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Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)

From Optical Lattice Clocks to the Measurement of Forces in the Casimir Regime

Peter Wolf, P. Lemonde, Astrid Lambrecht, S. Bize, Arnaud Landragin, André Clairon

Published Jun 1, 2006• 6 citations
Publisher

Abstract

The authors propose a novel experiment based on atoms trapped close to a macroscopic surface, to study the interactions between the atoms and the surface at very small separations (0.6 to 10 mum). In this range the dominant potential is the QED interaction (Casimir-Polder and Van der Waals) between the surface and the atom. Additionally, several theoretical models suggest the possibility of Yukawa type potentials with sub-mm range, arising from new physics related to gravity. The paper proposes a set-up very similar to neutral atom optical lattice clocks, but with the atoms trapped in lattice sites close to the reflecting mirror. A sequence of pulses of the probe laser at different frequencies is then used to create an interferometer with a coherent superposition between atomic states at different distances from the mirror (in different lattice sites). Assuming atom interferometry state of the art measurement of the phase difference and a duration of the superposition of about 0.1s we expect to be able to measure the potential difference between separated states with an uncertainty of about 10-4Hz. A preliminary analysis of systematic effects for different atoms (Sr, Yb, Rb, Cs) indicates no fundamentally limiting effect at the same level of uncertainty, but does influence the choice of atom and isotope. Based on those estimates, we expect that such an experiment would improve the best existing measurements of the atom-wall QED interaction by <2 orders of magnitude, whilst gaining up to 4 orders of magnitude on the best present limits on new interactions in the range between 100 nm and 100mum

DOI
10.1109/freq.2006.275357

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From optical lattice clocks to the measurement of forces in the Casimir regime

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The Casimir-Polder (CP) effect -- the force between a neutral atom and an uncharged conducting plate in empty space -- is an intriguing consequence of quantum vacuum fluctuations. The typically attractive CP potential crosses over from a scaling of $z^{-3}$ at short separations to $z^{-4}$ at long distances, where retardation effects due to the finite speed of light become important. At intermediate distances, where the atom--surface separation is of the order of the wavelength of the dominant atomic transition, experiments have so far relied on indirect methods, such as diffraction or quantum reflection, to observe the CP effect. Here, we directly reveal the CP force between strontium atoms and a dielectric surface via the induced shifts in the atomic energy levels in the intermediate regime. We spectroscopically probe the CP-induced kHz-frequency shift of ultracold atoms confined by a magic-wavelength optical lattice at 189(2)~nm from the surface -- on the scale of the dominant 461-nm transition. Our measurements agree well with QED calculations and differ from the short-range approximation, while excluding the long-distance one. This paves the way for studying the CP effect across various surface properties and geometries, as well as exploring the tensor nature of the atom-surface potential -- all important for the development of hybrid atomic optical-magnetic quantum devices.

