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arXiv:cond-mat/0608449 · Physical Review A

Investigation and comparison of multistate and two-state atom laser-output couplers

Julien Dugué, Nicholas P. Robins, C. Figl, Matthew Jeppesen, P. Summers, Mattias Johnsson, J. J. Hope, J. D. Close

Published May 4, 2007• 12 citations
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Abstract

We investigate the spatial structure and temporal dynamics created in a Bose-Einstein condensate by radio-frequency atom laser-output couplers using a one-dimensional mean-field model. We compare the behavior of a ``pure'' two-state atom laser to the multilevel systems demonstrated in laboratories. In particular, we investigate the peak homogeneous output flux, classical fluctuations in the beam, and the onset of a bound state which shuts down the atom laser output.

DOI
10.1103/physreva.75.053602

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We investigate the spatial structure and temporal dynamics created in a Bose-Einstein condensate by radio-frequency atom laser-output couplers using a one-dimensional mean-field model. We compare the behavior of a ``pure'' two-state atom laser to the multilevel systems demonstrated in laboratories. In particular, we investigate the peak homogeneous output flux, classical fluctuations in the beam, and the onset of a bound state which shuts down the atom laser output.
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 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.
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
We present experimental results demonstrating that the flux of a continuous atom laser beam cannot be arbitrarily increased by increasing the strength of output-coupling. We find that a state changing output-coupler for a continuous atom laser switches off as the output-coupling strength, parameterized by the Rabi frequency, is increased above a critical value of four times the radial trapping frequency. In addition, we find that the continuous atom laser has large classical fluctuations when the Rabi frequency is greater than the radial trapping frequency, due to the output-coupling populating all accessible Zeeman states. The numerical solution of a one-dimensional 5-state Gross-Pitaevskii model for the atom laser is in good qualitative agreement with the experiment.
We develop the quantum-mechanical description of output coupling of macroscopic coherent matter waves from a Bose-Einstein condensate (BEC) via a radio-frequency field in the pulsed and cw limits for both strong and weak field coupling. The theory is converted into a Fock state description to point out the stimulated (in Bose particle) nature of the output coupling. A useful analogy with the theory of molecular photodissociation is used to explain the various regimes of output coupling BECs using radiation sources. We present specific calculations of the rates of output coupling as a function of the number of Bose atoms in the condensate and the frequency, detuning, and intensity of the radio-frequency field.
The regions of validity of the Markov approximation for the coupling of atoms out of an atomic trap are determined. We consider radio-frequency output coupling in the presence of gravity and collisional repulsion, and Raman output coupling. The Markov approximation is crucial in most theoretical descriptions of an atom laser that assume a continuous process of output coupling from a trapped Bose-Einstein condensate. In this regime many techniques that have proved to be useful for modeling the optical laser, such as master equations, can be used to describe the dynamics of the damping of the condensate mode undergoing output coupling.