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Broadband Lamb shift in an engineered quantum system

Abstract

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.

Data availability

The data that support the findings of this study are available at https://doi.org/10.5281/zenodo.1995361.

References

  1. 1.

    Lamb, W. E. & Retherford, R. C. Fine structure of the hydrogen atom by a microwave method. Phys. Rev. 72, 241–243 (1947).

    ADS  Article  Google Scholar 

  2. 2.

    Bethe, H. A. The electromagnetic shift of energy levels. Phys. Rev. 72, 339–341 (1947).

    ADS  Article  Google Scholar 

  3. 3.

    Heinzen, D. J. & Feld, M. S. Vacuum radiative level shift and spontaneous-emission linewidth of an atom in an optical resonator. Phys. Rev. Lett. 59, 2623–2626 (1987).

    ADS  Article  Google Scholar 

  4. 4.

    Brune, M. et al. From Lamb shift to light shifts: vacuum and subphoton cavity fields measured by atomic phase sensitive detection. Phys. Rev. Lett. 72, 3339–3342 (1994).

    ADS  Article  Google Scholar 

  5. 5.

    Marrocco, M., Weidinger, M., Sang, R. T. & Walther, H. Quantum electrodynamic shifts of Rydberg energy levels between parallel metal plates. Phys. Rev. Lett. 81, 5784–5787 (1998).

    ADS  Article  Google Scholar 

  6. 6.

    Carmichael, H. J. Statistical Methods in Quantum Optics 1 (Springer, Berlin, 1999).

  7. 7.

    Gisin, N. & Thew, R. Quantum communication. Nat. Photon. 1, 165–171 (2007).

    ADS  Article  Google Scholar 

  8. 8.

    Ladd, T. D. et al. Quantum computers. Nature 464, 45–53 (2010).

    ADS  Article  Google Scholar 

  9. 9.

    Rentrop, T. et al. Observation of the phononic Lamb shift with a synthetic vacuum. Phys. Rev. X 6, 041041 (2016).

    Google Scholar 

  10. 10.

    Fragner, A. et al. Resolving vacuum fluctuations in an electrical circuit by measuring the Lamb shift. Science 322, 1357–1360 (2008).

    ADS  Article  Google Scholar 

  11. 11.

    Yoshihara, F. et al. Inversion of qubit energy levels in qubit-oscillator circuits in the deep-strong-coupling regime. Phys. Rev. Lett. 120, 183601 (2018).

    ADS  Article  Google Scholar 

  12. 12.

    Mirhosseini, M. et al. Superconducting metamaterials for waveguide quantum electrodynamics. Nat. Commun. 9, 3706 (2018).

    ADS  Article  Google Scholar 

  13. 13.

    Partanen, M. et al. Quantum-limited heat conduction over macroscopic distances. Nat. Phys. 12, 460–464 (2016).

    Article  Google Scholar 

  14. 14.

    Tan, K. Y. et al. Quantum-circuit refrigerator. Nat. Commun. 8, 15189 (2017).

    ADS  Article  Google Scholar 

  15. 15.

    Masuda, S. et al. Observation of microwave absorption and emission from incoherent electron tunneling through a normal-metal–insulator–superconductor junction. Sci. Rep. 8, 3966 (2018).

    ADS  Article  Google Scholar 

  16. 16.

    Houck, A. A., Türeci, H. E. & Koch, J. On-chip quantum simulation with superconducting circuits. Nat. Phys. 8, 292–299 (2012).

    Article  Google Scholar 

  17. 17.

    Fitzpatrick, M., Sundaresan, N. M., Li, A. C., Koch, J. & Houck, A. A. Observation of a dissipative phase transition in a one-dimensional circuit QED lattice. Phys. Rev. X 7, 011016 (2017).

    Google Scholar 

  18. 18.

    Ma, R. et al. A dissipatively stabilized Mott insulator of photons. Nature 556, 51–57 (2019).

    ADS  Article  Google Scholar 

  19. 19.

    Gramich, V., Solinas, P., Möttönen, M., Pekola, J. P. & Ankerhold, J. Measurement scheme for the Lamb shift in a superconducting circuit with broadband environment. Phys. Rev. A 84, 052103 (2011).

    ADS  Article  Google Scholar 

  20. 20.

