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Close examination of the ground-state Casimir–Polder interaction: time-ordered versus covariant formalism and radiative corrections
摘要： The purpose of this paper is twofold. First, we compare, in detail, the derivation of the Casimir–Polder interaction using time-ordered perturbation theory, to the matching of the scattering amplitude using quantum electrodynamics. In the first case, a total of twelve time-ordered diagrams need to be considered, while in the second case, one encounters only two Feynman diagrams, namely, the ladder and crossed-ladder contributions. For ground-state interactions, we match the contribution of six of the time-ordered diagrams against the corresponding Feynman diagrams, showing the consistency of the two approaches. Second, we also examine the leading radiative correction to the long-range interaction, which is of relative order α(a). In doing so, we uncover logarithmic terms, in both the interatomic distance as well as the fine-structure constant, in higher-order corrections to the Casimir–Polder interaction.
关键词： propagator denominator,covariant formalism,time-ordered perturbation theory,scattering matrix,radiative corrections,Casimir–Polder interactions
更新于2025-09-23 15:19:57
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[IEEE 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Munich, Germany (2019.6.23-2019.6.27)] 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Spectroscopic Probing of Retardation Effects in the Casimir-Polder Interaction: A Theoretical Study
摘要： Spectroscopic probing of retardation effects in the Casimir-Polder interaction: a theoretical study. Lennard-Jones theory describes the atom-surface interaction as the instantaneous interaction between a fluctuating dipole and its image predicting a surface induced shift of the atomic energy levels given by -C3/z3, where z is the atom-surface distance and C3 is the van der Waals (vdW) coefficient. In Casimir-Polder theory, demonstrated experimentally with ground state atoms in ~1μm thick metallic cavities [1], atom-surface interactions arise from the modification of vacuum fluctuations next to a dielectric boundary. More recently, Casimir-Polder theory has been tested with ground state cold atoms at intermediate distances from a dielectric surface [2]. Nevertheless, testing the limits of the van der Waals law in the extreme near field remains an important experimental challenge. Additionally, excited state atoms are also of fundamental importance, as their interaction with surfaces can also be of resonant nature. This is of particular interest when atomic dipole transitions couple resonantly to surface polaritons, allowing for exotic near field effects. Selective reflection spectroscopy is a major experimental method testing Casimir-Polder interaction of excited state atoms in the near field. Up to now, experimental results have been interpreted exclusively under the prism of the van der Waals approximation. Here, we show calculations of the fully retarded, spectroscopically relevant, Casimir-Polder potentials for the 6S1/2→6P1/2 and 6S1/2→5D5/2 (Fig.1a) Cs transitions (difference between the Casimir-Polder potentials between probed states) taking into account temperature corrections [3]. The dipole forbidden 6S1/2→6D5/2 transition was recently probed by selective reflection spectroscopy [4]. We demonstrate that accounting for a fully retarded potential leads to significantly different predictions of selective reflection spectra compared to a -C3/z3 vdW approximation. Surprisingly, a vdW model when allowing for an adjustable, ad hoc, van der Waals coefficient can accommodate these differences (Fig1b). However, careful analysis shows that this ad hoc coefficient is not a constant but strongly depends on transition linewidth (collisional broadening) as seen in Fig1c. This is because the contribution of atoms to the experimental spectra depends on their relative detuning, i.e. Casimir-Polder shift divided by the transition linewidth. As the linewidth increases, atoms closer to the surface become more ‘resonant’ with the excitation lasers increasing their contribution [5]. Our analysis shows that by increasing the collisional broadening in selective reflection spectroscopy one can tune the experimental probing depth thus probing atoms that are closer to the surface. This can provide an important experimental tool for measuring the effects of retardation in atom-surface potentials of low lying atomic transitions using selective reflection spectroscopy. Retardation effects can have an impact in atom-metamaterial interactions where plasmons can be tuned in resonance with D1 and D2 lines of alkali atoms at near infrared wavelengths [6].
