Abstract
Photons are neutral particles that do not interact directly with a magnetic field. However, recent theoretical work1,2 has shown that an effective magnetic field for photons can exist if the phase of light changes with its direction of propagation. This direction-dependent phase indicates the presence of an effective magnetic field, as shown experimentally for electrons in the Aharonov–Bohm experiment. Here, we replicate this experiment using photons. To create this effective magnetic field we construct an on-chip silicon-based Ramsey-type interferometer3,4,5,6,7. This interferometer has been traditionally used to probe the phase of atomic states and here we apply it to probe the phase of photonic states. We experimentally observe an effective magnetic flux between 0 and 2π corresponding to a non-reciprocal 2π phase shift with an interferometer length of 8.35 mm and an interference-fringe extinction ratio of 2.4 dB. This non-reciprocal phase is comparable to those of common monolithically integrated magneto-optical materials.
This is a preview of subscription content, access via your institution
Relevant articles
Open Access articles citing this article.
-
All-optical nonreciprocity due to valley polarization pumping in transition metal dichalcogenides
Nature Communications Open Access 18 June 2021
-
Tidal surface states as fingerprints of non-Hermitian nodal knot metals
Communications Physics Open Access 09 March 2021
-
Loss-induced nonreciprocity
Light: Science & Applications Open Access 04 February 2021
Access options
Subscribe to this journal
Receive 12 print issues and online access
$209.00 per year
only $17.42 per issue
Rent or buy this article
Prices vary by article type
from$1.95
to$39.95
Prices may be subject to local taxes which are calculated during checkout




References
Fang, K., Yu, Z. & Fan, S. Photonic Aharonov–Bohm effect based on dynamic modulation. Phys. Rev. Lett. 108, 153901 (2012).
Fang, K., Yu, Z. & Fan, S. Realizing effective magnetic field for photons by controlling the phase of dynamic modulation. Nature Photon. 6, 782–787 (2012).
Ramsey, N. F. A new molecular beam resonance method. Phys. Rev. 76, 996 (1949).
Ramsey, N. F. Molecular Beams (Oxford Univ. Press, 1963).
Bordé, C. J. Atomic interferometry with internal state labelling. Phys. Lett. A 140, 10–12 (1989).
Ramsey, N. F. Experiments with separated oscillatory fields and hydrogen masers. Rev. Mod. Phys. 62, 541–552 (1990).
Dubetsky, B. & Kasevich, M. A. Atom interferometer as a selective sensor of rotation or gravity. Phys. Rev. A 74, 023615 (2006).
Shoji, Y., Mizumoto, T., Yokoi, H., Hsieh, I-W. & Osgood, R. M. Jr Magneto-optical isolator with silicon waveguides fabricated by direct bonding. Appl. Phys. Lett. 92, 071117 (2008).
Bi, L. et al. On-chip optical isolation in monolithically integrated non-reciprocal optical resonators. Nature Photon. 5, 758–762 (2011).
Tien, M.-C., Mizumoto, T., Pintus, P., Kromer, H. & Bowers, J. E. Silicon ring isolators with bonded nonreciprocal magneto-optic garnets. Opt. Express 19, 11740–11745 (2011).
Haldane, F. D. M. & Raghu, S. Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry. Phys. Rev. Lett. 100, 013904 (2008).
Wang, Z., Chong, Y. D., Joannopoulos, J. D. & Soljačić, M. Reflection-free one-way edge modes in a gyromagnetic photonic crystal. Phys. Rev. Lett. 100, 013905 (2008).
Raghu, S. & Haldane, F. D. M. Analogs of quantum-Hall-effect edge states in photonic crystals. Phys. Rev. A 78, 033834 (2008).
Wang, Z., Chong, Y., Joannopoulos, J. D. & Soljačić, M. Observation of unidirectional backscattering-immune topological electromagnetic states. Nature 461, 772–775 (2009).
Poo, Y., Wu, R., Lin, Z., Yang, Y. & Chan, C. T. Experimental realization of self-guiding unidirectional electromagnetic edge states. Phys. Rev. Lett. 106, 093903 (2011).
Hwang, I. K., Yun, S. H. & Kim, B. Y. All-fiber-optic nonreciprocal modulator. Opt. Lett. 22, 507–509 (1997).
