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Chinese Physics Letters

Strong Outcoupling from Spin-2 87 Rb Bose–Einstein Condensates

Yang Fan, Xia Lin, Xiaoji Zhou, Xiuquan Ma, Xuzong Chen

Published Jun 16, 2005• 6 citations
Publisher

Abstract

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.

DOI
10.1088/0256-307x/22/7/010

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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.
Summary form only given. We report results concerning both theoretical and experimental studies of collective excitations in connection with the atom laser operation. We use a radio-frequency field to out-couple a coherent matter-wave beam, either continuous or pulsed, from a /sup 87/Rb condensate. The latter scheme itself induces collective excitations in the atom laser. Starting from a condensate in the F=2, m/sub F/=2 state the radio-frequency field populates both trapped and untrapped Zeeman sublevels. A rich phenomenology arises including the production of multiple condensates exhibiting different dynamical behaviour, which make clear evidence of mutual interactions. The use of a static very elongated Ioffe trap allows a precise experimental investigation which can be compared with the predictions based on the solution of the time-dependent Gross-Pitaevskii equation. In the pulsed regime, the sudden change of the internal energy produces collective oscillations in the shape both for the m/sub F/=2 and the m/sub F/=1 trapped condensate. Preliminary results for the m/sub F/=2 atom laser show that the experimental behaviour is likely to be reproduced by the simulations only if mutual interactions are taken into account.
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 87Rb{}^{87}\mathrm{Rb}87Rb in the F=1F=1F=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.
Atom lasers have been demonstrated in both pulsed and semi-continuous modes. The dynamics of these devices is predicted to be dramatically different to the optical laser due to fundamental differences between the two types of boson fields, however to date it is the similarities that have been emphasized. Here we show how the atom laser dynamics are strongly affected by coupling of the output beam back to the condensate. Typically research in the field of Bose-Einstein condensation (BEC) 1 relates to studies of fundamental properties, such as collective modes 2 or to the response of the BEC to external stimuli 3. In contrast, the atom laser is one of the most promising technologies to arise from BEC, being the di-rect atomic equivalent of the optical laser 4. Mewes et al. 5 demonstrated the first atom laser, based on the application of pulsed radio-frequency (RF) fields to induce controlled spin flips from magnetically trapped to un-trapped states of a Bose-Einstein condensate. Later it was shown by Hagley et al. 6 that a pulsed Raman out-coupling could be used to achieve a quasi-continuous multi-state atomic beam. Bloch et al. 7 achieved con-tinuous RF out-coulping for up to 100ms, producing a single state atom laser beam, and showed that this beam could be coherently manipulated in direct analogy to the optical laser 8. These experiments, and others 9,10, have conclusively demonstrated that the outcoupling process can be made coherent. They have also demonstrated a number of other similarities be-tween the optical and atomic lasers such as high flux and low divergence of the output beam. In all these works, the similarities between the two sys-tems have been emphasized, however, ultimately it is the differences such as mass and wavelength that will lead to applications of the atom laser. 1
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.
An atom laser based on RF-outcoupling can be operated in a coherently pulsed way by using two radio frequencies. Such a two-mode atom laser can be described by coupled Gross-Pitaevskii equations which are valid for very low temperatures (T≈0). We have derived analytic expressions for the output rate and the visibility of the pulsed atomic beam in the weak coupling regime. A comparison between the analytical and numerical results shows a good agreement. This proves our assumption that the outcoupling process may be seen as the coherent outcoupling of two independent atomic beams. Though our model is only one-dimensional, we expect also a good agreement with the full 3D situation of experiment; the estimate for the value of the output rate might be only in the right order of magnitude16. Summarizing, the manipulation of trapped Bose condensates with electromagnetic waves opens a wide new area for the field of coherent atom optics.
We present a novel, ultra-bright atom laser and an ultra-cold thermal atom beam. Using rf-radiation we strongly couple the magnetic hyperfine levels of 87 Rb atoms in a trapped Bose–Einstein condensate. The resulting time-dependent adiabatic potential forms a trap, which at low rf-frequencies opens just below the condensate and thus allows an extremely bright well-collimated atom laser beam to emerge. As opposed to traditional atom lasers based on weak coupling of the magnetic hyperfine levels, this technique allows us to outcouple atoms at an arbitrarily large rate. We achieve a flux of 4 × 10 7 atom s -1 , a seven fold increase compared to the brightest atom lasers to date. Furthermore, we demonstrate by two orders of magnitude the coldest thermal atom beam (200 nK).