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Journal of Physics Conference Series

Calculation of the Casimir-Polder interaction between Bose-Einstein condensates and microengineered surfaces: a pairwise-summation approach

Mohamad Nazri Abdul Halif, Riccardo Messina, T. M. Fromhold

Published Mar 1, 2011• 4 citations
Publisher

Abstract

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.

DOI
10.1088/1742-6596/286/1/012045

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The Casimir-Polder interaction between atoms and macroscopic surfaces is a fundamental prediction of quantum electrodynamics of importance for precision measurements, quantum technologies and our understanding of the electromagnetic properties of materials. In the near field, Casimir-Polder interactions are described as the interaction of the fluctuating atomic dipole with its surface induced image, which evolves as -C3/z3 where z is the atom-surface distance and C3 is the van der Waals coefficient. In this thesis, we study both theoretically and experimentally the Casimir-Polder interaction between a highly excited cesium atom (Rydberg atom) and a dielectric surface. Our theory extends previous studies to[3]include higher-order terms in the atom-surface interaction, beyond the dipole-dipole interaction term investigated in the seminal work of Casimir and Polder. In particular, we include quadrupole-quadrupole and dipole-octupole interaction terms with a distance dependence of ?C5/z5 giving explicit calculations of the C5 coefficients for most common alkali atoms. We also describe a new selective reflection experiment probing Cs Rydberg atoms (15-17D3/2 and 16-17S1/2) at nanometric distances away from a sapphire surface. The experiment is performed in an all-sapphire vapour cell using stepwise excitation spectroscopy that includes a pumping step at 6S1/2?6P1/2 (894nm) and a selective reflection probing step at 6P1/2?nS1/2 , nD3/2 with n=15-17 (~510nm). In order to analyze our experimental spectra, we extend selective reflection theory beyond the infinite Doppler approximation, including in our analysis the Maxwell-Boltzmann distribution of atomic velocities. Fitting our experimental spectra with our theoretical models allows us to extract the C3 van der Waals coefficient for the probed cesium excited states. The experimental results exceed our theoretical predictions (by a factor of about 1.5-2, depending on the probed state). Finally, we describe a new thin-cell experiment that aims to illuminate the reported disagreement between theory and experiment for the C3 coefficient and provide a first experimental measurement of the C5 coefficient (experimental study of higher-order interactions).

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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.
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.
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 (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.
The Casimir-Polder interaction between atoms and macroscopic surfaces is a fundamental prediction of quantum electrodynamics of importance for precision measurements, quantum technologies and our understanding of the electromagnetic properties of materials. In the near field, Casimir-Polder interactions are described as the interaction of the fluctuating atomic dipole with its surface-induced image, which evolves as −C3/z3 where z is the atom-surface distance and C3 is the van derWaals coefficient. In this thesis, we study boththeoretically and experimentally the Casimir-Polder interaction between a highly excited caesium atom (Rydberg atom) and a dielectric surface. Our theoretical study extends previous studies to include higher-order terms in the atom-surface interaction, beyond the dipole-dipole interaction term investigated in the seminal work of Casimir and Polder. In particular, we include quadrupole-quadrupole and dipole-octupole interaction terms with a distance dependence of −C5/z5 giving explicit calculations of the C5 coefficients for most common alkali atoms. We also describe a new selective reflection experiment probing Cs Rydberg atoms (15 − 17D3/2 and 16 − 17S1/2) at nanometric distances away from a sapphire surface. The experiment is performed in an all-sapphire vapour cell using stepwise excitation spectroscopy that includes a pumping step at 6S1/2 → 6P1/2 (894nm) and a selective reflection probing step at 6P1/2 → nS1/2,nD3/2 with n = 15 - 17 (∼ 510nm). To analyze our experimental spectra, we extend selective reflection theory beyond the infinite Doppler approximation, including in our analysis the Maxwell-Boltzmann distribution of atomic velocities. Fitting our theoretical lineshape model to our experimental spectra allows us to extract the C3 van der Waals coefficient for the probed caesium excited states. This C3 measurement exceeds the theoretical predictions of Casimir-Polder theory by a factor of about 1.5 - 2, depending on the probed state. Finally, we describe a new thin-cell experiment that aims to illuminate the reported disagreement between theory and experiment for the C3 coefficient and provide a first experiment
The 1%-accurate calculations of the van der Waals interaction between an atom and a cavity wall are performed in the separation region from 3nmto150nm3\phantom{\rule{0.3em}{0ex}}\mathrm{nm}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}150\phantom{\rule{0.3em}{0ex}}\mathrm{nm}3nmto150nm. The cases of metastable He∗{\mathrm{He}}^{*}He∗ and Na atoms near metal, semiconductor, and dielectric walls are considered. Different approximations to the description of wall material and atomic dynamic polarizability are carefully compared. The smooth transition to the Casimir-Polder interaction is verified. It is shown that to obtain accurate results for the atom-wall van der Waals interaction at short separations with an error less than 1% one should use the complete optical-tabulated data for the complex refractive index of the wall material and the accurate dynamic polarizability of an atom. The obtained results may be useful for the theoretical interpretation of recent experiments on quantum reflection and Bose-Einstein condensation of ultracold atoms on or near surfaces of different kinds.
The Casimir-Polder interaction between atoms and macroscopic surfaces is a fundamental prediction of quantum electrodynamics of importance for precision measurements, quantum technologies and our understanding of the electromagnetic properties of materials. In the near field, Casimir-Polder interactions are described as the interaction of the fluctuating atomic dipole with its surface induced image, which evolves as -C3/z3 where z is the atom-surface distance and C3 is the van der Waals coefficient. In this thesis, we study both theoretically and experimentally the Casimir-Polder interaction between a highly excited cesium atom (Rydberg atom) and a dielectric surface. Our theory extends previous studies to[3]include higher-order terms in the atom-surface interaction, beyond the dipole-dipole interaction term investigated in the seminal work of Casimir and Polder. In particular, we include quadrupole-quadrupole and dipole-octupole interaction terms with a distance dependence of ?C5/z5 giving explicit calculations of the C5 coefficients for most common alkali atoms. We also describe a new selective reflection experiment probing Cs Rydberg atoms (15-17D3/2 and 16-17S1/2) at nanometric distances away from a sapphire surface. The experiment is performed in an all-sapphire vapour cell using stepwise excitation spectroscopy that includes a pumping step at 6S1/2?6P1/2 (894nm) and a selective reflection probing step at 6P1/2?nS1/2 , nD3/2 with n=15-17 (~510nm). In order to analyze our experimental spectra, we extend selective reflection theory beyond the infinite Doppler approximation, including in our analysis the Maxwell-Boltzmann distribution of atomic velocities. Fitting our experimental spectra with our theoretical models allows us to extract the C3 van der Waals coefficient for the probed cesium excited states. The experimental results exceed our theoretical predictions (by a factor of about 1.5-2, depending on the probed state). Finally, we describe a new thin-cell experiment that aims to illuminate the reported disagreement between theory and experiment for the C3 coefficient and provide a first experimental measurement of the C5 coefficient (experimental study of higher-order interactions).