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arXiv:1304.6278 · Physical Review A

Lifetimes of atoms trapped in an optical lattice in proximity of a surface

Sophie Pelisson, Riccardo Messina, Marie-Christine Angonin, Peter Wolf

Published Jul 15, 2013• 4 citations
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Abstract

We study the lifetime of an atom trapped in an optical vertical lattice in proximity of a massive surface using a complex-scaling approach. We analyze how the presence of the surface modifies the known lifetimes of Wannier-Stark states associated with Landau-Zener tunneling. We also investigate how the existence of a hypothetical short-distance deviation from Newton's gravitational law could affect these lifetimes. Our study is relevant in order to discuss the feasibility of any atomic-interferometry experiment performed near a surface. Finally, the difficulties encountered in applying the complex-scaling approach to the atom-surface Casimir-Polder interaction are addressed.

DOI
10.1103/physreva.88.013411

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We study the lifetime of an atom trapped in an optical vertical lattice in proximity of a massive surface using a complex-scaling approach. We analyze how the presence of the surface modifies the known lifetimes of Wannier-Stark states associated with Landau-Zener tunneling. We also investigate how the existence of a hypothetical short-distance deviation from Newton's gravitational law could affect these lifetimes. Our study is relevant in order to discuss the feasibility of any atomic-interferometry experiment performed near a surface. Finally, the difficulties encountered in applying the complex-scaling approach to the atom-surface Casimir-Polder interaction are addressed.
We study the energy spectrum of atoms trapped in a vertical one-dimensional optical lattice in close proximity to a reflective surface. We propose an effective model to describe the interaction between the atoms and the surface at any distance. Our model includes the long-range Casimir-Polder potential together with a short-range Lennard-Jones potential, which are considered nonperturbatively with respect to the optical lattice potential. We find an intricate energy spectrum which contains a pair of loosely bound states localized close to the surface in addition to a surface-modified Wannier-Stark ladder at long distances. Atomic interferometry involving those loosely bound atom-surface states is proposed to probe the adsorption dynamics of atoms on mirrors.
In this paper, we discuss the atomic states in a vertical optical lattice in proximity of a surface. We study the modifications to the ordinary Wannier-Stark states in the presence of a surface, and we characterize the energy shifts produced by the Casimir-Polder interaction between atom and mirror. In this context, we introduce an effective model describing the finite size of the atom in order to regularize the energy corrections. In addition, the modifications to the energy levels due to a hypothetical non-Newtonian gravitational potential as well as their experimental observability are investigated.
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 propose a novel method to measure the interaction between an ultracold gas of neutral atoms and a surface. This solution combines an optical dipole trap reflected by the surface, a magnetic trap formed by current carrying wires embedded below the surface, and a rotation of the surface itself. It allows to adiabatically transport a 87^{87}87Rb BEC from few μμμm to few hundred nm of the surface. At such distances, atom-surface interaction strongly affects the trapping potential, causing an increase of the tunneling rate towards the surface. In this paper, we show that the measurement of the lifetime of the cloud and its comparison to a tunneling model will allow to extract the Casimir-Polder (CP) force coefficient in the retarded regime (c4c_4c4​). Our model includes noise-induced heating, calibration biases of experimentally controlled parameters and accuracy of the atom lifetime measurement. Using typical trapping parameters and experimental uncertainties, we numerically estimate the relative uncertainty of c4c_4c4​ to be 10%. This method can be implemented with any atomic species that can be magnetically and optically trapped.
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 study the feasibility of precision measurements of surface potentials at micrometre distances using resonant tunnelling of cold atoms trapped in vertical optical lattices. A modulation of an amplitude of the lattice potential induces atomic tunnelling among the lattice sites. The resonant modulation frequency corresponds to a difference of potential energy between lattice sites, which is defined by an external force, i.e. gravity. The vicinity of the surface alters the external potentials, and hence the resonant frequency. Application of this method allows the accurate study of Casimir-type potentials and improvement of the present experimental validity of the Newtonian gravitational potential at a distance range of 5–30 μm.