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 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.
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
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).
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).
Abstract We theoretically propose that electromagnetically induced transparency (EIT) with cold Rydberg atoms in the proximity to a metallic chip surface can be applied to detect and investigate the Casimir–Polder effect. The absorption spectrum of the probe laser is numerically computed by the Monte Carlo method, taking into account atom-surface interactions (Casimir–Polder effect). The results show that the Casimir–Polder effect shifts the energy level of the Rydberg state and leads to a shift in the EIT transparency window. The shift of resonant frequency depends on the principal quantum number, atom-surface distance and atomic density. The atom-surface interactions have observable impacts on the nonlinear optic response of the ‘Rydberg EIT medium’ near atom chips.