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arXiv:1906.05196

Outcoupling from a Bose-Einstein condensate in the strong-field limit

Arnold, Caroline, Carola Beck, Peter Federsel, Malte Reinschmidt, József Fortágh, Andreas Günther, Daniel Braun

Published Jun 12, 2019• 0 citations

Abstract

Atoms can be extracted from a trapped Bose-Einstein condensate (BEC) by driving spin-flips to untrapped states. The coherence properties of the BEC are transfered to the released atoms, creating a coherent beam of matter refered to as an atom laser. In this work, the extraction of atoms from a BEC is investigated numerically by solving a coupled set of Gross-Pitaevskii equations in up to three dimensions. The result is compared to experimental data and a semiclassical rate model. In the weak-coupling regime, quantitative agreement is reached between theory and experiment and a semiclassical rate model. In the strong-coupling regime, the atom laser enters a trapped state that manifests itself in a saturation of the rate of out-coupled atoms observed in new experimental data. The semiclassical rate model fails, but the numerical descriptions yield qualitative agreement with experimental data at the onset of saturation.

DOI: 10.48550/arxiv.1906.05196

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Atoms can be extracted from a trapped Bose-Einstein condensate (BEC) by driving spin-flips to untrapped states. The coherence properties of the BEC are transfered to the released atoms, creating a coherent beam of matter refered to as an atom laser. In this work, the extraction of atoms from a BEC is investigated numerically by solving a coupled set of Gross-Pitaevskii equations in up to three dimensions. The result is compared to experimental data and a semiclassical rate model. In the weak-coupling regime, quantitative agreement is reached between theory and experiment and a semiclassical rate model. In the strong-coupling regime, the atom laser enters a trapped state that manifests itself in a saturation of the rate of out-coupled atoms observed in new experimental data. The semiclassical rate model fails, but the numerical descriptions yield qualitative agreement with experimental data at the onset of saturation.

Atom lasers based on rf outcoupling from a trapped Bose-Einstein condensate can be described by a set of generalized, coupled Gross-Pitaevskii equations (GPEs). If not only one but two radio frequencies are used for outcoupling, the atoms emerging from the trap have two different energies and the total wave function of the untrapped spin state is a coherent superposition which leads to a pulsed atomic beam. We present results for such a situation obtained from a one-dimensional GPE model for magnetically trapped

{}^{87}\mathrm{Rb}

in the

F=1

state. The wave function of the atomic beam can be approximated by a sum of two Airy functions. In the limit of weak coupling we calculate the intensity analytically.

We study the dynamics of a magnetically trapped Bose-Einstein condensate in the presence of an external electromagnetic-field coupling trapped, untrapped, and antitrapped Zeeman sublevels. For large condensates an approximate analytical solution of the coupled Gross-Pitaevskii equations is given in the regime of strong outcoupling. The theory is developed for the cases of rf outcoupling within a hyperfine manifold of states, microwave outcoupling connecting states in two different hyperfine manifolds, and Raman outcoupling.

We study the coherence properties of an atom laser, which operates by extracting atoms from a gaseous Bose-Einstein condensate via a two-photon Raman process, by analysing a recent experiment (Hagley et al 1999 Phys. Rev. Lett. 83 3112). We obtain good agreement with the experimental data by solving the time-dependent Gross-Pitaevskii equation in three dimensions both numerically and with a Thomas-Fermi model. The coherence is strongly affected by the space-dependent phase developed by the condensate when the trapping potential is turned off.

We consider the possibility of a discrete set of energies of a weakly outcoupled atom laser beam to the homogeneous Schrödinger equation with anisotropic harmonic trap in Cartesian coordinates outside the Bose–Einstein condensate region. This treatment is used because working in the cylindrical coordinates is not really possible, even though we implement the cigar-shaped trap case. The Schrödinger equation appears to replace a set of two-coupled Gross– Pitaevskii equations by enabling the weak-coupling assumption. This atom laser can be produced in a simple way that only involves extracting the atoms in a condensate from by using the radio frequency field. We initially present the relation between condensates as sources and atom laser as an output by exploring the previous work of Riou et al. in the case of theoretical work for the propagation of atom laser beams. We also show that even though the discrete energies are obtained by means of an approaching harmonic oscillator, degeneracy is only available in two states because of the anisotropic external potential

A pulsed atom laser is experimentally demonstrated by means of outcoupling coherent atoms from 87 Rb Bose–Einstein condensates in magnetic trap via radio-frequency pulses. To study the strong outcoupling dynamics of the atom laser, the original | F = 2, m F = 2⟩ condensate and the coupled | F = 2, m F = 1⟩ component, both of which overlap in space usually, are separated spatially by collective oscillations. The number of atoms in three of the five Zeeman states are measured and compared with the theoretical results.