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IEEE International Conference on Sensors and Nanotechnology (SENNANO)

Tuning Casimir-Polder Interactions in Alkali BEC Atoms via Carbon Nanotube Geometry: A Comparative Study of [Li, Na, Cs, Rb]

Ahmad Firdaus Khaidir, Mohamad Nazri Abdul Halif, Zulfi Abdullah, Ahmad Ripai, Trengginas Eka Putra Sutantyo, Hanifah Azzaura Musyayyadah

Published Sep 10, 2025• 0 citations
Publisher

Abstract

Atom-surface dispersion has become a subject of studies involving the process of efficient trapping and manipulating ultracold alkali atoms, Bose-Einstein Condensation (BEC) near the carbon nanotubes (CNT). Known as Casimir-Polder (CP) interaction, it has been approximated as analytical expression using Hamaker's approach of pairwise summation (PWS) by summing up every contribution imposed by ground state BEC treated as single atom over densely packed atoms inside CNT. At larger atom-surface distances, the CP interaction is found to be strikingly weaker on a cylindrical shell compared to a solid cylinder, with this weakening increasing further as the alkali atoms become much lighter. We examine how these results will be beneficial to BEC experiment especially when cold atoms are magnetically or optically trapped above a relatively few microns-distance CNT atom chip, fabricated as a pristine graphene and sustained under high vacuum conditions.

DOI
10.1109/sennano64909.2025.11472917

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Atom-surface dispersion has become a subject of studies involving the process of efficient trapping and manipulating ultracold alkali atoms, Bose-Einstein Condensation (BEC) near the carbon nanotubes (CNT). Known as Casimir-Polder (CP) interaction, it has been approximated as analytical expression using Hamaker's approach of pairwise summation (PWS) by summing up every contribution imposed by ground state BEC treated as single atom over densely packed atoms inside CNT. At larger atom-surface distances, the CP interaction is found to be strikingly weaker on a cylindrical shell compared to a solid cylinder, with this weakening increasing further as the alkali atoms become much lighter. We examine how these results will be beneficial to BEC experiment especially when cold atoms are magnetically or optically trapped above a relatively few microns-distance CNT atom chip, fabricated as a pristine graphene and sustained under high vacuum conditions.
Understanding the Casimir-Polder (CP) attraction between ultracold atoms and dielectric surfaces is of fundamental importance to the design and miniaturization of atom chips [1] and for understanding quantum reflection from, and sticking to, the surface [2 - 6]. So far, calculations have focussed on planar dielectrics, either semi-infinite or of finite width [7-9], and non-planar geometries including corrugated surfaces [10], spheres and carbon nanotubes [11-12]. Here, we present a simple scheme, based on the Pairwise-Summation (PWS) approximation, for estimating the CP interaction between a ground-state alkali atom and a dielectric volume of arbitrary shape. The PWS approximation integrates the van der Waals interaction between two ground-state atoms over the many atoms in the surface volume. We relate the microscopic polarizability of atoms in the surface to the bulk dielectric constant via the Clausius-Mossotti relation within the Lorentz local-field theory. We find that the CP potential depends strongly on both the geometry and density of the surface, which modify the fluctuation spectrum of the electromagnetic field that couples the alkali atoms to the dielectric. We compare our results with known analytical expressions for the CP potential near planar surfaces and use them to investigate how BECs interact with, and may quantum reflect from, curvilinear surface structures.
We investigate the possibility of trapping ultracold 87Rb^{87}\mathrm{Rb}87Rb atoms near the outside of a metallic carbon nanotube, which we imagine using as a miniaturized current-carrying wire. We calculate atomic spin-flip lifetimes and compare the strength of the Casimir-Polder potential with the magnetic trapping potential. Our analysis indicates that the Casimir-Polder force is the dominant loss mechanism, and we compute the minimum distance to the carbon nanotube at which the atoms can be trapped to be larger than 100nm100\phantom{\rule{0.3em}{0ex}}\mathrm{nm}100nm.
Cold atoms can be trapped and guided using nanofabricated wires on microengineered surfaces, achieving the scales required by quantum information proposals on the consequences of Casimir-Polder (CP) force to its stability and lifetime. The atoms are found to be less attractive to the thin films compared to dielectric half plate, where the attractive potential drops even further when the thickness of the surface is lower than both thermal wavelength and the spacing length. Amiably, for the spherical surface, the CP potential decays even further as radial thickness decreases. We approximate the CP potential using the analytical expression obtained from the pairwise summation (PWS) calculated by taking a sum of single atom with the jumbled atoms inside the surface, treating them as two-bodies system as a whole. The means of PWS are to calculate the possibilities of geometrical effect: planar and curved surface on the CP potential.
The Casimir-Polder force acts on polarizable particles due to quantum fluctuations of the electromagnetic field that are modified by the presence of material bodies. We investigate the Casimir-Polder interaction for atoms near cylindrical fibers with hollow cores. This geometry represents one of the archetypal configurations encountered in numerous experimental setups designed to control and manipulate atoms in fundamental and quantum technological applications. Specifically, we analyze how the interplay of both geometrical and material-related length scales characterize the interaction, emphasizing the impact of the shell thickness. We develop a flexible and fast-converging numerical scheme for evaluating the interaction over a wide range of atom-cylinder separations at both zero and finite temperature. Furthermore, we provide a detailed analytical investigation of how various material properties modify the Casimir-Polder potential. Finally, we analyze and discuss a number of limiting cases and compare numerical computations with corresponding analytical asymptotic expressions. In particular, in this geometry the Casimir-Polder potential is able to distinguish between an ohmic and non-ohmic description of conductors. One of the most significant outcomes of our work is that the shell thickness emerges as a useful parameter for controlling the interaction, opening avenues for both fundamental physics and applications in quantum technologies.
We derive an expression for the collective Casimir-Polder interaction of a trapped gas of condensed bosons with a plane surface through coupling of the condensate atoms with the electromagnetic field. A systematic perturbation theory is developed based on a diagrammatic expansion of the electromagnetic self-energy. In the leading order, the result for the interaction energy is proportional to the number of atoms and involves the one-body density matrix of the trapped gas. At this order, atom-atom interactions and recoil effects lead to corrections compared to the single-atom theory, through shifts of the atomic transition energies. We also discuss the impact of spatial delocalization of the condensate mode.
The Casimir-Polder (CP) effect -- the force between a neutral atom and an uncharged conducting plate in empty space -- is an intriguing consequence of quantum vacuum fluctuations. The typically attractive CP potential crosses over from a scaling of z−3z^{-3}z−3 at short separations to z−4z^{-4}z−4 at long distances, where retardation effects due to the finite speed of light become important. At intermediate distances, where the atom--surface separation is of the order of the wavelength of the dominant atomic transition, experiments have so far relied on indirect methods, such as diffraction or quantum reflection, to observe the CP effect. Here, we directly reveal the CP force between strontium atoms and a dielectric surface via the induced shifts in the atomic energy levels in the intermediate regime. We spectroscopically probe the CP-induced kHz-frequency shift of ultracold atoms confined by a magic-wavelength optical lattice at 189(2)~nm from the surface -- on the scale of the dominant 461-nm transition. Our measurements agree well with QED calculations and differ from the short-range approximation, while excluding the long-distance one. This paves the way for studying the CP effect across various surface properties and geometries, as well as exploring the tensor nature of the atom-surface potential -- all important for the development of hybrid atomic optical-magnetic quantum devices.