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Programmable All-Optical Spin Simulator with Artificial Gauge Fields
Phys. Rev. Lett. 135, 083804 – Published 22 August, 2025
DOI: https://doi.org/10.1103/chxf-fq9v
Abstract
The coupling of lasers plays an important role in a variety of research activities, from generating high-power lasers to investigating out-of-equilibrium coupled systems. This Letter presents our investigations of Hermitian coupling in arrays of lasers, where it is possible to control both the amplitude and phase of the coupling and generate artificial gauge fields. The Hermitian coupling is demonstrated in three laser array geometries: a square array of 100 lasers with controlled laser coupling for obtaining continuous control over the phase-locked state, a triangular array of 130 lasers with controlled chirality of the lasers, and a ring array of eight lasers with a controlled topological charge. In the square array, we implemented arbitrary laser coupling with a precision of radians, enabling the attainment of arbitrary phase-locking states. In the triangular array, we controlled the chirality of the lasers with 99% purity. In the ring array, the introduction of an artificial gauge field revealed discrete quantized first-order transitions between distinct topological phase-locking states. The results pave the way for exploring spin systems with programmable coupling in an all-optical spin simulator.
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References (71)
- I. Buluta and F. Nori, Science 326, 108 (2009).
- G. Vidal, Phys. Rev. Lett. 93, 040502 (2004).
- E. Altman et al., PRX Quantum 2, 017003 (2021).
- F. Tacchino, A. Chiesa, S. Carretta, and D. Gerace, Adv. Quantum Technol. 3, 1900052 (2020).
- E. Zohar, J. I. Cirac, and B. Reznik, Rep. Prog. Phys. 79, 014401 (2015).
- C. Gross and I. Bloch, Science 357, 995 (2017).
- F. Schäfer, T. Fukuhara, S. Sugawa, Y. Takasu, and Y. Takahashi, Nat. Rev. Phys. 2, 411 (2020).
- R. M. Kroeze, B. P. Marsh, D. A. Schuller, H. S. Hunt, S. Gopalakrishnan, J. Keeling, and B. L. Lev, arXiv:2311.04216.
- B. P. Marsh, Y. Guo, R. M. Kroeze, S. Gopalakrishnan, S. Ganguli, J. Keeling, and B. L. Lev, Phys. Rev. X 11, 021048 (2021).
- A. Periwal, E. S. Cooper, P. Kunkel, J. F. Wienand, E. J. Davis, and M. Schleier-Smith, Nature (London) 600, 630 (2021).
- A. J. Kollár, A. T. Papageorge, K. Baumann, M. A. Armen, and B. L. Lev, New J. Phys. 17, 043012 (2015).
- J. G. Bohnet, B. C. Sawyer, J. W. Britton, M. L. Wall, A. M. Rey, M. Foss-Feig, and J. J. Bollinger, Science 352, 1297 (2016).
- R. Blatt and C. F. Roos, Nat. Phys. 8, 277 (2012).
- B. P. Lanyon, C. Hempel, D. Nigg, M. Müller, R. Gerritsma, F. Zähringer, P. Schindler, J. T. Barreiro, M. Rambach, G. Kirchmair, M. Hennrich, P. Zoller, R. Blatt, and C. F. Roos, Science 334, 57 (2011).
- D. Porras and J. I. Cirac, Phys. Rev. Lett. 92, 207901 (2004).
- K. Kim, M.-S. Chang, S. Korenblit, R. Islam, E. E. Edwards, J. K. Freericks, G.-D. Lin, L.-M. Duan, and C. Monroe, Nature (London) 465, 590 (2010).
- U. L. Heras, A. Mezzacapo, L. Lamata, S. Filipp, A. Wallraff, and E. Solano, Phys. Rev. Lett. 112, 200501 (2014).
- A. A. Houck, H. E. Türeci, and J. Koch, Nat. Phys. 8, 292 (2012).
- G. S. Paraoanu, J. Low Temp. Phys. 175, 633 (2014).
- V. Pal, S. Mahler, C. Tradonsky, A. A. Friesem, and N. Davidson, Phys. Rev. Res. 2, 033008 (2020).
