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arXiv:cond-mat/9912045 · Journal of Physics B Atomic Molecular and Optical Physics

Radio-frequency coupling of a Bose-Einstein condensate in a TOP trap

J L Martin, C R McKenzie, N R Thomas, D M Warrington, A C Wilson

Published Sep 14, 2000• 9 citations
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Abstract

A radio-frequency (RF) transition is used to convert a pure F = 2, m F = 2 87 Rb Bose-Einstein condensate confined in a TOP trap into a mixture of F = 2, m F = 2 and F = 2, m F = 1 states. We show that the nature of this coupling process is strongly influenced by the presence of the time-varying field of the TOP trap, and complicated by the presence of multiple Zeeman substates. In particular, the effective Rabi frequency associated with the applied RF field is not constant across the spatial extent of the cloud leading to a complex geometry for atom-laser output coupling and `averaging out' of Rabi oscillations. Further, a time-varying detuning can give rise to complex spatial structures.

DOI
10.1088/0953-4075/33/19/307

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A radio-frequency (RF) transition is used to convert a pure F = 2, m F = 2 87 Rb Bose-Einstein condensate confined in a TOP trap into a mixture of F = 2, m F = 2 and F = 2, m F = 1 states. We show that the nature of this coupling process is strongly influenced by the presence of the time-varying field of the TOP trap, and complicated by the presence of multiple Zeeman substates. In particular, the effective Rabi frequency associated with the applied RF field is not constant across the spatial extent of the cloud leading to a complex geometry for atom-laser output coupling and `averaging out' of Rabi oscillations. Further, a time-varying detuning can give rise to complex spatial structures.
Two distinct mechanisms are investigated for transferring a pure 87 Rb Bose-Einstein condensate in the | F = 2, m F = 2 state into a mixture of condensates in all the m F states within the F = 2 manifold. Some of these condensates remain trapped whilst others are output coupled in the form of an elementary pulsed atom laser. Here we present details of the condensate preparation and results of the two condensate output coupling schemes. The first scheme is a radio-frequency technique which allows controllable transfer into available m F states, and the second makes use of Majorana spin-flips to populate all the manifold sub-states equally.
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.
Bose-Einstein condensates present to us the opportunity to probe into the atomic interac- tions that govern a macroscopic quantum mechanical system. The degenerate hyperfine manifold in the bosonic atoms splits in the presence of an external B-field; radio-frequency induced coupling releases experimentally-attainable knowledge about the Zeeman mani- fold in 87Rb. The purpose of this study is to investigate quantum dynamics in two and three-component Bose-Einstein condensate (BEC) systems. We start with a theoretical analysis of Josephson tunneling dynamics between identical BECs trapped in a double potential well, paying particular attention to the non-linear self-trapping effect observed as a consequence of the intra-well interaction. We present a model for the non-equilibrium dynamics in a two-level system and introduce the Rabi oscillations. This is followed by a numerical and experimental investigation of Rabi oscillations in a three-level 87Rb BEC between the F = 1 hyperfine level spin states mF = {1, 0, 1}. The relation between the observed total Rabi frequency and the detuning, along with its effect on the BEC population dynamics is explored. Finally, we explore the possible suspects for the shift of the resonance at strong Rabi frequencies .
We study the effect of strong radio-frequency (rf) fields on a Bose-Einstein condensate (BEC) of chromium atoms, in a regime where the rf frequency is much larger than the Larmor frequency. We use the modification of the Land\'e factor by the rf field to bring all Zeeman states to degeneracy, despite the presence of a static magnetic field of up to 100mG100\phantom{\rule{0.3em}{0ex}}\mathrm{mG}100mG. This is demonstrated by analyzing the trajectories of the atoms under the influence of dressed magnetic potentials in the strong-field regime. We investigate the problem of adiabaticity of the rf dressing process and relate it to how close the dressed states are to degeneracy. Finally, we measure the lifetime of the rf dressed BECs and identify a rf-assisted two-body loss process induced by dipole-dipole interactions.
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.
With radio-frequency fields one can control ultracold atoms in magnetic traps. These fields couple the atomic spin states, and are used in evaporative cooling that can lead to Bose-Einstein condensation in the atom cloud. Also, they can be used in controlled release of the condensate from the trap, thus providing output couplers for atom lasers. In this paper we show that the time-dependent multistate models for these processes have exact solutions that are polynomials of the solutions of the corresponding two-state models. This allows simple, in many cases analytic, descriptions for the time-dependent control of the magnetically trapped ultracold atoms.