quant-pharXiv:2604.14721•Apr 17, 2026•0 citations
The authors propose a novel experiment based on atoms trapped close to a macroscopic surface, to study the interactions between the atoms and the surface at very small separations (0.6 to 10 mum). In this range the dominant potential is the QED interaction (Casimir-Polder and Van der Waals) between the surface and the atom. Additionally, several theoretical models suggest the possibility of Yukawa type potentials with sub-mm range, arising from new physics related to gravity. The paper proposes a set-up very similar to neutral atom optical lattice clocks, but with the atoms trapped in lattice sites close to the reflecting mirror. A sequence of pulses of the probe laser at different frequencies is then used to create an interferometer with a coherent superposition between atomic states at different distances from the mirror (in different lattice sites). Assuming atom interferometry state of the art measurement of the phase difference and a duration of the superposition of about 0.1s we expect to be able to measure the potential difference between separated states with an uncertainty of about 10-4Hz. A preliminary analysis of systematic effects for different atoms (Sr, Yb, Rb, Cs) indicates no fundamentally limiting effect at the same level of uncertainty, but does influence the choice of atom and isotope. Based on those estimates, we expect that such an experiment would improve the best existing measurements of the atom-wall QED interaction by <2 orders of magnitude, whilst gaining up to 4 orders of magnitude on the best present limits on new interactions in the range between 100 nm and 100mum
We describe an experiment based on atoms trapped close to a macroscopic surface, to study the interactions between the atoms and the surface at very small separations $(0.6--10\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m})$. In this range the dominant potential is the QED interaction (Casimir-Polder and van der Waals) between the surface and the atom. Additionally, several theoretical models suggest the possibility of Yukawa-type potentials with sub-millimeter range, arising from new physics related to gravity. The proposed setup is very similar to neutral atom optical lattice clocks, but with the atoms trapped in lattice sites close to the reflecting mirror. A sequence of pulses of the probe laser at different frequencies is then used to create an interferometer with a coherent superposition between atomic states at different distances from the mirror (in different lattice sites). Assuming atom interferometry state-of-the-art measurement of the phase difference and a duration of the superposition of about 0.1s0.1\phantom{\rule{0.3em}{0ex}}\mathrm{s}0.1s, we expect to be able to measure the potential difference between separated states with an uncertainty of $\ensuremath{\approx}{10}^{\ensuremath{-}4}\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}$. An analysis of systematic effects for different atoms and surfaces indicates no fundamentally limiting effect at the same level of uncertainty, but does influence the choice of atom and surface material. Based on those estimates, we expect that such an experiment would improve the best existing measurements of the atom-wall QED interaction by \ensuremath{\geqslant} 2 orders of magnitude, while gaining up to four orders of magnitude on the best present limits on new interactions in the range between 100nm100\phantom{\rule{0.3em}{0ex}}\mathrm{nm}100nm and $100\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$.
We explore the feasibility of probing atom-wall interaction with atomic clocks based on atoms trapped in engineered optical lattices. Optical lattice is normal to the wall. By monitoring the wall-induced clock shift at individual wells of the lattice, one would measure the dependence of the atom-wall interaction on the atom-wall separation. We find that the induced clock shifts are large and observable at already experimentally demonstrated levels of accuracy. We show that this scheme may uniquely probe the long-range atom-wall interaction in all three qualitatively distinct regimes of the interaction: van der Waals (image-charge interaction), Casimir-Polder (QED vacuum fluctuations), and Lifshitz (thermal-bath fluctuations) regimes.
This dissertation describes our experimental investigations of quantum transport and atomic motion control using optical potentials.The system we study consists of ultracold sodium atoms under the influence of light forces.First, we introduce the dynamics of neutral atoms in a periodic optical potential.The system resembles the textbook problem of an electron inside the crystalline lattice, and we review the main characteristics of the interaction for the atom optics case.In particular, atoms trapped in a lattice subject to large accelerations undergo Landau-Zener tunneling, process which makes the system unstable.The number of atoms trapped in the potential shows the characteristic exponential decay over time.However, deviations from this law are predicted by quantum mechanics.We use the experimental access to the non-exponential time to demonstrate the Quantum Zeno and Anti-Zeno effects.These effects show the influence of frequent observations on the decay rate of a quantum unstable system.The second part of the dissertation introduces a new system we plan to study, namely, the quantum interaction between sodium atoms in the ground ix state and a conductive surface.We are interested in the measurement of the Casimir-Polder potential with a precision of better than 1%.In order to do this, we have chosen to launch the atoms towards the surfaces at very small incident velocities (a few mm/s), and measure the influence of the interaction on the reflection probability.Atoms reflect from the purely attractive potential due to quantum reflection, an effect with no classical analogy.The experimental observation of quantum reflection requires atomic distributions with temperatures below 1 µK.For this purpose, we have produced and studied a Bose-Einstein condensate (BEC) with sodium atoms.The region where the BEC is created is separated spatially form the surfaces by a distance of 10 cm, vertically.In order to bring the atoms close to the surfaces prior to their launching, we have developed an optical elevator.The elevator uses a moving optical lattice in the regime where tunneling is negligible.Results of the macroscopic optical transport technique, and current progress towards a measurement of the Casimir-Polder interaction, are reported.
Casimir and Casimir-Polder effects are forces between electrically neutral bodies and particles in vacuum, arising entirely from quantum fluctuations. The modification to the vacuum electromagnetic-field modes imposed by the presence of any particle or surface can result in these mechanical forces, which are often the dominant interaction at small separations. These effects play an increasingly critical role in the operation of micro- and nano-mechanical systems as well as miniaturized atomic traps for precision sensors and quantum-information devices. Despite their fundamental importance, calculations present theoretical and numeric challenges, and precise atom-surface potential measurements are lacking in many geometric and distance regimes. \n \nThe spectroscopic measurement of Casimir-Polder-induced energy level shifts in optical-lattice trapped atoms offers a new experimental method to probe atom-surface interactions. Strontium, the current front-runner among optical frequency metrology systems, has demonstrated characteristics ideal for such precision measurements. An alkaline earth atom possessing ultra-narrow intercombination transitions, strontium can be loaded into an optical lattice at the “magic” wavelength where the probe transition is unperturbed by the trap light. Translation of the lattice will permit controlled transport of tightly-confined atomic samples to well-calibrated atom- surface separations, while optical transition shifts serve as a direct probe of the Casimir-Polder potential. \n \nWe have constructed a strontium magneto-optical trap (MOT) for future Casimir-Polder experiments. This thesis will describe the strontium apparatus, initial trap performance, and some details of the proposed measurement procedure.
We present the first direct measurements of Casimir-Polder forces between solid surfaces and atomic gases in the transition regime between the electrostatic short-distance and the retarded long-distance limit. The experimental method is based on ultracold ground-state Rb atoms that are reflected from evanescent wave barriers at the surface of a dielectric glass prism. Our novel approach does not require assumptions about the potential shape. The experimental data are compared to the theoretical predictions valid in the different regimes. They agree best with a full QED calculation.
The Casimir-Polder (CP) effect -- the force between a neutral atom and an uncharged conducting plate in empty space -- is an intriguing consequence of quantum vacuum fluctuations. The typically attractive CP potential crosses over from a scaling of z−3z^{-3}z−3 at short separations to z−4z^{-4}z−4 at long distances, where retardation effects due to the finite speed of light become important. At intermediate distances, where the atom--surface separation is of the order of the wavelength of the dominant atomic transition, experiments have so far relied on indirect methods, such as diffraction or quantum reflection, to observe the CP effect. Here, we directly reveal the CP force between strontium atoms and a dielectric surface via the induced shifts in the atomic energy levels in the intermediate regime. We spectroscopically probe the CP-induced kHz-frequency shift of ultracold atoms confined by a magic-wavelength optical lattice at 189(2)~nm from the surface -- on the scale of the dominant 461-nm transition. Our measurements agree well with QED calculations and differ from the short-range approximation, while excluding the long-distance one. This paves the way for studying the CP effect across various surface properties and geometries, as well as exploring the tensor nature of the atom-surface potential -- all important for the development of hybrid atomic optical-magnetic quantum devices.