Abstract
Pumps are transport mechanisms in which direct currents result from a cyclic evolution of the potential1,2. As Thouless showed, the pumping process can have topological origins, when considering the motion of quantum particles in spatially and temporally periodic potentials3. However, the periodic evolution that drives these pumps has always been assumed to be imparted from outside, as has been the case in the experimental systems studied so far4,5,6,7,8,9,10,11,12. Here we report on an emergent mechanism for pumping in a quantum gas coupled to an optical resonator, where we observe a particle current without applying a periodic drive. The pumping potential experienced by the atoms is formed by the self-consistent cavity field interfering with the static laser field driving the atoms. Owing to dissipation, the cavity field evolves between its two quadratures13, each corresponding to a different centrosymmetric crystal configuration14. This self-oscillation results in a time-periodic potential analogous to that describing the transport of electrons in topological tight-binding models, such as the paradigmatic Rice–Mele pump15. In the experiment, we directly follow the evolution by measuring the phase winding of the cavity field with respect to the driving field and observing the atomic motion in situ. The observed mechanism combines the dynamics of topological and open systems, and features characteristics of continuous dissipative time crystals.
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Data availability
The data to reproduce the figures of this study are available in the data repository of ETH Zurich’s Research Collection (http://www.research-collection.ethz.ch) at https://doi.org/10.3929/ethz-b-000547966.
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Acknowledgements
We thank A. Frank for support with the heterodyne electronics; and O. Zilberberg and N. Spaldin for discussion. We acknowledge funding from SNF project numbers IZBRZ2_186312, 182650 and 175329 (NAQUAS QuantERA) and NCCR QSIT, from EU Horizon2020 ERCadvanced grant TransQ (project number 742579) and ITN grant ColOpt (project number 721465).
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D.D., A.B. and X.L. prepared the experiment, D.D., A.B., X.L. and S.H. took and analysed the data. D.D. performed the numerical simulations. T.D. and T.E. supervised the work. All authors contributed to discussions of the manuscript.
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Extended data figures and tables
Extended Data Fig. 1 Non-averaged phase diagram and repeated measurement results.
a, Phase diagram using the phase data ϕ(t) from the heterodyne detector by varying cavity detuning ΔC of cavity 1. The two different self-organized phases can be well observed for values around ϕ = 0 and ϕ = π/2. At low transverse beam fields the system shows no self-organization and ϕ is not well defined. Between the two self-organized phases the dynamical phase with varying ϕ(t) is visible. b, Many repetitions of the same trace with constant ΔC = −1.1 MHz. The extent of the instability region varies slightly at each repetition.c, Same data as in b, but shifted in time such that the onset of pumping coincides for all traces. The dashed line as guide to the eye illustrates that the rate at which the phase evolves is robust.
Extended Data Fig. 2 Schematic representation of the theoretical models.
a, Self-consistent loop between cavity field α, optical lattice Vlattice and wavefunction ψ as described by the set of equations Eq. (5) and Eq. (11).b, Minimal model given by the three-level momentum expansion of Eq. (14). The coherent coupling (solid arrows) mixes the condensate mode ψ0 with the spatially modulated ψp,q, which are then mutually coupled by dissipation (dashed arrows).
Extended Data Fig. 3 Comparison of experimental and numerical phase diagrams.
Figures show the amplitude of the intracavity light field dependent on V0 and the cavity detuning Δc for cavity 2. a, Dataset showing in each row a trace of single experimental realization for the given cavity detuning Δc. The transverse beam lattice is linearly ramped to the final transverse lattice strength V0 = 40 Er within 5 ms. b, Corresponding simulation of the experimental results with GPE simulation.
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Dreon, D., Baumgärtner, A., Li, X. et al. Self-oscillating pump in a topological dissipative atom–cavity system. Nature 608, 494–498 (2022). https://doi.org/10.1038/s41586-022-04970-0
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DOI: https://doi.org/10.1038/s41586-022-04970-0
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