Driven-dissipative topological phases in parametric resonator arrays

Álvaro Gómez-León; Tomás Ramos; Alejandro González-Tudela; Diego Porras

doi:10.22331/q-2023-05-23-1016

Driven-dissipative topological phases in parametric resonator arrays

Álvaro Gómez-León, Tomás Ramos, Alejandro González-Tudela, and Diego Porras

Instituto de Física Fundamental (IFF), CSIC, Calle Serrano 113b, 28006 Madrid, Spain.

Published:	2023-05-23, volume 7, page 1016
Eprint:	arXiv:2207.13715v3
Doi:	https://doi.org/10.22331/q-2023-05-23-1016
Citation:	Quantum 7, 1016 (2023).

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

We study the phenomena of topological amplification in arrays of parametric oscillators. We find two phases of topological amplification, both with directional transport and exponential gain with the number of sites, and one of them featuring squeezing. We also find a topologically trivial phase with zero-energy modes which produces amplification but lacks the robust topological protection of the others. We characterize the resilience to disorder of the different phases and their stability, gain, and noise-to-signal ratio. Finally, we discuss their experimental implementation with state-of-the-art techniques.

Featured image: Array of resonators with losses being parametrically driven.

Popular summary

Amplifiers are fundamental tools in today’s technology. Their uses range from quantum computation to astronomical and NMR devices, and their usefulness requires several properties to be fulfilled. For example, large gain allows to amplify weak signals fast, wide frequency bandwidth allows to maximize the range of applications, and low noise allows to separate the signals of interest from the background fluctuations.
For this reason, it is important to investigate new approaches to build amplifiers which can overcome those already existing.
In this work we have explored the phenomena of amplification in parametric resonator arrays.
We have shown that it is useful to harness ideas from topological systems and combine them with those of dissipative ones. In particular regimes, this leads to phases of topological amplification where one finds large directional gain, quantum-limited noise and broad bandwidth. In addition, amplification is topologically protected to perturbations and the steady-state can be used to generate squeezed states. Our results also provide a way to test new dissipative topological phases, where in contrast with the well-known case of the quantum Hall effect, now photons populate the system and their interaction with the environment is fundamental for their existence.
These types of topological amplifiers can be fabricated in several platforms, such as Josephson junctions, nano-mechanical oscillators and trapped ions. This means that their use can be widespread, and that their realization will also tackle fundamental questions about the physics of dissipative topological phases.

► BibTeX data

@article{GomezLeon2023drivendissipative,
  doi = {10.22331/q-2023-05-23-1016},
  url = {https://doi.org/10.22331/q-2023-05-23-1016},
  title = {Driven-dissipative topological phases in parametric resonator arrays},
  author = {G{\'{o}}mez-Le{\'{o}}n, {\'{A}}lvaro and Ramos, Tom{\'{a}}s and Gonz{\'{a}}lez-Tudela, Alejandro and Porras, Diego},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {7},
  pages = {1016},
  month = may,
  year = {2023}
}

► References

[1] K. v. Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45, 494 (1980).
https://doi.org/10.1103/PhysRevLett.45.494

[2] D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Phys. Rev. Lett. 49, 405 (1982).
https://doi.org/10.1103/PhysRevLett.49.405

[3] K. von Klitzing, Nature Physics 13, 198 (2017).
https://doi.org/10.1038/nphys4029

[4] A. K. Geim and K. S. Novoselov, Nature Materials 6, 183 (2007).
https://doi.org/10.1038/nmat1849

[5] B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, Science 314, 1757 (2006).
https://doi.org/10.1126/science.1133734

[6] M. Bello, G. Platero, J. I. Cirac, and A. González-Tudela, Science Advances 5, eaaw0297 (2019).
https://doi.org/10.1126/sciadv.aaw0297

[7] E. Kim, X. Zhang, V. S. Ferreira, J. Banker, J. K. Iverson, A. Sipahigil, M. Bello, A. González-Tudela, M. Mirhosseini, and O. Painter, Phys. Rev. X 11, 011015 (2021).
https://doi.org/10.1103/PhysRevX.11.011015

[8] S. Barik, A. Karasahin, C. Flower, T. Cai, H. Miyake, W. DeGottardi, M. Hafezi, and E. Waks, Science 359, 666 (2018).
https://doi.org/10.1126/science.aaq0327

