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Pattern formation in a driven Bose–Einstein condensate


Pattern formation is ubiquitous in nature at all scales, from morphogenesis and cloud formation to galaxy filamentation. How patterns emerge in a homogeneous system is a fundamental question across interdisciplinary research including hydrodynamics1, condensed matter physics2, nonlinear optics3, cosmology4 and bio-chemistry5,6. Paradigmatic examples, such as Rayleigh–Bénard convection rolls and Faraday waves7,8, have been studied extensively and found numerous applications9,10,11. How such knowledge applies to quantum systems and whether the patterns in a quantum system can be controlled remain intriguing questions. Here we show that the density patterns with two- (D2), four- (D4) and six-fold (D6) symmetries can emerge in Bose–Einstein condensates on demand when the atomic interactions are modulated at multiple frequencies. The D6 pattern, in particular, arises from a resonant wave-mixing process that establishes phase coherence of the excitations that respect the symmetry. Our experiments explore a novel class of non-equilibrium phenomena in quantum gases, as well as a new route to prepare quantum states with desired correlations.

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Fig. 1: Pattern formation in a BEC with interaction modulation at two frequencies.
Fig. 2: Formation of density waves with D6 symmetry.
Fig. 3: Density wave patterns in real space.
Fig. 4: Coherent properties of D4 and D6 density waves.

Data availability

The data represented in Figs. 2d, 3c, 4b,f are available as Source Data Figs. 2, 3 and 4. All other data that support the plots within this paper are available from the corresponding author upon reasonable request.


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We thank K. Patel for careful reading of the manuscript. This work is supported by National Science Foundation (NSF) grant no. PHY-1511696, the Army Research Office Multidisciplinary Research Initiative under grant no. W911NF-14-1-0003 and the University of Chicago Materials Research Science and Engineering Center, which is funded by the NSF under grant no. DMR-1420709. J.H. acknowledges financial support from the National Natural Science Foundation of China under grant no. 11974202.

Author information




Z.Z. and K.-X.Y. performed the experiments, built the theoretical model and analysed the data. L.F. contributed to development of the modulation hardware and pattern recognition scheme. J.H. contributed to the discussion of the results. C.C. supervised the work. All authors contributed to writing the manuscript.

Corresponding author

Correspondence to Cheng Chin.

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The authors declare no competing interests.

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Peer review information Nature Physics thanks Simon Cornish and other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Information.

Source data

Source Data Fig. 2

Correlation of D6 pattern formation.

Source Data Fig. 3

Spatial correlation for different schemes.

Source Data Fig. 4

Angular correlation and phase histogram.

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Zhang, Z., Yao, KX., Feng, L. et al. Pattern formation in a driven Bose–Einstein condensate. Nat. Phys. 16, 652–656 (2020).

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