关键词： van der Waals coefficient,selective reflection spectroscopy,Casimir-Polder interaction,atom-surface interaction,retardation effects
更新于2025-09-16 10:30:52
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[IEEE 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Munich, Germany (2019.6.23-2019.6.27)] 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Probing Molecules Next to Surfaces
摘要： Selective reflection spectroscopy at normal incidence provides signals with sub-Doppler resolution, linear with optical intensity. Frequency modulated (FM) selective reflection probes atomic vapours at distances comparable to the excitation wavelength (~λ/2π) and is used extensively to probe the Casimir-Polder interactions between an excited state atom and a macroscopic surface. Extending selective reflection spectroscopy to molecular gases allows probing a thin layer of molecular gas next to a surface. This is a very attractive prospect that allows envisaging high-resolution molecular spectroscopy and molecular frequency references in a compact and miniaturised apparatus, such as a thin cell [1] or a photonic crystal [2]. Additionally, it paves the way for spectroscopic probing of the Casimir-Polder interaction with molecules. The molecule-surface interaction has been the object of extensive theoretical investigations, focusing on the effects of molecular orientation and chirality. However, experimental tests are few and comparison with theoretical predictions has been challenging [3]. Here, we present selective reflection measurements on polyatomic molecules in gaseous form. We probe rovibrational molecular transitions of NH3 and SF6 using a Quantum Cascade Laser (QCL) at ~10.6μm. Reflection spectroscopy is performed in a vacuum chamber with transparent ZnSe windows. In a separate chamber, we perform simultaneous saturated absorption measurements, to get molecular frequency references in the volume. We also use an auxiliary set-up to lock the QCL laser, either on the derivative (after FM demodulation) of a Doppler linear absorption, or on the wings of the NH3 linear absorption (direct signal). This allows us to eliminate a frequency drift of the QCL source due to temperature fluctuations. By tuning the molecular pressure and therefore the absorption profile, the latter method (lock on the direct signal) allows stable frequency scanning for hundreds of MHz. A system of electronic valves allows us to empty and refill the chamber with molecules within tens of seconds. Detecting the difference between signals, as well as using multiple vibrating mirrors in our set-up, eliminates to about 0.1ppm an interferometric parasitic background, typical in infrared spectroscopy. Fig.1 shows our experimental results obtained for the isolated saP(1) transition of NH3 (Fig. 1a) and a multitude of transitions of SF6, mostly unidentified in molecular databases (Fig. 1b). Linear selective reflection allows us to pinpoint these transitions and easily determine their relative amplitude. At sufficiently low molecular pressure, the frequency resolution of our measurements is limited to ~0.5MHz essentially by laser linewidth. This allows partially resolving the hyperfine structure of NH3. The dotted curves represent theoretical predictions of selective reflection spectra, with transition amplitude adjustments, accounting for FM and laser linewidth. We are working on the fabrication of thin cells using ZnSe windows for rovibrational transmission spectroscopy in the mid-infrared, as well as glass windows, for probing C2H2 at telecommunication wavelengths. Due to the Dicke narrowing effect, thin cells are a step towards compact high-resolution frequency references. Furthermore, achieving, nanometric molecular confinement, defined by cell thickness, instead of wavelength (λ/2π for selective reflection, here ~1.5μm) will allow us to measure the Casimir-Polder interaction with molecules and to study the thermal coupling and energy transfer between rovibrational molecular transitions and surface polaritons [4].
关键词： SF6,Casimir-Polder interactions,molecular gases,Quantum Cascade Laser,NH3,Selective reflection spectroscopy
更新于2025-09-16 10:30:52
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Development of a snow kernel to better model the anisotropic reflectance of pure snow in a kernel-driven BRDF model framework
摘要： The linear kernel-driven RossThick-LiSparseReciprocal (RTLSR) bidirectional reflectance distribution function (BRDF) model was originally developed from the simplified scenarios of continuous and discrete vegetation canopies, and has been widely used to fit multiangle observations of vegetation-soil systems of the land surface in many fields. Although this model was not developed explicitly for snow surfaces, it can capture the geometric-optical effect caused by the shadowing of rugged or undulating snow surfaces. However, in this study, this model has been further developed to better characterize the scattering properties of snow surface, which can also exhibit strongly forward-scattering behavior. This study proposes a new snow kernel to characterize the reflectance anisotropy of pure snow based on the asymptotic radiative transfer (ART) model that assumes snow can be modeled as a semi-infinite, plane-parallel, weakly absorbing light scattering layer. This new snow kernel adopts a correction term with a free parameter α to correct the analytic form of the ART model that has been reported to underestimate observed snow reflectance in the forward-scattering direction in the principal plane (PP), particularly in cases of a large viewing zenith angle (> 60°). This snow kernel has now been implemented in the kernel-driven RTLSR BRDF model framework in conjunction with two additional kernels (i.e., the volumetric scattering kernel and geometric-optical scattering kernel) and is validated using observed and simulated multiangle data from three data sources. Pure snow targets were selected from the extensive archive of the Polarization and Directionality of the Earth's Reflectance (POLDER) BRDF data. Antarctic snow field measurements, which were taken from the top of a 32-m-tall tower at Dome C Station and include 6336 spectral bidirectional reflectance factors (BRFs), were also utilized. Finally, a set of simulated BRFs, generated by a hybrid scattering snow model that combines the geometric optics with vector radiative transfer theory, were used to further assess the proposed method. We first retrieve the value of the free parameter α for a comprehensive analysis using single multiangle snow data with a sufficient BRDF sampling. Then, we determine the optimally fixed value of the α parameter as prior information for potential users. The new snow kernel method is shown to be quite accurate, presenting a high correlation coefficient (R2 = ~0.9) and a negligible bias between the modeled BRFs and the various snow BRDF validation data. The finding demonstrates that this snow kernel provides an improved potential compared to that of the original kernel-driven model framework for a pure snow surface in many applications, particularly those involving the global water cycle and radiation budget, where snow cover plays an important role.