[9] C. Vega, M. Bello, D. Porras, and A. González-Tudela, Phys. Rev. A 104, 053522 (2021).
https://doi.org/10.1103/PhysRevA.104.053522

[10] I. García-Elcano, A. González-Tudela, and J. Bravo-Abad, Phys. Rev. Lett. 125, 163602 (2020).
https://doi.org/10.1103/PhysRevLett.125.163602

[11] I. García-Elcano, J. Bravo-Abad, and A. González-Tudela, Phys. Rev. A 103, 033511 (2021).
https://doi.org/10.1103/PhysRevA.103.033511

[12] L. Leonforte, D. Valenti, B. Spagnolo, A. Carollo, and F. Ciccarello, Nanophotonics 10, 4251 (2021).

[13] D. De Bernardis, Z.-P. Cian, I. Carusotto, M. Hafezi, and P. Rabl, Phys. Rev. Lett. 126, 103603 (2021).
https://doi.org/10.1103/PhysRevLett.126.103603

[14] M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
https://doi.org/10.1038/nature12066

[15] A. B. Khanikaev, S. Hossein Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, Nature Materials 12, 233 (2013).
https://doi.org/10.1038/nmat3520

[16] 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).
https://doi.org/10.1103/RevModPhys.91.015006

[17] M. Kim, Z. Jacob, and J. Rho, Light: Science & Applications 9, 130 (2020).
https://doi.org/10.1038/s41377-020-0331-y

[18] Y. Yang, Z. Gao, H. Xue, L. Zhang, M. He, Z. Yang, R. Singh, Y. Chong, B. Zhang, and H. Chen, Nature 565, 622 (2019).
https://doi.org/10.1038/s41586-018-0829-0

[19] L. Lu, J. D. Joannopoulos, and M. Soljačić, Nature Photonics 8, 821 (2014).
https://doi.org/10.1038/nphoton.2014.248

[20] A. B. Khanikaev and G. Shvets, Nature Photonics 11, 763 (2017).
https://doi.org/10.1038/s41566-017-0048-5

[21] S. Ma and S. M. Anlage, Applied Physics Letters 116, 250502 (2020).
https://doi.org/10.1063/5.0008046

[22] J. C. Budich and E. J. Bergholtz, Phys. Rev. Lett. 125, 180403 (2020).
https://doi.org/10.1103/PhysRevLett.125.180403

[23] A. McDonald and A. A. Clerk, Nature Communications 11, 5382 (2020).
https://doi.org/10.1038/s41467-020-19090-4

[24] F. Koch and J. C. Budich, Phys. Rev. Research 4, 013113 (2022).
https://doi.org/10.1103/PhysRevResearch.4.013113

[25] K. E. Arledge, B. Uchoa, Y. Zou, and B. Weng, Phys. Rev. Research 3, 033106 (2021).
https://doi.org/10.1103/PhysRevResearch.3.033106

[26] C.-E. Bardyn, M. A. Baranov, C. V. Kraus, E. Rico, A. İmamoğlu, P. Zoller, and S. Diehl, New Journal of Physics 15, 085001 (2013).
https://doi.org/10.1088/1367-2630/15/8/085001

[27] Z. Gong, Y. Ashida, K. Kawabata, K. Takasan, S. Higashikawa, and M. Ueda, Phys. Rev. X 8, 031079 (2018).
https://doi.org/10.1103/PhysRevX.8.031079

[28] K. Kawabata, K. Shiozaki, M. Ueda, and M. Sato, Phys. Rev. X 9, 041015 (2019).
https://doi.org/10.1103/PhysRevX.9.041015

[29] H. Zhou and J. Y. Lee, Phys. Rev. B 99, 235112 (2019).
https://doi.org/10.1103/PhysRevB.99.235112

[30] S. Yao and Z. Wang, Phys. Rev. Lett. 121, 086803 (2018a).
https://doi.org/10.1103/PhysRevLett.121.086803

[31] A. McDonald, R. Hanai, and A. A. Clerk, Phys. Rev. B 105, 064302 (2022).
https://doi.org/10.1103/PhysRevB.105.064302

[32] D. S. Borgnia, A. J. Kruchkov, and R.-J. Slager, Phys. Rev. Lett. 124, 056802 (2020).
https://doi.org/10.1103/PhysRevLett.124.056802

