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arXiv:0704.0291 · Physical Review A

Approaching the Heisenberg limit in an atom laser

Matthew Jeppesen, Julien Dugué, G. R. Dennis, Mattias Johnsson, C. Figl, Nicholas P. Robins, J. D. Close

Published Jun 19, 2008• 25 citations
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Abstract

We present experimental and theoretical results showing the improved beam quality and reduced divergence of an atom laser produced by an optical Raman transition, compared to one produced by an rf transition. We show that Raman outcoupling can eliminate the diverging lens effect that the condensate has on the outcoupled atoms. This substantially improves the beam quality of the atom laser, and the improvement may be greater than a factor of 10 for experiments with tight trapping potentials. We show that Raman outcoupling can produce atom lasers whose quality is only limited by the wave function shape of the condensate that produces them, typically a factor of 1.3 above the Heisenberg limit.

DOI
10.1103/physreva.77.063618

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We present experimental and theoretical results showing the improved beam quality and reduced divergence of an atom laser produced by an optical Raman transition, compared to one produced by an rf transition. We show that Raman outcoupling can eliminate the diverging lens effect that the condensate has on the outcoupled atoms. This substantially improves the beam quality of the atom laser, and the improvement may be greater than a factor of 10 for experiments with tight trapping potentials. We show that Raman outcoupling can produce atom lasers whose quality is only limited by the wave function shape of the condensate that produces them, typically a factor of 1.3 above the Heisenberg limit.
We study the properties of an atom laser beam derived from a Bose-Einstein condensate using three different outcouplers, one based on multistate radio-frequency transitions and two others based on Raman transitions capable of imparting momentum to the beam. We first summarize the differences that arise in such systems, and how they may impact on the use of an atom laser in interferometry. Experimentally, we examine the formation of a bound state in all three outcouplers, a phenomenon which limits the atom laser flux, and find that a two-state Raman outcoupler is the preferred option for high-flux, low-divergence atom laser beams.
We present results on a Raman laser-system that resonantly drives a closed two-photon transition between two levels in different hyperfine ground states of (87)Rb. The coupler is based on a novel optical design for producing two phase-coherent optical beams to drive a Raman transition. Operated as an outcoupler, it produces an atom laser in a single internal atomic state, with the lower divergence and increased brightness typical of a Raman outcoupler. Due to the optical nature of the outcoupling, the two-state outcoupler is an ideal candidate for transferring photon correlations onto atom-laser beams. As our laser system couples just two hyperfine ground states, it has also been used as an internal state beamsplitter, taking the next major step towards free space Ramsey interferometry with an atom laser.
We report the experimental realization of a multibeam atom laser. A single continuous atom laser is outcoupled from a Bose-Einstein condensate via an optical Raman transition. The atom laser is subsequently split into up to five atomic beams with slightly different momenta, resulting in multiple, nearly copropagating, coherent beams which could be of use in interferometric experiments. The splitting process itself is a realization of Bragg diffraction, driven by each of the optical Raman laser beams independently. This presents a significantly simpler implementation of an atomic beam splitter, one of the main elements of coherent atom optics.
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
In the present paper, the authors start from the interaction of a system of two-level atoms with an electromagnetic field to drive the interaction Hamiltonian between these two-level atoms. Second, introduce the equations of motion which describing the dynamics of atom laser depending on the interaction Hamiltonian, this interaction Hamiltonian will be used to describe the outcoupling process in a Raman atom laser. Also, the authors model the dynamics of an atom laser produced by outcoupling three-level atoms from a Bose-Einstein condensate (BEC) via a Raman transition and investigate the transfer of quantum statistics from one of the optical modes to the atomic field. Finally, the authors mathematical treatment leads to the same as equations appears in literature which allowed obtaining the dynamics for any atom laser systems.
We have studied the characteristics of an atom laser created by removing atoms from a Bose-Einstein condensate (BEC) via a two-photon Raman process. In contrast with outcoupling by RF transitions, Raman outcoupling offers spatial selectivity within the condensate and delivers significant momentum transfer to the outcoupled atoms. We develop a version of zero-temperature mean-field theory for BECs which includes the internal state of the atom and the effect of laser fields focused into the cloud. For a model condensate we find that the outcoupled matter wave develops sharp peaks at spatial positions where the two-photon Raman process is resonant with the hyperfine splitting of the atomic ground state. As time proceeds the width of the outcoupled wave expands and a steady stream of matter waves travels outside the condensate volume.