Controlling matter to simultaneously support coupled properties is of fundamental and technological importance1 (for example, in multiferroics2,3,4,5 or high-temperature superconductors6,7,8,9). However, determining the microscopic mechanisms responsible for the simultaneous presence of different orders is difficult, making it hard to predict material phenomenology10,11 or modify properties12,13,14,15,16. Here, using a quantum gas to engineer an adjustable interaction at the microscopic level, we demonstrate scenarios of competition, coexistence and mutual enhancement of two orders. For the enhancement scenario, the presence of one order lowers the critical point of the other. Our system is realized by a Bose–Einstein condensate that can undergo self-organization phase transitions in two optical resonators17, resulting in two distinct crystalline density orders. We characterize the coupling between these orders by measuring the composite order parameter and the elementary excitations and explain our results with a mean-field free-energy model derived from a microscopic Hamiltonian. Our system is ideally suited to explore quantum tricritical points18 and can be extended to study the interplay of spin and density orders19 as a function of temperature20.
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We thank E. Demler, S. Gopalakrishnan, A. Narayan, Y. E. Shchadilova and N. Spaldin for insightful discussions. We thank D. Dreon for careful reading of the manuscript and X. Li for experimental assistance. We acknowledge funding for the SBFI Horizon2020 project QUIC (grant agreement 641122) and the Horizon2020 European Training Network ColOpt (grant agreement 721465), and SNF support for the NCCR QSIT and the DACH project ‘Quantum Crystals of Matter and Light’.
The authors declare no competing interests.
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Morales, A., Zupancic, P., Léonard, J. et al. Coupling two order parameters in a quantum gas. Nature Mater 17, 686–690 (2018). https://doi.org/10.1038/s41563-018-0118-1
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