[33] C. C. Wanjura, M. Brunelli, and A. Nunnenkamp, Nature Communications 11, 3149 (2020).
https://doi.org/10.1038/s41467-020-16863-9

[34] T. Ramos, J. J. García-Ripoll, and D. Porras, Phys. Rev. A 103, 033513 (2021).
https://doi.org/10.1103/PhysRevA.103.033513

[35] V. P. Flynn, E. Cobanera, and L. Viola, Phys. Rev. Lett. 127, 245701 (2021).
https://doi.org/10.1103/PhysRevLett.127.245701

[36] A. Gómez-León, T. Ramos, D. Porras, and A. González-Tudela, Phys. Rev. A 105, 052223 (2022a).
https://doi.org/10.1103/PhysRevA.105.052223

[37] F. Song, S. Yao, and Z. Wang, Phys. Rev. Lett. 123, 170401 (2019).
https://doi.org/10.1103/PhysRevLett.123.170401

[38] V. Peano, M. Houde, F. Marquardt, and A. A. Clerk, Phys. Rev. X 6, 041026 (2016a).
https://doi.org/10.1103/PhysRevX.6.041026

[39] A. McDonald, T. Pereg-Barnea, and A. A. Clerk, Phys. Rev. X 8, 041031 (2018).
https://doi.org/10.1103/PhysRevX.8.041031

[40] D. Porras and S. Fernández-Lorenzo, Phys. Rev. Lett. 122, 143901 (2019).
https://doi.org/10.1103/PhysRevLett.122.143901

[41] C. C. Wanjura, M. Brunelli, and A. Nunnenkamp, Phys. Rev. Lett. 127, 213601 (2021).
https://doi.org/10.1103/PhysRevLett.127.213601

[42] A. L. CULLEN, Nature 181, 332 (1958).
https://doi.org/10.1038/181332a0

[43] T. C. White, J. Y. Mutus, I.-C. Hoi, R. Barends, B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, A. Megrant, C. Neill, P. J. J. O'Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, S. Chaudhuri, J. Gao, and J. M. Martinis, Applied Physics Letters 106, 242601 (2015).
https://doi.org/10.1063/1.4922348

[44] C. Macklin, K. O’Brien, D. Hover, M. E. Schwartz, V. Bolkhovsky, X. Zhang, W. D. Oliver, and I. Siddiqi, Science 350, 307 (2015).
https://doi.org/10.1126/science.aaa8525

[45] V. Peano, M. Houde, F. Marquardt, and A. A. Clerk, Phys. Rev. X 6, 041026 (2016b).
https://doi.org/10.1103/PhysRevX.6.041026

[46] T. Ramos, A. Gómez-León, J. J. García-Ripoll, A. González-Tudela, and D. Porras, arXiv:2207.13728 (2022), submitted.
arXiv:2207.13728

[47] J. Bourassa, F. Beaudoin, J. M. Gambetta, and A. Blais, Phys. Rev. A 86, 013814 (2012).
https://doi.org/10.1103/PhysRevA.86.013814

[48] A. Gómez-León, T. Ramos, A. González-Tudela, and D. Porras, Phys. Rev. A 106, L011501 (2022b).
https://doi.org/10.1103/PhysRevA.106.L011501

[49] C. Gardiner and P. Zoller, Quantum Noise. A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics (Springer Berlin, Heidelberg, 2004).

[50] A. Y. Kitaev, Physics-Uspekhi 44, 131 (2001).
https://doi.org/10.1070/1063-7869/44/10s/s29

[51] L. Herviou, Topological Phases and Majorana Fermions: Section 1.3., Thesis url, Université Paris-Saclay (2017).
https://pastel.archives-ouvertes.fr/tel-01651575

[52] J. Colpa, Physica A: Statistical Mechanics and its Applications 134, 417 (1986).
https://doi.org/10.1016/0378-4371(86)90057-9

[53] G. Engelhardt and T. Brandes, Physical Review A 91, 053621 (2015).
https://doi.org/10.1103/PhysRevA.91.053621

[54] S. Ryu, A. P. Schnyder, A. Furusaki, and A. W. W. Ludwig, New Journal of Physics 12, 065010 (2010).
https://doi.org/10.1088/1367-2630/12/6/065010

