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Sorting ultracold atoms in a three-dimensional optical lattice in a realization of Maxwell’s demon


In 1872, Maxwell proposed his famous ‘demon’ thought experiment1. By discerning which particles in a gas are hot and which are cold, and then performing a series of reversible actions, Maxwell’s demon could rearrange the particles into a manifestly lower-entropy state. This apparent violation of the second law of thermodynamics was resolved by twentieth-century theoretical work2: the entropy of the Universe is often increased while gathering information3, and there is an unavoidable entropy increase associated with the demon’s memory4. The appeal of the thought experiment has led many real experiments to be framed as demon-like. However, past experiments had no intermediate information storage5, yielded only a small change in the system entropy6,7 or involved systems of four or fewer particles8,9,10. Here we present an experiment that captures the full essence of Maxwell’s thought experiment. We start with a randomly half-filled three-dimensional optical lattice with about 60 atoms. We make the atoms sufficiently vibrationally cold so that the initial disorder is the dominant entropy. After determining where the atoms are, we execute a series of reversible operations to create a fully filled sublattice, which is a manifestly low-entropy state. Our sorting process lowers the total entropy of the system by a factor of 2.44. This highly filled ultracold array could be used as the starting point for a neutral-atom quantum computer.

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Fig. 1: Motion steps and sorting algorithm.
Fig. 2: Perfect filling of 4 × 4 × 3 and 5 × 5 × 2 sublattices.
Fig. 3: Filling fraction and entropy.
Fig. 4: Microwave spectra showing the results of projection sideband cooling18.


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This work was supported by the US National Science Foundation through grant PHY-1520976.

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Authors and Affiliations



All authors contributed to the design, execution and analysis of the experiment and the writing of the manuscript. A.K., T.-Y.W. and F.G. collected all the data.

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Correspondence to David S. Weiss.

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The authors declare no competing interests.

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Extended data figures and tables

Extended Data Fig. 1 Motion step.

A motion step to move n atoms is shown. n atoms are sequentially targeted by the addressing beams and transferred from the ‘stationary’ state to the ‘motion’ state using microwaves. The electro-optic modulator (EO) voltages are ramped up to the half-wave voltage (Vλ/2) in order to move atoms by half of the lattice spacing. After motion, the atoms are optically pumped so that they all return to the stationary state. The EO voltages are then ramped back down. A final optical pumping (OP) ensures optimal preparation for the next motion step.

Extended Data Fig. 2 Motion fidelities.

a, b, Measured motion fidelity as a function of the number of motion steps in |F = 4, mF = −4〉 (a) and |F = 3, mF = −3〉 (b) in the x (maroon circles), y (blue squares) and z (green diamonds) directions. The lines are fits to the data. The error bars represent one standard deviation. Each point corresponds to about 600 atoms.

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Kumar, A., Wu, TY., Giraldo, F. et al. Sorting ultracold atoms in a three-dimensional optical lattice in a realization of Maxwell’s demon. Nature 561, 83–87 (2018).

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  • Three-dimensional Optical Lattice
  • Full Essence
  • Step Motion
  • Motion Fidelity
  • Field Programmable Gate Array (FPGAs)

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