19 99 Heating of trapped atoms near thermal surfaces

We study the electromagnetic coupling and concomitant heating of a particle in a miniaturized trap close to a solid surface. Two dominant heating mechanisms are identified: proximity fields generated by thermally excited currents in the absorbing solid and time-dependent image potentials due to elastic surface distortions (Rayleigh phonons). Estimates for the lifetime of the trap ground state are given. Ions are particularly sensitive to electric proximity fields: for a silver substrate, we find a lifetime below one second at distances closer than some ten μm to the surface. Neutral atoms may approach the surface more closely: if they have a magnetic moment, a minimum distance of one μm is estimated in tight traps, the heat being transferred via magnetic proximity fields. For spinless atoms, heat is transferred by inelastic scattering of virtual photons off surface phonons. The corresponding lifetime, however, is estimated to be extremely long compared to the timescale of typical experiments. 03.75 – Matter waves 32.80.Lg – Mechanical effects of light on atoms and ions 03.67 – Quantum computation The last few years have witnessed an increasing interest in tightly confining traps of cold particles. These devices allow to envisage a broad spectrum of applications ranging from single-mode coherent matter wave manipulation and low-dimensional quantum gases [1, 2, 3, 4] to quantum logical registers [5, 6]. Since steep trapping fields exist near surfaces, traps in their vicinity enjoy increasing popularity. This raises the question at what timescale the cold particles in these “surface assisted traps” will be heated up, and how they are coupled to the nearby bulk which is typically at room temperature [7, 8]. The question is of primordial importance for the above-mentioned applications since the heat transfer to the trap inevitably destroys the coherence of the matter waves [6]. In this Letter, we outline simple models that allow to compute the lifetime of the trapped particle which is limited due to its coupling to thermal excitations of the nearby solid. The interaction with thermal blackbody radiation is certainly a candidate for a mechanism of heating and decoherence. Estimates given by Lamoreaux [7] show, however, that this source is negligible for typical trap configurations. This is mainly due to the fact that the trapped particles are most sensitive to the field fluctuations at the resonant trap oscillation frequency (a few MHz at most) which is rather low compared to thermal frequencies which are in the THz range. More importantly, the resonant photon wavelengths are at least several meters. This means that the particle is always located in the near field of its macroscopic environment where the electromagnetic field fluctuations differ from the free-space blackbody field [9, 10]. The excitations of the solid that give rise to this near-field effect come in two species: fluctuating electric currents related to the dissipation in the solid (finite electric conductivity), and elastic waves (Rayleigh phonons) that propagate along the surface. Current fluctuations generate electric and magnetic fields above the surface (“proximity fields”) that couple to the particle’s charge, spin or polarisability. Surface waves, on the other hand, distort the electrostatic image of the particle in the solid and lead to a time-dependent image potential. We find that ions are particularly sensitive to proximity fields and estimate a typical lifetime of less than a second for distances smaller than 10μm above a metal surface. Atoms, beemail: [email protected]