Doerr, C. R., Dupuis, N. & Zhang, L. Optical isolator using two tandem phase modulators. Opt. Lett. 36, 4293–4295 (2011).
Lira, H., Yu, Z., Fan, S. & Lipson, M. Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip. Phys. Rev. Lett. 109, 033901 (2012).
Doerr, C. R., Chen, L. & Vermeulen, D. Silicon photonics broadband modulation-based isolator. Opt. Express 22, 4493–4498 (2014).
Aharonov, Y. & Bohm, D. Significance of electromagnetic potentials in the quantum theory. Phys. Rev. 115, 485–491 (1959).
Fang, K., Yu, Z. & Fan, S. Experimental demonstration of a photonic Aharonov–Bohm effect at radio frequencies. Phys. Rev. B 87, 060301(R) 10.1103/PhysRevB.87.060301(2013).
Soref, R. & Bennett, B. R. Electrooptical effects in silicon. IEEE J. Quantum Electron. 23, 123–129 (1987).
Gardes, F. Y. et al. High-speed modulation of a compact silicon ring resonator based on a reverse-biased pn diode. Opt. Express 17, 21986–21991 (2009).
Spector, S. J. et al. Operation and optimization of silicon-diode-based optical modulators. IEEE J. Sel. Top. Quantum Electron. 16, 165–172 (2010).
Hafezi, M., Demler, E. A., Lukin, M. D. & Taylor, J. M. Robust optical delay lines with topological protection. Nature Phys. 7, 907–912 (2011).
Umucalilar, R. O. & Carusotto, I. Artificial gauge field for photons in coupled cavity arrays. Phys. Rev. A 84, 043804 (2011).
Rechtsman, M. C. et al. Photonic Floquet topological insulators. Nature 496, 196–200 (2013).
Khanikaev, A. B. et al. Photonic topological insulators. Nature Mater. 12, 233–239 (2013).
Liang, G. Q. & Chong, Y. D. Optical resonator analog of a two-dimensional topological insulator. Phys. Rev. Lett. 110, 203904 (2013).
Longhi, S. Effective magnetic fields for photons in waveguide and coupled resonator lattices. Opt. Lett. 38, 3570–3573 (2013).
Hafezi, M., Mittal, S., Fan, J., Migdall, A. & Taylor, J. M. Imaging topological edge states in silicon photonics. Nature Photon. 7, 1001–1005 (2013).
Acknowledgements
This work was supported by the National Science Foundation (NSF) through CIAN ERC (grant no. EEC 0812072) and by NSF grant no. 1202265. This work was performed in part at the Cornell Nanoscale Facility, a member of the National Nanotechnology Infrastructure Network, which is supported by the NSF. P.N. acknowledges support from Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP grant no. 2011/12140-6). The authors acknowledge support from the US Air Force (AFOSR; program FA9550-09-1-0704 on ‘Robust and Complex on-chip Nanophotonics’ supervised by G. Pomrenke).
Author information
Authors and Affiliations
Contributions
L.D.T. performed the experiment. L.D.T. and K.F. designed the experiment and analysed the data. P.N., S.F. and M.L. supervised the project. L.D.T and M.L. prepared the manuscript. K.F., P.N. and S.F. edited the manuscript.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing financial interests.
Supplementary information
Supplementary information
Supplementary information (PDF 932 kb)
Rights and permissions
About this article
Cite this article
Tzuang, L., Fang, K., Nussenzveig, P. et al. Non-reciprocal phase shift induced by an effective magnetic flux for light. Nature Photon 8, 701–705 (2014). https://doi.org/10.1038/nphoton.2014.177
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/nphoton.2014.177
This article is cited by
-
Integrated electro-optic isolator on thin-film lithium niobate
Nature Photonics (2023)
-
Integrated passive nonlinear optical isolators
Nature Photonics (2023)
-
Optical quantum modeling for Heisenberg ferromagnetic normalized phase
Optical and Quantum Electronics (2023)
-
Mirror symmetric on-chip frequency circulation of light
Nature Photonics (2022)
-
Optomechanically induced tunable ideal nonreciprocity in optomechanical system with Coulomb interaction
Quantum Information Processing (2022)