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arXiv:1909.08377 · Physical Review A

Casimir-Polder-induced Rydberg macrodimers

Johannes Block, Stefan Scheel

Published Dec 13, 2019• 7 citations
arXivHTMLPDF

Abstract

We theoretically investigate Rydberg atom pair potentials of Rb atoms in front of a perfectly conducting plate. The pair potentials are perturbed by both the Casimir-Polder potential acting on a single atom and the scattering contribution to the interatomic interaction. In contrast to the pair potentials in free space, at atom-surface distances ${d}_{s}\ensuremath{\lesssim}4\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{m}$, avoided crossings appear. In the associated potential wells that are entirely due to dispersion interactions with the surface, there exist vibrational bound states, i.e., Rydberg macrodimers, with ground-state energies of up to $E=\ensuremath{-}68\phantom{\rule{0.16em}{0ex}}\mathrm{MHz}$ and radial expectation values of the order of several $\ensuremath{\mu}\mathrm{m}$.

DOI
10.1103/physreva.100.062508

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We theoretically investigate Rydberg atom pair potentials of Rb atoms in front of a perfectly conducting plate. The pair potentials are perturbed by both the Casimir-Polder potential acting on a single atom and the scattering contribution to the interatomic interaction. In contrast to the pair potentials in free space, at atom-surface distances ds\ensuremath≲4\ensuremathμm{d}_{s}\ensuremath{\lesssim}4\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{m}ds​\ensuremath≲4\ensuremathμm, avoided crossings appear. In the associated potential wells that are entirely due to dispersion interactions with the surface, there exist vibrational bound states, i.e., Rydberg macrodimers, with ground-state energies of up to E=\ensuremath−68MHzE=\ensuremath{-}68\phantom{\rule{0.16em}{0ex}}\mathrm{MHz}E=\ensuremath−68MHz and radial expectation values of the order of several \ensuremathμm\ensuremath{\mu}\mathrm{m}\ensuremathμm.
Highly excited (Rydberg) atoms have exaggerated properties making them extremely sensitive to external electromagnetic fields and interacting strongly with their environment. Atomic vapor cells represent an attractive platform for studying Rydberg atoms and fabricating quantum devices. For example, Rydberg atoms in vapor cells have been used as sensitive detectors of electric fields of frequencies ranging from DC up to the THz range but also as single photon sources for quantum technology applications exploiting collective phenomena due to the Rydberg blockade effect [1]. Rydberg atoms also find applications in fundamental physics, in particular for the measurement of dispersive interactions of the Casimir-Polder type (atom-surface interactions) [2]. One major advantage of Rydberg atoms is that they expose limitations in the traditional perturbative approach of Casimir-Polder (CP) theory [3, 4]. Indeed, in the extreme near-field, the dipole approximation breaks down and higher-order terms need to be considered. We report on extensive experimental measurements of the Rydberg-surface interaction using spectroscopy in cesium vapor nanocells of a thickness ranging roughly from 200-700nm, as well as selective reflection spectroscopy on a macroscopic cesium all-sapphire cell. Atoms are first excited to the Cs(6P) level with a 894nm pump laser and subsequently a green laser ≈ 510nm probes Rydberg nD or nS states, where the principal quantum number n ranges between 15-17. Our experiments evidence the dipole-dipole term of the Casimir-Polder interaction providing a measurement of the C3 coefficient for cesium Rydberg states. Furthermore, our experiment clearly evidences an additional interaction that induces shifts and broadens the linewidth of the probed transitions in the vicinity of the dielectric windows of our cells. We believe that this interaction is due to electric fields that are either generated by patch charges (trapped on the surface or induced by the excitation lasers), or by cesium adsorbants. We show that the different polarizability (of opposing sign) between S and D Rydberg states can be exploited to extract quantitative measurements of the strength and distance scaling (z-dependence) of such parasitic electrostatic interactions.Our experiments suggest that the sensitivity of Rydberg atoms to external electric fields could provide a unique tool for probing electrostatic interactions in the vicinity of surfaces. This could allow systematic error corrections in Casimir-Polder experiments with excited or even ground state atoms that aim at putting bounds on the existence of non-Newtonian gravity [5]. We are currently exploring the possibility of coating the internal window interfaces with conducting 2D material such as graphene to reduce the influence of parasitic charges. This could allow us to probe atoms closer to the surface, where quadrupole interactions could be experimentally attainable for the first time [4].References[1] H. Kubler, J. P. Shaffer, T. Baluktsian, R. Loew, T. Pfau, Nat. Photon., 4, 112–116 (2013).[2] V. Sandoghdar et al., Phys. Rev. Lett 68, 3432–3435 (1993).[3] J. A. Crosse et al., Phys. Rev. A 82, 3010901 (2010).[4] B. Dutta et al., Phys. Rev. Res. 6, L022035 (2024).[5] A. Laliotis, B-S. Lu, M. Ducloy, D. Wilkowski, AVS Quantum Sci. 3, 043501 (2021).
