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arXiv:2106.13845 · Physical Review A

Focusing of Bragg-outcoupled paraxial atom lasers

R. Richberg, A. Martin

Published Sep 10, 2021• 2 citations
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Abstract

We theoretically study the focusing of a quasicontinuous atom laser beam of rubidium-85 $(^{85}\mathrm{Rb})$. A two-state model analysis based on the Gross-Pitaevskii equation is used which comprises the effects of two-body atom-atom interactions and three-body recombination losses. Utilizing optical focusing potentials such as harmonic potentials, the essential factors such as the width, peak density, and atom loss rate of the focused atom laser beam profile are investigated. Our analysis predicts that using an atom laser offers a dramatic improvement in resolutions of up to 8 nm.

DOI
10.1103/physreva.104.033314

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We theoretically study the focusing of a quasicontinuous atom laser beam of rubidium-85 (85Rb)(^{85}\mathrm{Rb})(85Rb). A two-state model analysis based on the Gross-Pitaevskii equation is used which comprises the effects of two-body atom-atom interactions and three-body recombination losses. Utilizing optical focusing potentials such as harmonic potentials, the essential factors such as the width, peak density, and atom loss rate of the focused atom laser beam profile are investigated. Our analysis predicts that using an atom laser offers a dramatic improvement in resolutions of up to 8 nm.
We theoretically investigate the optical focusing of a rubidium Bose-Einstein condensate onto a planar surface. Our analysis uses a Gaussian variational method that includes the effects of two-body atom-atom interactions and three-body recombination losses. The essential factors such as the width, peak density, and atom loss rate of the focused BEC profile on the surface are investigated and compared to Gross-Pitaevskii numerical simulations. We find a reasonable agreement in the results between our analytical approach and the numerical simulations. Our analysis predicts that condensates of 105{10}^{5}105 atoms could be focused down to $\ensuremath{\sim}$10 nm widths, potentially allowing nanometer-scale atomic deposition with peak densities greater than 105{10}^{5}105 atoms/$\ensuremath{\mu}{\mathrm{m}}^{2}$.
The focusing of a rubidium Bose–Einstein condensate via an optical lattice potential is numerically investigated. The results are compared with a classical trajectory model which underestimates the width of the focused beam. Via the inclusion of the effects of interactions into the classical trajectories model, we show that it is possible to obtain reliable estimates for the width of the focused beam when compared to numerical integration of the Gross–Pitaevskii equation. Finally, we investigate the optimal regimes for focusing and find that for a strongly interacting Bose–Einstein condensate focusing of order 20 nm may be possible.
An atom laser based on RF-outcoupling can be operated in a coherently pulsed way by using two radio frequencies. Such a two-mode atom laser can be described by coupled Gross-Pitaevskii equations which are valid for very low temperatures (T≈0). We have derived analytic expressions for the output rate and the visibility of the pulsed atomic beam in the weak coupling regime. A comparison between the analytical and numerical results shows a good agreement. This proves our assumption that the outcoupling process may be seen as the coherent outcoupling of two independent atomic beams. Though our model is only one-dimensional, we expect also a good agreement with the full 3D situation of experiment; the estimate for the value of the output rate might be only in the right order of magnitude16. Summarizing, the manipulation of trapped Bose condensates with electromagnetic waves opens a wide new area for the field of coherent atom optics.
Atom lasers based on rf outcoupling from a trapped Bose-Einstein condensate can be described by a set of generalized, coupled Gross-Pitaevskii equations (GPEs). If not only one but two radio frequencies are used for outcoupling, the atoms emerging from the trap have two different energies and the total wave function of the untrapped spin state is a coherent superposition which leads to a pulsed atomic beam. We present results for such a situation obtained from a one-dimensional GPE model for magnetically trapped 87Rb{}^{87}\mathrm{Rb}87Rb in the F=1F=1F=1 state. The wave function of the atomic beam can be approximated by a sum of two Airy functions. In the limit of weak coupling we calculate the intensity analytically.
The two-level atom focusing in a Gaussian standing wave laser field was analyzed from the perspective of both classical mechanics and wave mechanics. The effects of source imperfection such as velocity spread and beam spread on atom focusing were analyzed by numerically integrating the classical equation of atomic motion. The ideal focal plane can be easily determined by the variation of atomic density at the minimal potential of the standing wave laser field as a function of traveling distance. In the absence of source imperfection, the contribution of diffractive aberration originating from the wave nature of the atom to broadening of feature width is larger than that of spherical aberration. Several methods for improving atom lithography experiments were presented.
Using the unique detection properties offered by metastable helium atoms we have produced high resolution images of the transverse spatial profiles of an atom laser beam. We observe transverse fringes on the beam, resulting from quantum mechanical interference between atoms that start from rest at different transverse locations within the outcoupling surface and end up at a later time with different velocities at the same transverse position. Further, for high outcoupling rates we see the emergence of structure on the beam profile, which is not predicted by the usual Gross-Pitaevskii equation.