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Nature Physics

Cooling by numbers

Andreas H. Trabesinger

Published Dec 22, 2011• 1 citation
Publisher
DOI
10.1038/nphys2201

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We explore degenerate Raman sideband cooling in which neighboring Zeeman states of a fixed hyperfine level are coupled via a two-photon Raman transition. The degenerate coupling between ∣F,mF⟩→∣F,mF−1⟩|F,m_F\rangle\rightarrow |F,m_F-1\rangle∣F,mF​⟩→∣F,mF​−1⟩ facilitates the removal of multiple motional quanta in a single cycle. This method greatly reduces the number of cooling cycles required to reach the ground state compared to traditional sideband cooling. We show that near ground state cooling can be achieved with a pulse number as low as nˉ\bar{n}nˉ where nˉ\bar{n}nˉ is the average phonon number in the initial thermal state. We demonstrate proof-of-concept in 176Lu+^{176}\mathrm{Lu}^+176Lu+ by coupling neighboring Zeeman levels on the motional sideband for the F=7F=7F=7 hyperfine level in 3D1^3D_13D1​. Starting from a thermal distribution with an average phonon number of 6, we demonstrate near ground-state cooling with ∼10\sim10∼10 pulses. A theoretical description is given that applies to any FFF level and demonstrates how effective this approach can be.
The dynamics of evaporative cooling of magnetically trapped 87 Rb atoms is studied on the basis of the quantum kinetic theory of a Bose gas. The theoretical optimization of the cooling trajectory clarifies that the acceleration of evaporative cooling around the transition point of Bose-Einstein condensation is very effective against serious three-body recombination loss. The number of condensed atoms is expected to be largely enhanced by the optimization as compared with the typical value produced by the conventional evaporative cooling, where the frequency of the radio-frequency magnetic field is swept exponentially. Next, we precisely examine how the growth of a condensate depends on the experimental parameters of evaporative cooling in this inefficient exponential-sweep cooling. We find that, due to large nonlinear three-body loss, the number of condensed atoms finally becomes insensitive to the initial number of trapped atoms, the initial temperature, and the bias field of a magnetic trap. This result opens up the experimental possibility that the final number of condensed atoms can be well stabilized against the shot-to-shot fluctuations of experimental conditions in evaporative cooling.