Thermometry and cooling of a Bose gas to 0.02 times the condensation temperature

Journal name:
Nature Physics
Year published:
Published online
Corrected online

Trapped quantum gases can be cooled to impressively low temperatures1, 2, but it is unclear whether their entropy is low enough to realize phenomena such as d-wave superconductivity and magnetic ordering3. Estimated critical entropies per particle for quantum magnetic ordering are ~0.3kB and ~0.03kB for bosons in three- and two-dimensional lattices, respectively4, with similar values for Néel ordering of lattice-trapped Fermi gases5. Here we report reliable single-shot temperature measurements of a degenerate Rb gas by imaging the momentum distribution of thermalized magnons, which are spin excitations of the atomic gas. We record average temperatures fifty times lower than the Bose–Einstein condensation temperature, indicating an entropy per particle of ~0.001kB at equilibrium, nearly two orders of magnitude lower than the previous best in a dilute atomic gas2, 6 and well below the critical entropy for antiferromagnetic ordering of a Bose–Hubbard system. The magnons can reduce the temperature of the system by absorbing energy during thermalization and by enhancing evaporative cooling, allowing the production of low-entropy gases in deep traps.

At a glance


  1. Magnon thermometry.
    Figure 1: Magnon thermometry.

    a, Magnons are created and decohere rapidly in a non-degenerate spinor Bose gas at an intermediate trap depth. Forced evaporative cooling to a final, variable, trap depth reduces the temperature and the majority gas undergoes Bose–Einstein condensation. b,c, Images and corresponding integrated line profiles of the momentum distribution of the majority (b) and magnon gas (c) are each shown at three different final trap depths. Line profiles are shown offset for clarity. A condensate obscures the momentum distribution of the non-condensed fraction of the majority gas, especially at low temperatures. In contrast, the magnons can have little to no condensed fraction, allowing non-condensed magnons to be identified and the temperature determined.

  2. Thermometry results.
    Figure 2: Thermometry results.

    a,b, Two runs (blue circles, green squares) differ in initial atom number (about three and five million atoms at T = Tc, respectively). T (a) and T/Tc (b) are measured at various optical trap depths. Lower T and T/Tc are achieved in runs with larger initial atom number. a, Thermometry using the majority gas (light grey diamonds) agree with the thermalized magnon thermometry extrapolated to the zero-magnon values (circles and squares). Error bars show the statistical uncertainty of extrapolated temperature (vertical) and the systematic uncertainty in trap depth (horizontal). Thin diagonal grey lines show contours of η, the ratio of trapping potential depth to temperature. Inset: the magnon-free temperature is determined by extrapolating single-shot temperatures (‘crosses) versus total number of magnons imaged, here at trap depth of kB × 800 nK, to the zero-magnon limit (circle). A similar extrapolation determines the value of T/Tc achieved by evaporation only. b, Efficiency of evaporation only (circles, squares), with error bars showing statistical uncertainty of the extrapolated T/Tc, is compared against magnon-assisted evaporation (‘crosses). Solid lines connecting points are guides to the eye, with a steeper slope indicating more efficient evaporation. Dotted lines connect corresponding points at the same trap depth. The thick grey lines showing μ/kBTc are calculated using the frequencies of the kB × 60 nK deep trap.

  3. Cycled decoherence cooling.
    Figure 3: Cycled decoherence cooling.

    a, Magnons are created at the final trap depth and cool the gas as they thermalize. Thermalized magnons can be removed from the trap and the cooling process repeated before measuring the temperature by imaging the momentum distribution of the thermalized magnons. b, Each non-condensed magnon removed from the trap takes energy from the gas. Decoherence cooling trajectories are plotted versus cumulative number of magnons removed. Filled circles show temperatures after a single cycle of decoherence, but with varying numbers of magnons. Some additional magnon-assisted evaporative cooling may also be present. Open triangles show repeated cycles of magnon creation, thermalization and purge, with representative error bars on the first and last triangles giving statistical error over several repetitions. Solid lines show zero-free-parameter theory predictions assuming each non-condensed magnon removes 3 kBT energy. Shaded areas indicate the range of predictions included within the uncertainty in the cumulative number of magnons removed (we image 75% ± 10% of the magnons present). Inset: the amount of energy removed by each magnon, in units of kBT, is plotted versus the ratio of μ/kBT, where each point is based on an estimate of the slope over four consecutive triangle points. We observe that the net energy carried away by magnons vanishes when T μ/kB. c, Efficiency of evaporation only (open circles) is compared against cycled decoherence cooling (open triangles), with error bars representing statistical uncertainty. The solid line between circles is a guide to the eye. Dotted lines connect corresponding points at the same trap depth. Compared to evaporation, decoherence cooling can reach considerably lower T/Tc at the same trap depth in the regime T μ/kBT and T/Tc 0.9.

Change history

Corrected online 20 August 2015
In the version of this Letter originally published ref. 2 was mistakenly reproduced as ref. 26. Ref. 26 has been removed and the reference list has been renumbered in all versions of the Letter.


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Author information

  1. Present address: JILA, National Institute of Standards and Technology and University of Colorado, Boulder, Colorado 80309-0440, USA.

    • G. Edward Marti


  1. Department of Physics, University of California, Berkeley, California 94720, USA

    • Ryan Olf,
    • Fang Fang,
    • G. Edward Marti,
    • Andrew MacRae &
    • Dan M. Stamper-Kurn
  2. Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

    • Dan M. Stamper-Kurn


All authors provided experimental support and commented on the manuscript. Experimental data were acquired by R.O. and F.F., and analysed by R.O. G.E.M. conceived and performed preliminary experiments with cycled decoherence cooling. The manuscript was prepared by R.O. and D.M.S.-K. R.O. performed the calculations of entropy per particle. D.M.S.-K. supervised all work.

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