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Physical Review Letters

Direct measurement of the van der Waals interaction between an atom and its images in a micron-sized cavity

Vahid Sandoghdar, Charles I. Sukenik, E. A. Hinds, S. Haroche

Published Jun 8, 1992• 204 citations
Publisher

Abstract

We have measured by laser spectroscopy the energy of interaction between a sodium atom and its images in the walls of a micron-sized cavity. This cavity-QED study is the first direct quantitative test of the Lennard-Jones van der Waals interaction as a function of controlled atom-surface separation and mean-square electric dipole moment.
DOI
10.1103/physrevlett.68.3432

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We have measured the energy of interaction between a sodium atom and its electrical images in the walls of a micron‐sized cavity. The atoms are centrally located between two plane parallel gold mirrors whose separation is varied from 500 nm to 2400 nm. In the smallest cavities, the atoms are held near the center by means of a one‐dimensional optical dipole trap. Energy level shifts are measured directly by laser spectroscopy of the states nS with n in the range 10–13. This cavity QED study provides the first direct, quantitative test of the Lennard‐Jones–van der Waals interaction as a function of controlled atom‐surface separation and mean square electric dipole moment.
We have measured the energy of interaction between a sodium atom and its electrical images in the walls of a micron‐sized cavity. The atoms are centrally located between two plane parallel gold mirrors whose separation is varied from 500 nm to 2400 nm. In the smallest cavities, the atoms are held near the center by means of a one‐dimensional optical dipole trap. Energy level shifts are measured directly by laser spectroscopy of the states nS with n in the range 10–13. This cavity QED study provides the first direct, quantitative test of the Lennard‐Jones–van der Waals interaction as a function of controlled atom‐surface separation and mean square electric dipole moment.
Over the past ten years, our group has investigated the effects of confinement on atoms inside metallic micron–sized cavities in order to elucidate some basic phenomena in the field of cavity quantum electrodynamics (QED). The first of these was the inhibition of spontaneous emission from an atom inside a cavity. This was followed by a laser spectroscopic measurement of the van der Waals interaction between a single Rydberg atom and a gold cavity, which showed that a simple electrostatic model of the atom–cavity interaction is correct when the cavity is small enough. More recently, the retarded Casimir–Polder force was measured between a ground state sodium atom and a large cavity, demonstrating that the van der Waals potential fails at long enough range and that the vacuum fluctuations of the field then have an important role in the interaction of the atom with the cavity. Our group is now pushing forward these investigations to study cavities whose walls have losses and dispersion, where the theory of cavity QED is significantly more complicated. With real surfaces, we have to deal with the complex dielectric response ε(ω) of the material, which exhibits frequency–dependent absorption and dispersion. One particularly interesting case is when a downward transition in the atom is resonant with an excitation of the cavity walls. This opens a new branch for the atomic decay: as an alternative to creating a photon within the space surrounded by the cavity walls the atomic decay can now create an electromagnetic excitation of the walls themselves. Another novel feature of our experiments is that the Bohr frequencies of the atom are close to the kT/h, where T is room temperature. We therefore expect to be able to measure effects associated with QED at finite temperature; in other words, to study how the blackbody radiation affects our experiments. By conducting experiments with real surfaces, we hope to elucidate and perhaps simplify the theoretical models used to describe these systems.
We report on the direct measurement of the van der Waals interaction between two isolated, single Rydberg atoms separated by a controlled distance of a few micrometers. By working in a regime where the single-atom Rabi frequency of the laser used for excitation to the Rydberg state is comparable to the interaction energy, we observe a \emph{partial} Rydberg blockade, whereby the time-dependent populations of the various two-atom states exhibit coherent oscillations with several frequencies. A quantitative comparison of the data with a simple model based on the optical Bloch equations allows us to extract the van der Waals energy, and to observe its characteristic C6/R6C_6/R^6C6​/R6 dependence. The magnitude of the measured C6C_6C6​ coefficient agrees well with an \emph{ab-initio} theoretical calculation, and we observe its dramatic increase with the principal quantum number nnn of the Rydberg state. Our results not only allow to test an important physical law, but also demonstrate a degree of experimental control which opens new perspectives in quantum information processing and quantum simulation using long-range interactions between the atoms.
We report the direct measurement of the van der Waals interaction between two isolated, single Rydberg atoms separated by a controlled distance of a few micrometers. Working in a regime where the single-atom Rabi frequency for excitation to the Rydberg state is comparable to the interaction, we observe partial Rydberg blockade, whereby the time-dependent populations of the various two-atom states exhibit coherent oscillations with several frequencies. Quantitative comparison of the data with a simple model based on the optical Bloch equations allows us to extract the van der Waals energy, and observe its characteristic C6/R6 dependence. The measured C6 coefficients agree well with ab initio calculations, and we observe their dramatic increase with the principal quantum number n of the Rydberg state.