Dispersion forces have a sizeable effect on the energy levels of highly excited Rydberg atoms when brought close to material surfaces. Rydberg atoms experience energy shifts in the GHz range at micrometer distances, suggestive of considerable state admixture. We show that despite the non-applicability of perturbation theory for Rydberg atoms near a surface, the energy shift due to the dispersion interaction can be obtained from an exact diagonalization of the interaction Hamiltonian by finding the zeros of the Pick function. Moreover, we show that contrary to intuition from single-mode approaches, surface-induced state mixing is generally suppressed even for large interaction energies. We give a tailored example where mixing is observable despite this effect.
Dispersion forces have a sizeable effect on the energy levels of highly excited Rydberg atoms when brought close to material surfaces. Rydberg atoms experience energy shifts in the GHz range at micrometer distances, suggestive of considerable state admixture. We show that despite the non-applicability of perturbation theory for Rydberg atoms near a surface, the energy shift due to the dispersion interaction can be obtained from an exact diagonalization of the interaction Hamiltonian by finding the zeros of the Pick function. Moreover, we show that contrary to intuition from single-mode approaches, surface-induced state mixing is generally suppressed even for large interaction energies. We give a tailored example where mixing is observable despite this effect.
In the extreme near-field, when the spatial extension of the atomic wavefunction is no longer negligible compared to the atom-surface distance, the dipole approximation is no longer sufficient to describe Casimir-Polder interactions. Here we calculate the higher-order, quadrupole and octupole, contributions to Casimir-Polder energy shifts of Rydberg atoms close to a dielectric surface. We subsequently investigate the effects of these higher-order terms in thin-cell and selective reflection spectroscopy. Beyond its fundamental interest, this new regime of extremely small atom surface separations is relevant for quantum technology applications with Rydberg or surface-bound atoms interfacing with photonic platforms.
In the extreme near field, when the spatial extension of the atomic wavefunction is no longer negligible compared to the atom-surface distance, the dipole approximation is no longer sufficient to describe Casimir-Polder interactions. Here we calculate the higher-order, quadrupole and octupole, contributions to Casimir-Polder energy shifts of Rydberg atoms close to a dielectric surface. We subsequently investigate the effects of these higher-order terms in thin-cell and selective reflection spectroscopy. Beyond its fundamental interest, this regime of extremely small atom surface separations is relevant for quantum technology applications with Rydberg or surface-bound atoms interfacing with photonic platforms. Published by the American Physical Society 2024
The modification of quantum fluctuations by a surface of finite reflectivity shifts the energy levels of atoms and changes their radiative properties (Casimir-Polder effect). At nanometric distances away from a surface (near field), the Casimir-Polder energy shift is given by −C3/z3 (where C3 is the van der Waals coefficient and z is the atom-surface distance) corresponding to the interaction of the fluctuating atomic dipole with its surface induced image. Near field Rydberg-surface interactions are of fundamental interest because the atomic size, scaling as n∗2 (where n∗ is the principle quantum number corrected by the quantum defect), is no longer negligible compared to the atom-surface separation, z. In this case, the dipole approximation, (−C3/z3 law of interaction), is no longer valid and higher-order terms, corresponding to the interaction of the fluctuation quadrupole with its own image, need to be taken into account. Quadrupole interaction terms in the atom-surface interaction manifest themselves with a novel distance dependence of z5 that has not been experimentally investigated yet1. Casimir-Polder experiments were first performed with low-lying Rydberg states (n= 10-14), demonstrating the −C3/z3 law of interaction2. Nevertheless, more recent experiments with high-lying rubidium Rydbergs (n=32-43)3 were not in agreement with Casimir-Polder theory thus highlighting the need for further experimental studies.