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Broadband Lamb shift in an engineered quantum system


The shift of the energy levels of a quantum system owing to broadband electromagnetic vacuum fluctuations—the Lamb shift—has been central for the development of quantum electrodynamics and for the understanding of atomic spectra1,2,3,4,5,6. Identifying the origin of small energy shifts is still important for engineered quantum systems, in light of the extreme precision required for applications such as quantum computing7,8. However, it is challenging to resolve the Lamb shift in its original broadband case in the absence of a tuneable environment. Consequently, previous observations1,2,3,4,5,9 in non-atomic systems are limited to environments comprising narrowband modes10,11,12. Here, we observe a broadband Lamb shift in high-quality superconducting resonators, a scenario also accessing static shifts inaccessible in Lamb’s experiment1,2. We measure a continuous change of several megahertz in the fundamental resonator frequency by externally tuning the coupling strength to the engineered broadband environment, which is based on hybrid normal-metal–insulator–superconductor tunnel junctions13,14,15. Our results may lead to improved control of dissipation in high-quality engineered quantum systems and open new possibilities for studying synthetic open quantum matter16,17,18 using this hybrid experimental platform.

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Fig. 1: Sample and measurement set-up.
Fig. 2: Observation of the Lamb shift.
Fig. 3: Temperature dependence.

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The data that support the findings of this study are available at


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We acknowledge discussions with G. Catelani, A. Clerk, J. Govenius, H. Grabert and J. Tuorila. This research was financially supported by the European Research Council under grant no. 681311 (QUESS) and Marie Skłodowska-Curie grant no. 795159; by the Academy of Finland under its Centres of Excellence Program grant nos. 312300 and 312059 and grant nos. 265675, 305237, 305306, 308161, 312300, 314302, 316551 and 316619; JST ERATO grant no. JPMJER1601, JSPS KAKENHI grant no. 18K03486 and by the Alfred Kordelin Foundation, the Emil Aaltonen Foundation, the Vilho, Yrjö and Kalle Väisälä Foundation, the Jane and Aatos Erkko Foundation and the Technology Industries of Finland Centennial Foundation. We are grateful for the provision of facilities and technical support by Aalto University at OtaNano – Micronova Nanofabrication Centre.

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Authors and Affiliations



M.S. carried out the theoretical analysis and wrote the manuscript with input from all the authors. S.M., V.S. and M.J. conducted the experiments and analysed the data. S.M. and K.Y.T. fabricated the samples. R.E.L., M.P. and J.G. contributed to the fabrication, development of the devices and the measurement scheme. L.G. fabricated the niobium layers. E.H., M.P. and J.G. contributed to the data analysis. E.H. and F.H. gave theory support. M.M. supervised the work in all respects.

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Correspondence to Matti Silveri or Mikko Möttönen.

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Silveri, M., Masuda, S., Sevriuk, V. et al. Broadband Lamb shift in an engineered quantum system. Nat. Phys. 15, 533–537 (2019).

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