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arXiv:2508.09390 · Low Temperature Physics

Bose–Einstein condensate sub-wavelength confinement via superoscillations

Dusty R. Lindberg, Gerard McCaul, Peisong Peng, Lev Kaplan, Diyar Talbayev, Denys I. Bondar

Published Dec 1, 2025• 0 citations
arXivHTMLPDF

Abstract

Optical lattices are essential tools in the field of ultra-cold atomic physics. In this study, we theoretically demonstrate that sub-wavelength confinement can be achieved in these lattices through superoscillations. This generic wave phenomenon occurs when a local region of the wave oscillates faster than any of the frequencies in its global Fourier decomposition. To illustrate this, we consider a one-dimensional tri-chromatic optical potential confining a spinless Bose–Einstein condensate of 87Rb atoms. By numerically optimizing the relative phases and amplitudes of the optical trap’s frequency components, it is possible to generate superoscillatory spatial regions. Such regions contain multiple density peaks at sub-wavelength spacing. This work establishes superoscillations as a viable method of confining a Bose–Einstein condensate in a blue-detuned optical lattice at the sub-wavelength scale.

DOI
10.1063/10.0039901

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Optical lattices are essential tools in the field of ultra-cold atomic physics. In this study, we theoretically demonstrate that sub-wavelength confinement can be achieved in these lattices through superoscillations. This generic wave phenomenon occurs when a local region of the wave oscillates faster than any of the frequencies in its global Fourier decomposition. To illustrate this, we consider a one-dimensional tri-chromatic optical potential confining a spinless Bose–Einstein condensate of 87Rb atoms. By numerically optimizing the relative phases and amplitudes of the optical trap’s frequency components, it is possible to generate superoscillatory spatial regions. Such regions contain multiple density peaks at sub-wavelength spacing. This work establishes superoscillations as a viable method of confining a Bose–Einstein condensate in a blue-detuned optical lattice at the sub-wavelength scale.
Optical lattices serve as fundamental building blocks for atomic quantum technology. However, the scale and resolution of these lattices are diffraction-limited to the light wavelength. In conventional lattices, achieving tight confinement of single sites requires high laser intensity, which unfortunately leads to reduced coherence due to increased scattering. This article presents a novel approach for creating an atomic optical lattice with a sub-wavelength spatial structure. The potential is generated by leveraging the nonlinear optical response of three-level Rydberg-dressed atoms, which allows us to overcome the diffraction limit of the driving fields. The resulting lattice comprises a three-dimensional array of ultra-narrow Lorentzian wells over nanometer scales. These unprecedented scales can now be accessed through a hybrid scheme that combines the dipolar interaction and optical twist of atomic eigenstates. The interaction-induced two-body resonance that forms the trapping potential, only occurs at a peculiar laser intensity, localizing the trap sites to ultra-narrow regions over the standing-wave driving field. The feasibility study shows that single-atom confinement in Lorentzian sites with 3nm width, and 37MHz depth are realizable with available lasers. The development of these ultra-narrow trapping techniques holds great promise for applications such as Rydberg-Fermi gates, atomtronics, quantum walks, Hubbard models, and neutral-atom quantum simulation.
We study the phase coherence property of Bose−Einstein condensates confined in a one-dimensional optical lattice formed by a standing-wave laser field. The lattice depth is determined using a method of Kapitza–Dirac scattering between a condensate and a short pulse lattice potential. Condensates are then adiabatically loaded into the optical lattice. The phase coherence property of the confined condensates is reflected by the interference patterns of the expanded atomic cloud released from the optical lattice. For weak lattice, nearly all of the atoms stay in a superfluid state. However, as the lattice depth is increased, the phase coherence of the whole condensate sample is gradually lost, which confirms that the sub-condensates in each lattice well have evolved into number-squeezed states.
We consider the problem of formation of small-amplitude spatially localized oscillatory structures for atomic Bose-Einstein condensates confined in two- and three-dimensional optical lattices, respectively. Our approach is based on applying the regions with different signs of atomic effective masses where an atomic system exhibits effective hyperbolic dispersion within the first Brillouin zone. By using the kp\mathbf{kp}kp method we have demonstrated mapping of the initial Gross-Pitaevskii equation on nonlinear Klein-Gordon and/or Ginzburg-Landau-Higgs equations, which is inherent in matter fields within ${\ensuremath{\phi}}^{4}$-field theories. Formation of breatherlike oscillating localized states---atomic oscillons---as well as kink-shaped states have been predicted in this case. Apart from classical field theories atomic field oscillons occurring in finite lattice structures possess a critical number of particles for their formation. The obtained results pave the way to simulating some analogues of fundamental cosmological processes occurring during our Universe's evolution and to modeling nonlinear hyperbolic metamaterials with condensed matter (atomic) systems.
We report an experimental demonstration of engineering phase wraps for sub-wavelength structure in a Bose-Einstein condensate (BEC) with two-dimensional optical lattices. A short lattice pulse is applied on BEC working in the Kapitza-Dirac (or Raman-Nath) regime, which corresponds to phase modulation imprint on matter wave. When the phase modulation on matter wave is larger than 2π2π2π in a lattice cell, there appears phase wraps with multiple 2π2π2π jumps, generating the sub-wavelength phase structure. The phase wraps for sub-wavelength structure are measured in momentum space via the time-of-flight absorption image, which corresponds to converting phase information into amplitude. %Two different kinds of two-dimensional optical lattice are studied, which show the different subwavelength phase structure. Moreover, we identify an additional condition for the validity of Kapitza-Dirac regime, which relies crucially on the lattice configurations. This scheme can be used for studying the property of optical lattices and topological defects in matter wave.
Abstract Optical tweezers have become essential tools to manipulate atoms or molecules at a single particle level. However, using standard diffraction-limited optical systems, the transverse size of the trap is lower bounded by the optical wavelength, limiting the application range of optical tweezers. Here we report trapping of single ultracold atom in an optical trap that can be continuously tuned from a standard Airy focus to a subwavelength hotspot smaller than the usual Abbe’s diffraction limit. The hotspot was generated using the effect of superoscillations, by the precise interference of multiple free-space coherent waves. We argue that superoscillatory trapping and continuous potential tuning offer not only a way to generate compact and tenable ensembles of trapped atoms for quantum simulators but will also be useful in single molecule quantum chemistry and the study of cooperative atom-photon interactions within subwavelength arrays of quantum emitters.