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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Atomic Vapor Confined in a Nanoscale Geometry: From Mesoscopic to Collective Effects

T. Peyrot, James Keaveney, Yvan R. P. Sortais, Armen D. Sargsyan, Ifan G. Hughes, Jean‐Jacques Greffet, Charles S. Adams, Antoine Browaeys

Published Jun 1, 2019• 0 citations
Publisher

Abstract

When many light emitters are subjected to an electromagnetic field with a wavelength λ, they may react collectively to the field. The resonant resulting, light-induced dipole-dipole interactions between atoms should lead to a collective frequency shift of the atomic lines. This shift, unfortunately named the cooperative or collective Lamb shift (CLS) despite its classical nature, depends on the shape of the sample. I will present a new investigation of the origin and validity of the CLS. To do so, we have measured the transmission resonance line shape of a dense hot vapor of potassium atoms confined in a slab with nanometer thickness. Using a complete model, we extract a density-dependent shift and width of the bulk atomic medium resonance (See Fig. 1(a)), deconvolved from the cavity effect [1].

DOI
10.1109/cleoe-eqec.2019.8871682

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When many light emitters are subjected to an electromagnetic field with a wavelength λ, they may react collectively to the field. The resonant resulting, light-induced dipole-dipole interactions between atoms should lead to a collective frequency shift of the atomic lines. This shift, unfortunately named the cooperative or collective Lamb shift (CLS) despite its classical nature, depends on the shape of the sample. I will present a new investigation of the origin and validity of the CLS. To do so, we have measured the transmission resonance line shape of a dense hot vapor of potassium atoms confined in a slab with nanometer thickness. Using a complete model, we extract a density-dependent shift and width of the bulk atomic medium resonance (See Fig. 1(a)), deconvolved from the cavity effect [1].
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.
Alkali vapors confined in nano-scale cells are promising tools for future integrated atom-based sensor. In this thesis, we investigate the interaction between light and an ensemble of atoms confined in a nano-geometry. We focus on the different processes that can modify the optical response of the atomic ensemble and possibly affect the sensitivity of a sensor based on that technology. First, we study the non-local response of atoms to a light excitation due the atomic motion in thermal vapors. When the distance over which the atoms relaxes is larger than the size of the cell, the optical response depends on the size of the system. We have observed that for transmission spectroscopy, this leads to a periodic modification of the optical response with a period equal to the wavelength of the optical transition. Subsequently we showed that when the density of atom increases, the atomic response becomes local again. In this dense regime, the resonant dipole-dipole interaction in a sub-wavelength geometry leads to collective frequency shifts of the spectral lines. We demonstrate that these shifts were induced by the cavity formed by the cell walls, hence clarifying a long-standing issue. We developed a model to extract the density shifts deconvolved from the cavity effects. Close to a surface, the optical response is also affected by the van der Waals atom-surface interaction. We introduced a new method to extract precisely the strength of this interaction. We also developed a new generation of super-polished glass nano-cells and we presented promising spectroscopic signals. Finally, using these cells, we have compared transmission and off-axis spectroscopic techniques.
We review the definition of cooperative Lamb shift originally introduced by ourselves and S. R. Hartmann in 1973. We point out that the definition specified the preparation of a sample of identical two-level atoms prepared with partial excitation by a short pulse. We spell out in some detail the reasoning behind our assertion that the CLS does not enter into the dielectric constant, which determines the transmission of cw radiation through a sample. We give a prescription, using the transfer matrix formalism, for determining the transmission coefficient through a slab, given the thickness in wavelengths and the dielectric constant. We explore the possibility of achieving a true measurement of the CLS in a gaseous cold-atom cloud, with the help of a large foreign gas broadening of the resonant line.
This thesis presents an investigation of the fundamental interaction between light and matter, realised with a rubidium vapour confined in a cell whose thickness (in the propagation direction) is less than the optical wavelength. This confinement allows observation of spectroscopic features not found in longer cells, such as Dicke narrowing. These effects are measured experimentally and a theoretical model is developed, which allows the characterisation of the medium in terms of the atomic electric susceptibility. Interactions between the atoms and their surroundings, whether this be the walls of the cell or other nearby atoms, are explored. In the frequency domain we ob- serve broadening and shifts of the spectral features due to these interactions. The atom-surface interaction shifts the spectral lines, following the expected 1/r^3 van-der-Waals behaviour. The interatomic dipole-dipole interactions are more complex, and we find cooperative effects play an important role. We present an experimental verification of the full spatial dependence of the cooperative Lamb shift, which follows the theoretical prediction made 40 years ago, an important demonstration of coherent interactions in a thermal ensemble. The interactions also play a role in determining the refractive index of the medium, limiting the maximum near-resonant index to n = 1.31. Using heterodyne interferometry, we experimentally measure an index of n = 1.26± 0.02. This index enhancement leads to large bandwidth regions where a significant slow- or fast-light effect is present. We verify the fast-light effect in the time domain by observing the superluminal propagation of a sub- nanosecond optical pulse, and measure the group index of the medium to be ng = −1.0 ± 0.1 × 10^5, the largest negative group index measured to date. We investigate the radiative decay rate using time-domain fluorescence, and we observe radiation trapping effects in a millimetre-thickness vapour. Fi- nally, we present results on sub-nanosecond coherent dynamics in the system which are achieved by pumping the medium with a strong optical pulse.
According to quantum electrodynamics, the exchange of virtual photons in a system of identical quantum emitters causes a shift of its energy levels. Such shifts, known as cooperative Lamb shifts, have been studied mostly in the near-field regime. However, the resonant electromagnetic interaction persists also at large distances, providing coherent coupling between distant atoms. Here, we report a direct spectroscopic observation of the cooperative Lamb shift of an optical electric-dipole transition in an array of Sr(+) ions suspended in a Paul trap at inter-ion separations much larger than the resonance wavelength. By controlling the precise positions of the ions, we studied the far-field resonant coupling in chains of up to eight ions, extending to a length of 40 μm. This method provides a novel tool for experimental exploration of cooperative emission phenomena in extended mesoscopic atomic arrays.