Decoherence of Bose-Einstein condensates in microtraps

Abstract

We discuss the impact of thermally excited near fields on the coherent expansion of a condensate in a miniaturized electromagnetic trap. Monte Carlo simulations are compared with a kinetic two-component theory and indicate that atom interactions can slow down decoherence. This is explained by a simple theory in terms of the condensate dynamic structure factor. 03.65.Yz, The decoherence of atomic de Broglie waves is a key issue for applications in atom interferometry and quantum information processing. It is particularly relevant for integrated atom optics based on miniaturized hybrid electromagnetic surface traps [1,2] because the atoms couple to a macroscopic, 'hot' substrate nearby. Loss processes due to spin flips driven by thermal magnetic near fields have very recently been observed in the laboratory [3], in agreement with predictions made by one of us [4]. In this paper, we discuss a simple decoherence scenario for Bose-Einstein condensed atomic matter waves in a quasi-one-dimensional microtrap. This setup provides a realization of the standard model of environment-induced decoherence [5] featuring two attractive advantages: (i) the coupling to the environment can be microscopically modelled in terms of the magnetic dipole interaction; (ii) due to atomic interactions, the matter wave equation becomes nonlinear and novel features are expected. We compare Monte Carlo simulations for the condensate order parameter to a kinetic theory for the matter wave coherence function and show that already for moderate interaction parameters, a Bose-Einstein condensate is more robust with respect to a fluctuating environment.We consider an elongated trap similar to those formed above current carrying wires [1]. In the confinement dominated regime, the matter waves can be described in a onedimensional mean field approximation [6] (units withh = m = 1),where the interaction parameter g = 2Ω r a/(1 − 1.46a/a r ) depends on the three-dimensional scattering length a, the radial confinement frequency Ω r and ground state size a r [7]. The density |ψ(x, t)| 2 is normalized to the total number of particles N . The potential V (x, t) determines the dynamics in the axial direction. We assume that for t < 0, the atoms are confined in a harmonic trap with frequency Ω and occupy all the zero-temperature condensate mode φ 0 (x) [8].For t ≥ 0, the axial confinement is switched off, the atoms expand, and we take into account their interaction with magnetic field fluctuations by letting V (x, t) be a random potential. Note that the radial confinement is kept constant. Eq. (1) thus describes the interplay between matter wave interactions and time-dependent noise in an essentially one-dimensional geometry. In contrast to previous work in the field of nonlinear random waves [9, 10], our initial condition does not correspond to a self-contained soliton because we assume repulsive interactions g > 0. Current experiments in wire traps have been hampered by the presence of a static field modulation that leads to the fragmentation of the expandi...

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