- M. Nixon, E. Ronen, A. A. Friesem, and N. Davidson, Phys. Rev. Lett. 110, 184102 (2013).
- D. Pierangeli, G. Marcucci, and C. Conti, Phys. Rev. Lett. 122, 213902 (2019).
- S. Mahler, V. Pal, C. Tradonsky, R. Chriki, A. A. Friesem, and N. Davidson, J. Phys. B 52, 205401 (2019).
- M. Honari-Latifpour and M.-A. Miri, Phys. Rev. Res. 2, 043335 (2020).
- G. Arwas, S. Gadasi, I. Gershenzon, A. Friesem, N. Davidson, and O. Raz, Sci. Adv. 8, eabm7454 (2022).
- A. Marandi, Z. Wang, K. Takata, R. L. Byer, and Y. Yamamoto, Nat. Photonics 8, 937 (2014).
- P. L. McMahon, A. Marandi, Y. Haribara, R. Hamerly, C. Langrock, S. Tamate, T. Inagaki, H. Takesue, S. Utsunomiya, K. Aihara, R. L. Byer, M. M. Fejer, H. Mabuchi, and Y. Yamamoto, Science 354, 614 (2016).
- N. G. Berloff, M. Silva, K. Kalinin, A. Askitopoulos, J. D. Töpfer, P. Cilibrizzi, W. Langbein, and P. G. Lagoudakis, Nat. Mater. 16, 1120 (2017).
- K. P. Kalinin and N. G. Berloff, Commun. Phys. 5, 20 (2022).
- V. G. Sala, D. D. Solnyshkov, I. Carusotto, T. Jacqmin, A. Lemaître, H. Terças, A. Nalitov, M. Abbarchi, E. Galopin, I. Sagnes, J. Bloch, G. Malpuech, and A. Amo, Phys. Rev. X 5, 011034 (2015).
- K. P. Kalinin and N. G. Berloff, Adv. Quantum Technol. 3, 1900065 (2020).
- M. Parto, W. E. Hayenga, A. Marandi, D. N. Christodoulides, and M. Khajavikhan, Nanophotonics 9, 4193 (2020).
- M. Parto, W. Hayenga, A. Marandi, D. N. Christodoulides, and M. Khajavikhan, Nat. Mater. 19, 725 (2020).
- G. D. las Cuevas and T. S. Cubitt, Science 351, 1180 (2016).
- T. S. Cubitt, A. Montanaro, and S. Piddock, Proc. Natl. Acad. Sci. U.S.A. 115, 9497 (2018).
- S. L. Sondhi, S. M. Girvin, J. P. Carini, and D. Shahar, Rev. Mod. Phys. 69, 315 (1997).
- M. Sarkar, T. Enss, and N. Defenu, Phys. Rev. B 110, 014208 (2024).
- G. Semeghini, H. Levine, A. Keesling, S. Ebadi, T. T. Wang, D. Bluvstein, R. Verresen, H. Pichler, M. Kalinowski, R. Samajdar, A. Omran, S. Sachdev, A. Vishwanath, M. Greiner, V. Vuletić, and M. D. Lukin, Science 374, 1242 (2021).
- A. Lucas, Front. Phys. 2, 5 (2014).
- C. Monroe, W. C. Campbell, L.-M. Duan, Z.-X. Gong, A. V. Gorshkov, P. W. Hess, R. Islam, K. Kim, N. M. Linke, G. Pagano, P. Richerme, C. Senko, and N. Y. Yao, Rev. Mod. Phys. 93, 025001 (2021).
- G. Csaba and W. Porod, Appl. Phys. Rev. 7, 011302 (2020).
- I. Gershenzon, B. Lacroix-A-Chez-Toine, O. Raz, E. Subag, and O. Zeitouni, Phys. Rev. Lett. 130, 237103 (2023).
- J. Struck, M. Weinberg, C. Ölschläger, P. Windpassinger, J. Simonet, K. Sengstock, R. Höppner, P. Hauke, A. Eckardt, M. Lewenstein, and L. Mathey, Nat. Phys. 9, 738 (2013).
