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Realizing spin Hamiltonians in nanoscale active photonic lattices

Nature Materials volume 19, pages 725–731 (2020)Cite this article

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Abstract

Spin models arise in the microscopic description of magnetic materials and have been recently used to map certain classes of optimization problems involving large degrees of freedom. In this regard, various optical implementations of such Hamiltonians have been demonstrated to quickly converge to the global minimum in the energy landscape. Yet, so far, an integrated nanophotonic platform capable of emulating complex magnetic materials is still missing. Here, we show that the cooperative interplay among vectorial electromagnetic modes in coupled metallic nanolasers can be utilized to implement certain types of spin Hamiltonians. Depending on the topology/geometry of the arrays, these structures can be governed by a classical XY Hamiltonian that exhibits ferromagnetic and antiferromagnetic couplings, as well as geometrical frustration. Our results pave the way towards a scalable nanophotonic platform to study spin exchange interactions and could address a variety of optimization problems.

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Fig. 1: Spin-like behaviour in coupled metallic nanolaser arrays.
Fig. 2: Lasing supermodes in coupled nanolasers and their corresponding pseudospins when arranged in simple geometric configurations.
Fig. 3: FM and AF interactions in four-element coupled nanodisc lasers.
Fig. 4: Frustrated states in spin-like lasing fields emerging from nanolaser arrays.
Fig. 5: Square lattice of 20 × 20 nanolasers exhibiting FM spin-like behaviour.
Fig. 6: Experimental observation of disorder effects in a kagome AF lattice of nanolasers.

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Data availability

The datasets used to generate Fig. 1 and Supplementary Figs. 5, 6 and 10 have been uploaded to FigShare39,40. The other datasets generated and/or analysed during the current study are available from the corresponding author on reasonable request.

Code availability

The codes associated with this manuscript are available from the corresponding author on reasonable request.

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Acknowledgements

We gratefully acknowledge the financial support from DARPA (D18AP00058, HR00111820042, HR00111820038), Army Research Office (ARO; W911NF-16-1-0013, W911NF-17-1-0481, W911NF-18-1-0285), National Science Foundation (ECCS 1454531, DMR 1420620, ECCS 1757025, CBET 1805200, ECCS 2000538, ECCS 2011171, 1846273), Office of Naval Research (N0001416-1-2640, N00014-18-1-2347, N00014-19-1-2052), Air Force Office of Scientific Research (FA9550-14-1-0037) and US–Israel Binational Science Foundation (BSF; 2016381).

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Author notes

  1. These authors contributed equally: Midya Parto, William Hayenga.

Authors and Affiliations

  1. CREOL, The College of Optics and Photonics, University of Central Florida, Orlando, FL, USA

    Midya Parto, William Hayenga, Demetrios N. Christodoulides & Mercedeh Khajavikhan

  2. Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, USA

    Alireza Marandi

  3. Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, USA

    Mercedeh Khajavikhan

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  1. Midya Parto
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  5. Mercedeh Khajavikhan
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Contributions

M.P., D.N.C. and M.K. conceived the idea. M.P. performed the theoretical and analytical modellings. W.H. fabricated the samples and designed the experiments. W.H. and M.P. characterized the samples. M.P., D.N.C., A.M. and M.K. analysed the results. All authors contributed to writing the manuscript. M.K. supervised the project.

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Correspondence to Mercedeh Khajavikhan.

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Supplementary Information

Supplementary Figs. 1–11 and discussion

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Parto, M., Hayenga, W., Marandi, A. et al. Realizing spin Hamiltonians in nanoscale active photonic lattices. Nat. Mater. 19, 725–731 (2020). https://doi.org/10.1038/s41563-020-0635-6

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