关键词： Kernel-driven model,POLDER BRDF data,Bidirectional reflectance distribution function (BRDF),Asymptotic radiative transfer (ART) model,Snow,Forward scattering,RTLSR model
更新于2025-09-09 09:28:46
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Purcell-Dicke enhancement of the Casimir-Polder potential
摘要： The emission by an initially completely inverted ensemble of two-level atoms in the long-wavelength regime is simultaneously enhanced by both collective effects (Dicke effect) and dielectric environments (Purcell effect), thus giving rise to a combined Purcell–Dicke effect. We study this effect by treating the ensemble of N atoms as a single effective N + 1-level "Dicke atom" which couples to the environment-assisted quantum electrodynamic field. We find that an environment can indeed alter the superradiant emission dynamics, as exemplified using a perfectly conducting plate. As the emission acquires an additional anisotropy in the presence of the plate, we find an associated resonant Casimir-Polder potential for the atom that is collectively enhanced and that exhibits a superradiant burst in its dynamics. An additional tuneability of the effect is introduced by applying an external driving laser field.
关键词： superradiant emission,quantum electrodynamics,Purcell-Dicke effect,Casimir-Polder potential
更新于2025-09-09 09:28:46
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Adjustment of Sentinel-2 Multi-Spectral Instrument (MSI) Red-Edge Band Reflectance to Nadir BRDF Adjusted Reflectance (NBAR) and Quantification of Red-Edge Band BRDF Effects
摘要： Optical wavelength satellite data have directional re?ectance effects over non-Lambertian surfaces, described by the bidirectional re?ectance distribution function (BRDF). The Sentinel-2 multi-spectral instrument (MSI) acquires data over a 20.6? ?eld of view that have been shown to have non-negligible BRDF effects in the visible, near-infrared, and short wave infrared bands. MSI red-edge BRDF effects have not been investigated. In this study, they are quanti?ed by an examination of 6.6 million (January 2016) and 10.7 million (April 2016) pairs of forward and back scatter re?ectance observations extracted over approximately 20? × 10? of southern Africa. Non-negligible MSI red-edge BRDF effects up to 0.08 (re?ectance units) across the 290 km wide MSI swath are documented. A recently published MODIS BRDF parameter c-factor approach to adjust MSI visible, near-infrared, and short wave infrared re?ectance to nadir BRDF-adjusted re?ectance (NBAR) is adapted for application to the MSI red-edge bands. The red-edge band BRDF parameters needed to implement the algorithm are provided. The parameters are derived by a linear wavelength interpolation of ?xed global MODIS red and NIR BRDF model parameters. The ef?cacy of the interpolation is investigated using POLDER red, red-edge, and NIR BRDF model parameters, and is shown to be appropriate for the c-factor NBAR generation approach. After adjustment to NBAR, red-edge MSI BRDF effects were reduced for the January data (acquired close to the solar principal where BRDF effects are maximal) and the April data (acquired close to the orthogonal plane) for all the MSI red-edge bands.
关键词： Landsat,NBAR,POLDER,bidirectional re?ectance distribution function (BRDF),Africa,Sentinel-2,red-edge,MODIS
更新于2025-09-04 15:30:14