    Paraoanu, G. S. Microwave-induced coupling of superconducting qubits. Phys. Rev. B 74, 140504 (2006).

    ADS  Article  Google Scholar 

  21. 21.

    Rigetti, C. & Devoret, M. Fully microwave-tunable universal gates in superconducting qubits with linear couplings and fixed transition frequencies. Phys. Rev. B 81, 134507 (2010).

    ADS  Article  Google Scholar 

  22. 22.

    Kerckhoff, J., Nurdin, H. I., Pavlichin, D. S. & Mabuchi, H. Designing quantum memories with embedded control: photonic circuits for autonomous quantum error correction. Phys. Rev. Lett. 105, 040502 (2010).

    ADS  Article  Google Scholar 

  23. 23.

    Kapit, E., Chalker, J. T. & Simon, S. H. Passive correction of quantum logical errors in a driven, dissipative system: a blueprint for an analog quantum code fabric. Phys. Rev. A 91, 062324 (2015).

    ADS  Article  Google Scholar 

  24. 24.

    Geerlings, K. et al. Demonstrating a driven reset protocol for a superconducting qubit. Phys. Rev. Lett. 110, 120501 (2013).

    ADS  Article  Google Scholar 

  25. 25.

    Partanen, M. et al. Optimized heat transfer at exceptional points in quantum circuits. Preprint at https://arxiv.org/abs/1812.02683 (2018).

  26. 26.

    Weiss, U. Quantum Dissipative Systems. (World Scientific, Singapore, 2012).

    Book  Google Scholar 

  27. 27.

    Frisk Kockum, A., Delsing, P. & Johansson, G. Designing frequency-dependent relaxation rates and Lamb shifts for a giant artificial atom. Phys. Rev. A 90, 013837 (2014).

    ADS  Article  Google Scholar 

  28. 28.

    Silveri, M., Grabert, H., Masuda, S., Tan, K. Y. & Möttönen, M. Theory of quantum-circuit refrigeration by photon-assisted electron tunneling. Phys. Rev. B 96, 094524 (2017).

    ADS  Article  Google Scholar 

  29. 29.

    Ingold, G.-L. & Nazarov, Y. V. in Single Charge Tunneling: Coulomb Blockade Phenomena in Nanostructures (eds Grabert, H. & Devoret, M. H.) (Plenum, New York, 1992).

  30. 30.

    Dynes, R. C., Narayanamurti, V. & Garno, J. P. Direct measurement of quasiparticle-lifetime broadening in a strong-coupled superconductor. Phys. Rev. Lett. 41, 1509–1512 (1978).

    ADS  Article  Google Scholar 

  31. 31.

    Landau, L. D. & Lifshitz, E. M. Statistical Physics Part 1 (Pergamon, Oxford, 1980).

    MATH  Google Scholar 

  32. 32.

    Caldeira, A. O. & Leggett, A. J. Quantum tunnelling in a dissipative system. Ann. Phys. 149, 374–456 (1983).

    ADS  Article  Google Scholar 

  33. 33.

    Gao, J. et al. Equivalence of the effects on the complex conductivity of superconductor due to temperature change and external pair breaking. J. Low Temp. Phys. 151, 557–563 (2008).

    ADS  Article  Google Scholar 

  34. 34.

    Goetz, J. et al. Loss mechanisms in superconducting thin film microwave resonators. J. Appl. Phys. 119, 015304 (2016).

    ADS  Article  Google Scholar 

  35. 35.

    Forn-Díaz, P. et al. Ultrastrong coupling of a single artificial atom to an electromagnetic continuum in the nonperturbative regime. Nat. Phys. 13, 39–43 (2017).

    Article  Google Scholar 

  36. 36.

    Catelani, G., Schoelkopf, R. J., Devoret, M. H. & Glazman, L. I. Relaxation and frequency shifts induced by quasiparticles in superconducting qubits. Phys. Rev. B 84, 064517 (2011).

    ADS  Article  Google Scholar 

  37. 37.

    Abramowitz, M. & Stegun, I. A. Handbook of Mathematical Functions (Dover, New York, 1972).

    MATH  Google Scholar 

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Acknowledgements

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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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.

Corresponding authors

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). https://doi.org/10.1038/s41567-019-0449-0

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