- R. O. Umucal𝚤lar and I. Carusotto, Phys. Rev. A 84, 043804 (2011).
- N. Goldman, G. Juzeliūnas, P. Öhberg, and I. B. Spielman, Rep. Prog. Phys. 77, 126401 (2014).
- C. Jörg, G. Queraltó, M. Kremer, G. Pelegrí, J. Schulz, A. Szameit, G. von Freymann, J. Mompart, and V. Ahufinger, Light Sci. Appl. 9, 150 (2020).
- M. Aidelsburger, S. Nascimbene, and N. Goldman, C.R. Phys. 19, 394 (2018).
- Y. Lumer, M. A. Bandres, M. Heinrich, L. J. Maczewsky, H. Herzig-Sheinfux, A. Szameit, and M. Segev, Nat. Photonics 13, 339 (2019).
- S. Mittal, J. Fan, S. Faez, A. Migdall, J. M. Taylor, and M. Hafezi, Phys. Rev. Lett. 113, 087403 (2014).
- E. Lustig, S. Weimann, Y. Plotnik, Y. Lumer, M. A. Bandres, A. Szameit, and M. Segev, Nature (London) 567, 356 (2019).
- M. Hafezi, Int. J. Mod. Phys. B 28, 1441002 (2014).
- C. Leefmans, A. Dutt, J. Williams, L. Yuan, M. Parto, F. Nori, S. Fan, and A. Marandi, Nat. Phys. 18, 442 (2022).
- C. R. Leefmans, M. Parto, J. Williams, G. H. Y. Li, A. Dutt, F. Nori, and A. Marandi, Nat. Phys. 20, 852 (2024).
- I. Gershenzon, G. Arwas, S. Gadasi, C. Tradonsky, A. Friesem, O. Raz, and N. Davidson, Nanophotonics 9, 4117 (2020).
- V. Pal, C. Tradonsky, R. Chriki, A. A. Friesem, and N. Davidson, Phys. Rev. Lett. 119, 013902 (2017).
- S. Mahler, M. L. Goh, C. Tradonsky, A. A. Friesem, and N. Davidson, Phys. Rev. Lett. 124, 133901 (2020).
- C. Tradonsky, S. Mahler, G. Cai, V. Pal, R. Chriki, A. A. Friesem, and N. Davidson, Optica 8, 880 (2021).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/chxf-fq9v, which includes Refs. [21,54,55,59], for further technical details, numerical simulations, and experimental results.
- R. W. Gerchberg and W. O. Saxton, Optik (Stuttgart) 35, 237 (1972), https://www.scirp.org/reference/referencespapers?referenceid=2890261.
The chirality results without the far-field circular aperture were very similar to those of Fig. 4 but with broader far-field peaks.
- S. Mahler, C. Tradonsky, R. Chriki, A. A. Friesem, and N. Davidson, OSA Continuum 2, 2077 (2019).
- D. R. Hofstadter, Phys. Rev. B 14, 2239 (1976).
- P. G. Harper, Proc. Phys. Soc. London Sect. A 68, 879 (1955).
- T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, Rev. Mod. Phys. 91, 015006 (2019).
- Y. Eliezer, S. Mahler, A. A. Friesem, H. Cao, and N. Davidson, Phys. Rev. Lett. 128, 143901 (2022).
- A. Pando, S. Gadasi, E. Bernstein, N. Stroev, A. Friesem, and N. Davidson, Phys. Rev. Lett. 133, 113803 (2024).
- S. Gadasi, E. Bernstein, A. Pando, A. Friesem, and N. Davidson, Opt. Express 31, 24615 (2023).
- A. N. K. Reddy, S. Mahler, A. Goldring, V. Pal, A. A. Friesem, and N. Davidson, Opt. Express 30, 1114 (2022).
- A. Pando, S. Gadasi, A. Friesem, and N. Davidson, Opt. Express 31, 6947 (2023).
- M. Fruchart, R. Hanai, P. B. Littlewood, and V. Vitelli, Nature (London) 592, 363 (2021).
- J. P. Moroney and P. R. Eastham, Phys. Rev. B 108, 195302 (2023).