atom is modeled by a three-level $\ensuremath{\Lambda}$ system in interaction with a pump and a Stokes laser pulse. Using a pump field with a node in its spatial profile, the atoms at all sites are transferred from one ground state of the system to the other via stimulated Raman adiabatic passage, except the one at the position of the node that remains in the initial ground state. This technique allows for the preparation, manipulation, and detection of atoms with a spatial resolution better than the diffraction limit, which either relaxes the requirements on the optical setup used or extends the achievable spatial resolution to lattice spacings smaller than accessible to date. In comparison to techniques based on coherent population trapping, SLAP gives a higher addressing resolution and has additional advantages such as robustness against parameter variations, coherence of the transfer process, and the absence of photon induced recoil. Additionally, the advantages of our proposal with respect to adiabatic spin-flip techniques are highlighted. Analytic expressions for the achievable addressing resolution and efficiency are derived and compared to numerical simulations for 87{}^{87}87Rb atoms in state-of-the-art optical lattices.
We consider a method of sub-wavelength superlocalization and patterning of atomic matter waves via a two dimensional stimulated Raman adiabatic passage (2D STIRAP) process. An atom initially prepared in its ground level interacts with a doughnut-shaped optical vortex pump beam and a traveling wave Stokes laser beam with a constant (top-hat) intensity profile in space. The beams are sent in a counter-intuitive temporal sequence, in which the Stokes pulse precedes the pump pulse. The atoms interacting with both the traveling wave and the vortex beam are transferred to a final state through the 2D STIRAP, while those located at the core of the vortex beam remain in the initial state, creating a super-narrow nanometer scale atomic spot in the spatial distribution of ground state atoms. By numerical simulations we show that the 2D STIRAP approach outperforms the established method of coherent population trapping, yielding much stronger confinement of atomic excitation. Numerical simulations of the Gross-Pitaevskii equation show that using such a method one can create 2D bright and dark solitonic structures in trapped Bose-Einstein condensates (BECs). The method allows one to circumvent the restriction set by the diffraction limit inherent to conventional methods for formation of localized solitons, with a full control over the position and size of nanometer resolution defects.
We propose the use of the subwavelength localization via adiabatic passage technique for fluorescence microscopy with nanoscale resolution in the far field. This technique uses a Λ-type medium coherently coupled to two laser pulses: the pump, with a node in its spatial profile, and the Stokes. The population of the Λ system is adiabatically transferred from one ground state to the other except at the node position, yielding a narrow population peak. This coherent localization allows fluorescence imaging with nanometer lateral resolution. We derive an analytical expression to asses the resolution and perform a comparison with the coherent population trapping and the stimulated-emission-depletion techniques.
We propose a new method based on the STIRAP technique to obtain state selective atom localization below the diffraction limit. Three-level atoms in a lambda configuration interact with a travelling wave beam and a standing wave field coupled to adjacent transitions under STIRAP conditions. In this configuration, atoms at the nodes of the standing wave do not interact with the light fields and become localized in regions in the nanoscale regime. The absence of interaction of the localized atoms with the fields guarantees the validity of the Raman-Nath approximation. Applications to Bose Einstein condensates, possible due to the full coherence of the STIRAP process, have been explored.
We describe a technique for creating superpositions of degenerate quantum states, such as are needed for beam splitters used in matter-wave optics, by manipulating the timing of three orthogonally polarized laser beams through which moving atoms (or molecules) pass; motion across the laser beams produces pulses in the atomic rest frame. As illustrated with representative simulations for transitions in metastable neon, a single pass through three overlapping laser beams can produce superpositions (with preselected phase) of atomic beams differing by transverse momentum corresponding to the momentum of four photons. Like the two-photon momentum transfer of the tripod linkage pattern which it extends, the method relies on controlled adiabatic time evolution in the Hilbert subspace of two degenerate dark states. It is thus a generalization to multiple dark states (and larger transfers of linear momentum to the atomic beam) of the single dark state occurring with the stimulated Raman adiabatic passage (STIRAP) technique, and therefore it is potentially insensitive to decoherence due to spontaneous emission. By extending the tripod-linkage system to more numerous degenerate states, the technique not only increases the atomic beam deflections but, as we demonstrate, allows control over the superposition phase and amplitudes. LIke other techniques based on adiabatic time evolution, the technique is robust with respect to variations of the intensity, timing, and other characteristics of the laser fields. Unlike STIRAP, the same robust partial population transfer occurs for opposite timings of the pulse sequence, as is needed for such procedures as Hadamard gates.