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Vacuum Bloch–Siegert shift in Landau polaritons with ultra-high cooperativity

Nature Photonics volume 12, pages 324–329 (2018)Cite this article

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Abstract

A two-level system resonantly interacting with an a.c. magnetic or electric field constitutes the physical basis of diverse phenomena and technologies. However, Schrödinger’s equation for this seemingly simple system can be solved exactly only under the rotating-wave approximation, which neglects the counter-rotating field component. When the a.c. field is sufficiently strong, this approximation fails, leading to a resonance-frequency shift known as the Bloch–Siegert shift. Here, we report the vacuum Bloch–Siegert shift, which is induced by the ultra-strong coupling of matter with the counter-rotating component of the vacuum fluctuation field in a cavity. Specifically, an ultra-high-mobility two-dimensional electron gas inside a high-Q terahertz cavity in a quantizing magnetic field revealed ultra-narrow Landau polaritons, which exhibited a vacuum Bloch–Siegert shift up to 40 GHz. This shift, clearly distinguishable from the photon-field self-interaction effect, represents a unique manifestation of a strong-field phenomenon without a strong field.

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Fig. 1: CR cavity QED setup.
Fig. 2: Landau polaritons in the USC regime with ultra-high cooperativity.
Fig. 3: Landau polariton dispersions as a function of B.
Fig. 4: Distinction between the VBS shift due to the CRTs and the shift due to the A2 terms in the USC regime.

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Acknowledgements

We thank K. Hazzard, Y. Todorov and C. Sirtori for discussions. We thank Y. Kawada, H. Takahashi and Hamamatsu Photonics K.K. for fabricating the achromatic terahertz quarter-wave plate. J.K. acknowledges support from the Army Research Office (grant W911NF-17-1-0259) for terahertz magneto-spectroscopy measurements and the National Science Foundation (grant DMR-1310138) for cavity fabrication. M.B. acknowledges support from JST PRESTO (grant JPMJPR1767), KAKENHI (grant 26287087), and ImPACT Program of Council for Science, Technology and Innovation (cabinet office, government of Japan). The work at Purdue was supported by the Department of Energy, Office of Basic Energy Sciences, under Award DE-SC0006671.

Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Rice University, Houston, TX, USA

    Xinwei Li, Weilu Gao, Minhan Lou & Junichiro Kono

  2. Department of Materials Engineering Science, Osaka University, Osaka, Japan

    Motoaki Bamba

  3. PRESTO, Japan Science and Technology Agency, Saitama, Japan

    Motoaki Bamba

  4. Argonne National Laboratories, Lemont, IL, USA

    Qi Zhang

  5. Department of Physics and Astronomy, Station Q Purdue, and Birck Nanotechnology Center, Purdue University, West Lafayette, IN, USA

    Saeed Fallahi, Geoff C. Gardner & Michael J. Manfra

  6. Department of Physics, Graduate School of Engineering, Yokohama National University, Yokohama, Japan

    Katsumasa Yoshioka

  7. School of Materials Engineering and School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA

    Michael J. Manfra

  8. Department of Material Science and NanoEngineering, Rice University, Houston, TX, USA

    Junichiro Kono

  9. Department of Physics and Astronomy, Rice University, Houston, TX, USA

    Junichiro Kono

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  1. Xinwei Li
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Contributions

X.L. fabricated terahertz cavity devices, performed all measurements, analysed all experimental data and performed semiclassical simulations under the supervision and guidance of Q.Z. and J.K. M.B. performed quantum mechanical and semiclassical calculations. S.F., G.C.G. and M.J.M. grew the 2DEG sample. Q.Z., W.G., M.L. and K.Y. assisted X.L. with cavity sample preparation and measurements. X.L., M.B. and J.K. wrote the manuscript. All authors discussed the results and commented on the manuscript.

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Correspondence to Junichiro Kono.

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Li, X., Bamba, M., Zhang, Q. et al. Vacuum Bloch–Siegert shift in Landau polaritons with ultra-high cooperativity. Nature Photon 12, 324–329 (2018). https://doi.org/10.1038/s41566-018-0153-0

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