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 nfining traps of cold particles. These devices allow to envisage broad spectrum of applications ranging from single-mode cohermatter wave manipulation and low-dimensional quantum gases 2, 3, 4] to quantum logical registers [5, 6]. Since steep trapping ds exist near surfaces, traps in their vicinity enjoy increasing popuity. This raises the question at what timescale the cold particles in ese “surface assisted traps” will be heated up, and how they are coud to the nearby bulk which is typically at room temperature [7, 8]. e question is of primordial importance for the above-mentioned apcations since the heat transfer to the trap inevitably destroys the herence of the matter waves [6]. In this Letter, we outline simple models that allow to compute the time of the trapped particle which is limited due to its coupling thermal excitations of the nearby solid. The interaction with theral blackbody radiation is certainly a candidate for a mechanism of ating and decoherence. Estimates given by Lamoreaux [7] show, wever, that this source is negligible for typical trap configurations. is is mainly due to the fact that the trapped particles are most nsitive to the field fluctuations at the resonant trap oscillation freency (a few MHz at most) which is rather low compared to thermal quencies which are in the THz range. More importantly, the resant photon wavelengths are at least several meters. This means at the particle is always located in the near field of its macroscopic vironment where the electromagnetic field fluctuations differ from e free-space blackbody field [9, 10]. The excitations of the solid at give rise to this near-field effect come in two species: fluctuating ctric currents related to the dissipation in the solid (finite electric nductivity), and elastic waves (Rayleigh phonons) that propagate along the surface. Current fluctuations generate electric and magne fields above the surface (“proximity fields”) that couple to the par cle’s charge, spin or polarisability. Surface waves, on the other han distort the electrostatic image of the particle in the solid and lead a time-dependent image potential. We find that ions are particula sensitive to proximity fields and estimate a typical lifetime of l than a second for distances smaller than 10μm above a metal surfa Atoms, being neutral particles, are less affected by the presence the “hot” surface: for a nonzero magnetic moment, they survive s eral minutes even at distances of a few micrometers. Finally, spinl atoms are completely decoupled from the surface at experimenta relevant time scales. 1 Model We consider a particle in the ground state |0〉 of a one-dimensio harmonic trap (oscillation frequency ωt) that is oriented along t unit vector n (see fig.1) To simplify the calculations, we assume th the trap is located above a flat surface whose distance z from the tr center is large compared to the size a = (h̄/(2Mωt)) of the grou state wave function (M is the particle’s mass). The interaction p tential for the particle is then of the form V (t) = −x · F(r, t) where x = xn is the displacement of the particle from the trap cen and F(r, t) is a fluctuating force field at the trap position r. If t force shows fluctuations at the trap frequency, it may resonantly exc ∗email: [email protected]