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arXiv:2011.14470 · Physical Review A

Optical focusing of Bose-Einstein condensates

R. Richberg, Stuart S. Szigeti, A. Martin

Published Jun 14, 2021• 7 citations
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Abstract

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 ${10}^{5}$ atoms could be focused down to $\ensuremath{\sim}$10 nm widths, potentially allowing nanometer-scale atomic deposition with peak densities greater than ${10}^{5}$ atoms/$\ensuremath{\mu}{\mathrm{m}}^{2}$.

DOI
10.1103/physreva.103.063304

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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∼\ensuremath{\sim}\ensuremath∼10 nm widths, potentially allowing nanometer-scale atomic deposition with peak densities greater than 105{10}^{5}105 atoms/\ensuremathμm2\ensuremath{\mu}{\mathrm{m}}^{2}\ensuremathμm2.
The focusing of a propagating untrapped Bose-Einstein condensate is studied theoretically. We use a scaling solution method comprising a time-dependent scaling function to analytically examine the dynamics of a falling Bose-Einstein condensate in different regimes of propagation including the expansion and compression zones. Our model is based on the Gross--Pitaevskii equation which involves the interparticle interactions between atoms and, consequently, their influence on the focused structures. We investigate the focused profile characteristic factors such as the resolution and peak density for various cases of the focusing optical potential parameters as well as the factors associated with the moving cloud. Our results are compared with numerical solutions of the Gross--Pitaevskii equation.
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.
The ability to create and manipulate strongly correlated quantum many-body states is of central importance to the study of collective phenomena in several condensed-matter systems. In the last decades, a great amount of work has been focused on ultracold atoms in optical lattices, which provide a flexible platform to simulate peculiar phases of matter both for fermionic and bosonic particles. The recent experimental demonstration of Bose-Einstein condensation (BEC) of light in dye-filled microcavities has opened the intriguing possibility to build photonic simulators of solid-state systems, with potential advantages over their atomic counterpart. A distinctive feature of photon BEC is the thermo-optical nature of the effective photon-photon interaction, which is intrinsically nonlocal and can thus induce interactions of arbitrary range. This offers the opportunity to systematically study the collective behavior of many-body systems with tunable interaction range. In this paper, we theoretically study the effect of nonlocal interactions in photon BEC. We first present numerical results of BEC in a double-well potential, and then extend our analysis to a short one-dimensional lattice with open boundaries. By resorting to a numerical procedure inspired by the Newton-Raphson method, we simulate the time-independent Gross-Pitaevskii equation and provide evidence of surface localization induced by nonlocality, where the condensate density is localized at the boundaries of the potential. Our work paves the way toward the realization of synthetic matter with photons, where the interplay between long-range interactions and low dimensionality can lead to the emergence of unexplored nontrivial collective phenomena.
We show that Fresnel zone plates (ZPs), fabricated in a solid surface, can sharply focus atomic Bose–Einstein condensates that quantum reflect from the surface or pass through the etched holes. The focusing process compresses the condensate by orders of magnitude despite inter-atomic repulsion. Crucially, the focusing dynamics are insensitive to quantum fluctuations of the atom cloud and largely preserve the condensates' coherence, suggesting applications in passive atom-optical elements, for example ZP lenses that focus atomic matter waves and light at the same point to strengthen their interaction. We explore transmission ZP focusing of alkali atoms as a route to erasable and scalable lithography of quantum electronic components in two-dimensional electron gases (2DEGs) embedded in semiconductor nanostructures. To do this, we calculate the density profile of a 2DEG immediately below a patch of alkali atoms deposited on the surface of the nanostructure by zone-plate focusing. Our results reveal that surface-induced polarization of only a few thousand adsorbed atoms can locally deplete the electron gas. We show that, as a result, the focused deposition of alkali atoms by existing ZPs can create quantum electronic components on the 50 nm scale, comparable to that attainable by ion beam implantation but with minimal damage to either the nanostructure or electron gas.
Bose-Einstein condensates of sodium atoms have been confined in an optical dipole trap using a single focused infrared laser beam. This eliminates the restrictions of magnetic traps for further studies of atom lasers and Bose-Einstein condensates. More than $5\ifmmode\times\else\texttimes\fi{}{10}^{6}$ condensed atoms were transferred into the optical trap. Densities of up to $3\ifmmode\times\else\texttimes\fi{}{10}^{15}{\mathrm{cm}}^{\ensuremath{-}3}$ of Bose condensed atoms were obtained, allowing for a measurement of the three-body loss rate constant for sodium condensates as ${K}_{3}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.1(3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}30}{\mathrm{cm}}^{6}{\mathrm{s}}^{\ensuremath{-}1}$. At lower densities, the observed 1/e1/e1/e lifetime was longer than 10 s. Simultaneous confinement of Bose-Einstein condensates in several hyperfine states was demonstrated.