Letter

Experimental measurement of the Berry curvature from anomalous transport

Received:
Accepted:
Published online:

Abstract

The geometric properties of energy bands underlie fascinating phenomena in many systems, including solid-state, ultracold gases and photonics. The local geometric characteristics such as the Berry curvature1 can be related to global topological invariants such as those classifying the quantum Hall states or topological insulators. Regardless of the band topology, however, any non-zero Berry curvature can have important consequences, such as in the semi-classical evolution of a coherent wavepacket. Here, we experimentally demonstrate that the wavepacket dynamics can be used to directly map out the Berry curvature. To this end, we use optical pulses in two coupled fibre loops to study the discrete time evolution of a wavepacket in a one-dimensional geometric ‘charge’ pump, where the Berry curvature leads to an anomalous displacement of the wavepacket. This is both the first direct observation of Berry curvature effects in an optical system, and a proof-of-principle demonstration that wavepacket dynamics can serve as a high-resolution tool for mapping out geometric properties.

  • Subscribe to Nature Physics for full access:

    $59

    Subscribe

Additional access options:

Already a subscriber?  Log in  now or  Register  for online access.

References

  1. 1.

    , & Berry phase effects on electronic properties. Rev. Mod. Phys. 82, 1959–2007 (2010).

  2. 2.

    , , & Quantized Hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett. 49, 405–408 (1982).

  3. 3.

    Quantization of particle transport. Phys. Rev. B 27, 6083–6087 (1983).

  4. 4.

    & Berry phase, hyperorbits, and the Hofstadter spectrum. Phys. Rev. Lett. 75, 1348–1351 (1995).

  5. 5.

    Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. Lond. A 392, 45–57 (1984).

  6. 6.

    & Spin gauge fields: from Berry phase to topological spin transport and Hall effects. Ann. Phys. 319, 13–47 (2005).

  7. 7.

    , & Quantum mechanics with a momentum-space artificial magnetic field. Phys. Rev. Lett. 113, 190403 (2014).

  8. 8.

    , & Topological photonics. Nat. Photon. 8, 821–829 (2014).

  9. 9.

    , , & Observation of unidirectional backscattering-immune topological electromagnetic states. Nature 461, 772–775 (2009).

  10. 10.

    et al. Experimental observation of large chern numbers in photonic crystals. Phys. Rev. Lett. 115, 253901 (2015).

  11. 11.

    et al. Experimental observation of Weyl points. Science 349, 622–624 (2015).

  12. 12.

    et al. Photonic Floquet topological insulators. Nature 496, 196–200 (2013).

  13. 13.

    , , , & Topological states and adiabatic pumping in quasicrystals. Phys. Rev. Lett. 109, 106402 (2012).

  14. 14.

    et al. Observation of topologically protected bound states in photonic quantum walks. Nat. Commun. 3, 882 (2012).

  15. 15.

    , , , & Imaging topological edge states in silicon photonics. Nat. Photon. 7, 1001–1005 (2013).

  16. 16.

    , , , & Measurement of topological invariants in a 2D photonic system. Nat. Photon. 10, 180–183 (2016).

  17. 17.

    et al. An Aharonov-Bohm interferometer for determining Bloch band topology. Science 347, 288–292 (2015).

  18. 18.

    et al. Direct measurement of the Zak phase in topological Bloch bands. Nat. Phys. 9, 795–800 (2013).

  19. 19.

    et al. Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms. Nat. Phys. 11, 162–166 (2014).

  20. 20.

    et al. Experimental realization of the topological Haldane model with ultracold fermions. Nature 515, 237–240 (2014).

  21. 21.

    et al. Observation of chiral edge states with neutral fermions in synthetic Hall ribbons. Science 349, 1510–1513 (2015).

  22. 22.

    , , , & Visualizing edge states with an atomic Bose gas in the quantum Hall regime. Science 349, 1514–1518 (2015).

  23. 23.

    , , , & A Thouless quantum pump with ultracold bosonic atoms in an optical superlattice. Nat. Phys. 12, 350–354 (2015).

  24. 24.

    et al. Topological Thouless pumping of ultracold fermions. Nat. Phys. 12, 296–300 (2016).

  25. 25.

    et al. Geometrical pumping with a Bose-Einstein condensate. Phys. Rev. Lett. 116, 200402 (2016).

  26. 26.

    et al. Experimental reconstruction of the Berry curvature in a Floquet Bloch band. Science 352, 1091–1094 (2016).

  27. 27.

    et al. Bloch state tomography using Wilson lines. Science 352, 1094–1097 (2016).

  28. 28.

    , & Topological states in photonic systems. Nat. Phys. 12, 626–629 (2016).

  29. 29.

    , , , & Topological pumping over a photonic Fibonacci quasicrystal. Phys. Rev. B 91, 064201 (2015).

  30. 30.

    & Quasiperiodicity and topology transcend dimensions. Nat. Phys. 12, 624–626 (2016).

  31. 31.

    et al. Photons walking the line: a quantum walk with adjustable coin operations. Phys. Rev. Lett. 104, 050502 (2010).

  32. 32.

    et al. Parity-time synthetic photonic lattices. Nature 488, 167–171 (2012).

  33. 33.

    , , & Optical mesh lattices with PT symmetry. Phys. Rev. A 86, 023807 (2012).

  34. 34.

    et al. Optical diametric drive acceleration through action–reaction symmetry breaking. Nat. Phys. 9, 780–784 (2013).

  35. 35.

    , & Topological field theory of time-reversal invariant insulators. Phys. Rev. B 78, 195424 (2008).

  36. 36.

    & Mapping the Berry curvature from semiclassical dynamics in optical lattices. Phys. Rev. A 85, 033620 (2012).

  37. 37.

    et al. Photon propagation in a discrete fiber network: an interplay of coherence and losses. Phys. Rev. Lett. 107, 233902 (2011).

Download references

Acknowledgements

M.W. acknowledges financial support from the Erlangen Graduate School of Advanced Optical Technologies. Additionally, M.W. would like to thank M. Kremer and A. Bisianov for fruitful discussions. Furthermore, this project was supported by PE 523/14-1 and by the GRK2101 funded by the DFG. H.M.P. was supported by the EC through the H2020 Marie Sklodowska-Curie Action, Individual Fellowship Grant No. 656093 SynOptic. I.C. was funded by the EU-FET Proactive grant AQuS, Project No. 640800, and by Provincia Autonoma di Trento, partially through the project ‘On silicon chip quantum optics for quantum computing and secure communications (SiQuro)’.

Author information

Affiliations

  1. Erlangen Graduate School in Advanced Optical Technologies (SAOT), 91058 Erlangen, Germany

    • Martin Wimmer
  2. Institute of Solid State Theory and Optics, Abbe Center of Photonics, Friedrich Schiller University Jena, Max-Wien-Platz 1, 07743 Jena, Germany

    • Martin Wimmer
    •  & Ulf Peschel
  3. INO-CNR BEC Center and Department of Physics, University of Trento, via Sommarive 14, 38123 Povo, Italy

    • Hannah M. Price
    •  & Iacopo Carusotto

Authors

  1. Search for Martin Wimmer in:

  2. Search for Hannah M. Price in:

  3. Search for Iacopo Carusotto in:

  4. Search for Ulf Peschel in:

Contributions

M.W. performed the experiments; all authors contributed to the theoretical background and the interpretation of the measurement.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Ulf Peschel.

Supplementary information

PDF files

  1. 1.

    Supplementary information

    Supplementary information