[55] M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010).
https://doi.org/10.1103/RevModPhys.82.3045

[56] S. Yao and Z. Wang, Phys. Rev. Lett. 121, 086803 (2018b).
https://doi.org/10.1103/PhysRevLett.121.086803

[57] N. Okuma, K. Kawabata, K. Shiozaki, and M. Sato, Phys. Rev. Lett. 124, 086801 (2020).
https://doi.org/10.1103/PhysRevLett.124.086801

[58] L. Ruocco and A. Gómez-León, Phys. Rev. B 95, 064302 (2017).
https://doi.org/10.1103/PhysRevB.95.064302

[59] C. M. Caves, Phys. Rev. D 26, 1817 (1982).
https://doi.org/10.1103/PhysRevD.26.1817

[60] A. A. Houck, H. E. Türeci, and J. Koch, Nature Physics 8, 292 (2012).
https://doi.org/10.1038/nphys2251

[61] J. J. García-Ripoll, Quantum Information and Quantum Optics with Superconducting Circuits (Cambridge University Press, Cambridge, 2022).

[62] C. Schneider, D. Porras, and T. Schaetz, Reports on Progress in Physics 75, 024401 (2012).
https://doi.org/10.1088/0034-4885/75/2/024401

[63] R. Blatt and C. F. Roos, Nature Physics 8, 277 (2012).
https://doi.org/10.1038/nphys2252

[64] M. Ludwig and F. Marquardt, Phys. Rev. Lett. 111, 073603 (2013).
https://doi.org/10.1103/PhysRevLett.111.073603

[65] A. Roy and M. Devoret, Comptes Rendus Physique Quantum microwaves / Micro-ondes quantiques, 17, 740 (2016).
https://doi.org/10.1016/j.crhy.2016.07.012

[66] C. Eichler and A. Wallraff, EPJ Quantum Technol. 1, 2 (2014).
https://doi.org/10.1140/epjqt2

[67] P. Kiefer, F. Hakelberg, M. Wittemer, A. Bermúdez, D. Porras, U. Warring, and T. Schaetz, Phys. Rev. Lett. 123, 213605 (2019).
https://doi.org/10.1103/PhysRevLett.123.213605

[68] A. Bermudez, T. Schaetz, and D. Porras, Phys. Rev. Lett. 107, 150501 (2011).
https://doi.org/10.1103/PhysRevLett.107.150501

[69] A. Bermudez, T. Schaetz, and D. Porras, New Journal of Physics 14, 053049 (2012).
https://doi.org/10.1088/1367-2630/14/5/053049

[70] P. Roushan, C. Neill, A. Megrant, Y. Chen, R. Babbush, R. Barends, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, et al., Nat. Phys. 13, 146 (2017).
https://doi.org/10.1038/nphys3930

[71] D. J. Gorman, P. Schindler, S. Selvarajan, N. Daniilidis, and H. Häffner, Phys. Rev. A 89, 062332 (2014).
https://doi.org/10.1103/PhysRevA.89.062332

[72] M. Esposito, A. Ranadive, L. Planat, S. Leger, D. Fraudet, V. Jouanny, O. Buisson, W. Guichard, C. Naud, J. Aumentado, F. Lecocq, and N. Roch, Phys. Rev. Lett. 128, 153603 (2022).
https://doi.org/10.1103/PhysRevLett.128.153603

[73] D. C. Brody, Journal of Physics A: Mathematical and Theoretical 47, 035305 (2013).
https://doi.org/10.1088/1751-8113/47/3/035305

Cited by

[1] Tomás Ramos, Álvaro Gómez-León, Juan José García-Ripoll, Alejandro González-Tudela, and Diego Porras, "Directional Josephson traveling-wave parametric amplifier via non-Hermitian topology", arXiv:2207.13728, (2022).

[2] Juan Zurita, Charles E. Creffield, and Gloria Platero, "Fast quantum transfer mediated by topological domain walls", arXiv:2208.00797, (2022).

[3] Liang-Liang Wan and Xin-You Lü, "Quantum-Squeezing-Induced Point-Gap Topology and Skin Effect", Physical Review Letters 130 20, 203605 (2023).

The above citations are from SAO/NASA ADS (last updated successfully 2023-06-09 01:28:50). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref's cited-by service no data on citing works was found (last attempt 2023-06-09 01:28:49).

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.