We measure the near-resonant transmission of light through a dense medium of potassium vapor confined in a cell with nanometer thickness in order to investigate the origin and validity of the collective Lamb shift. A complete model including the multiple reflections in the nanocell reproduces accurately the observed line shape. It allows the extraction of a density-dependent shift and width of the bulk atomic medium resonance, deconvolved from the cavity effect. We observe an additional, unexpected dependence of the shift with the thickness of the medium. This extra dependence demands further experimental and theoretical investigations.

By measuring the transmission of near-resonant light through an atomic vapor confined in a nano-cell we demonstrate a mesoscopic optical response arising from the non-locality induced by the motion of atoms with a phase coherence length larger than the cell thickness. Whereas conventional dispersion theory -where the local atomic response is simply convolved by the Maxwell-Boltzmann velocity distribution -is unable to reproduce the measured spectra, a model including a non-local, size-dependent susceptibility is found to be in excellent agreement with the measurements. This result improves our understanding of light-matter interaction in the mesoscopic regime and has implications for applications where mesoscopic effects may degrade or enhance the performance of miniaturized atomic sensors. arXiv:1809.08852v2 [physics.atom-ph]Here, we first derive the equations of the third (non-local) model of the main text, starting with the expression of the non-local susceptibility (Eq. (5)). Then, we derive the expression of the optical field transmitted through a thin layer of atomic gas, first in vacuum, and then accounting for the presence of glass interfaces. In Section II, we show that using a bimodal velocity distribution in the second model of the main text cannot reproduce consistently the data either. In Section III we give more details about the deviation of the transmission coefficient from the Beer-Lambert law. Finally, we analyze in more details the thickness dependence of the parameter Γ p extracted from the fit of the data by the local model. I. DERIVATION OF THE NON-LOCAL MODELIn this first Section, we derive the expression of the transmission through the atomic slab, including the cavity effect from the sapphire plates of the nanocell, making explicit the origin of the non-locality. A. The non-local susceptibilityWe start by deriving the expression of the non-local susceptibility χ(z, z , ω, v) of the ensemble of atoms for a velocity class v and at frequency ω. As explained in the main text, the presence of the cell walls makes it a challenging task in general. To simplify the situation, we will use the following procedure:1. We will treat the vapor as if it was homogeneous (i.e. in the absence of confining walls). In this case, the susceptibility depends only on the difference: χ(z, z , ω, v) = χ(z − z , ω, v).2. We will treat the effect of the surfaces separately. This will be done by assuming quenching collisions at the cell walls, i.e. the atomic coherence will be lost during these collisions [1] and reset to zero. In this way, there will not exist any relation between the coherence of atoms moving at +v or −v, contrarily to what would happen if the collisions with the walls were elastic. arXiv:1809.08852v2 [physics.atom-ph]

We report on the fabrication of an all-glass vapor cell with a thickness varying linearly between (exactly) 0 and ∼ 1 µm. The cell is made in Borofloat glass that allows super polish roughness, a full optical bonding assembling and easy filling with alkali vapors. We detail the challenging manufacture steps and present experimental spectra resulting from off-axis fluorescence and transmission spectroscopy of the Cesium D1 line. The very small surface roughness of 1Å rms is promising to investigate the atom-surface interaction or to minimize parasite stray light.

We demonstrate a method for measuring atom-surface interactions using transmission spectroscopy of thermal vapors confined in a wedged nano-cell. The wedged shape of the cell allows complementary measurements of both the bulk atomic vapor and atoms close to surfaces experiencing strong van der Waals atom-surface interaction. These are used to tightly constrain the dipole-dipole collisional parameters of a theoretical model for transmission spectra that accounts for atom-surface interactions, cavity effects, collisions with the surface of the cell and atomic motion. We illustrate this method on a cesium vapor in a sapphire cell, find C 3 = 1.3 ± 0.1 kHz.µm 3 and demonstrate that even the weakest of the van der Waals atom-surface interaction coefficients -for ground-state alkali atom transitions -can be determined with a very good precision. This result paves the way towards a precise quantitative characterization of atomsurface interactions in a wide range of atom-based nano-devices.

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