Dissipative stabilization of entangled cat states using a driven Bose-Hubbard dimer

M. Mamaev; L. C. G. Govia; A. A. Clerk

doi:10.22331/q-2018-03-27-58

Dissipative stabilization of entangled cat states using a driven Bose-Hubbard dimer

M. Mamaev¹, L. C. G. Govia², and A. A. Clerk²

¹Department of Physics, McGill University, Montréal, Québec, Canada.
²Institute for Molecular Engineering, University of Chicago, 5640 S. Ellis Ave., Chicago, IL 60637

Published:	2018-03-27, volume 2, page 58
Eprint:	arXiv:1711.06662v2
Doi:	https://doi.org/10.22331/q-2018-03-27-58
Citation:	Quantum 2, 58 (2018).

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

Abstract

We analyze a modified Bose-Hubbard model, where two cavities having on-site Kerr interactions are subject to two-photon driving and correlated dissipation. We derive an exact solution for the steady state of this interacting driven-dissipative system, and use it show that the system permits the preparation and stabilization of pure entangled non-Gaussian states, so-called entangled cat states. Unlike previous proposals for dissipative stabilization of such states, our approach requires only a linear coupling to a single engineered reservoir (as opposed to nonlinear couplings to two or more reservoirs). Our scheme is within the reach of state-of-the-art experiments in circuit QED.

► BibTeX data

@article{Mamaev2018dissipative,
  doi = {10.22331/q-2018-03-27-58},
  url = {https://doi.org/10.22331/q-2018-03-27-58},
  title = {Dissipative stabilization of entangled cat states using a driven {B}ose-{H}ubbard dimer},
  author = {Mamaev, M. and Govia, L. C. G. and Clerk, A. A.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {2},
  pages = {58},
  month = mar,
  year = {2018}
}

► References

[1] S. L. Braunstein and P. van Loock, Rev. Mod. Phys. 77, 513 (2005).
https://doi.org/10.1103/RevModPhys.77.513

[2] J. F. Poyatos, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 77, 4728 (1996).
https://doi.org/10.1103/PhysRevLett.77.4728

[3] A. S. Parkins, E. Solano, and J. I. Cirac, Phys. Rev. Lett. 96, 053602 (2006).
https://doi.org/10.1103/PhysRevLett.96.053602

[4] H. Krauter, C. A. Muschik, K. Jensen, W. Wasilewski, J. M. Petersen, J. I. Cirac, and E. S. Polzik, Phys. Rev. Lett. 107, 080503 (2011).
https://doi.org/10.1103/PhysRevLett.107.080503

[5] C. A. Muschik, E. S. Polzik, and J. I. Cirac, Phys. Rev. A 83, 052312 (2011).
https://doi.org/10.1103/PhysRevA.83.052312

[6] M. J. Woolley and A. A. Clerk, Phys. Rev. A 89, 063805 (2014).
https://doi.org/10.1103/PhysRevA.89.063805

[7] S. Haroche and J.-M. Raimond, Exploring the Quantum: Atoms, Cavities and Photons (Oxford University Press, Oxford, 2006).
https://doi.org/10.1093/acprof:oso/9780198509141.001.0001

[8] B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, Science 342, 607 (2013).
https://doi.org/10.1126/science.1243289

[9] M. Mirrahimi, Z. Leghtas, V. V. Albert, S. Touzard, R. J. Schoelkopf, L. Jiang, and M. H. Devoret, New J. Phys. 16, 045014 (2014).
https://doi.org/10.1088/1367-2630/16/4/045014

[10] C. Wang, Y. Y. Gao, P. Reinhold, R. W. Heeres, N. Ofek, K. Chou, C. Axline, M. Reagor, J. Blumoff, K. M. Sliwa, L. Frunzio, S. M. Girvin, L. Jiang, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, Science 352, 1087 (2016).
https://doi.org/10.1126/science.aaf2941

[11] B. C. Sanders, J. Phys. A: Math. Theor. 45, 244002 (2012).
https://doi.org/10.1088/1751-8113/45/24/244002

[12] Z. Leghtas, S. Touzard, I. M. Pop, A. Kou, B. Vlastakis, A. Petrenko, K. M. Sliwa, A. Narla, S. Shankar, M. J. Hatridge, M. Reagor, L. Frunzio, R. J. Schoelkopf, M. Mirrahimi, and M. H. Devoret, Science 347, 853 (2015).
https://doi.org/10.1126/science.aaa2085

[13] A. Sarlette, Z. Leghtas, M. Brune, J. M. Raimond, and P. Rouchon, Phys. Rev. A 86, 012114 (2012).
https://doi.org/10.1103/PhysRevA.86.012114

[14] C. Arenz, C. Cormick, D. Vitali, and G. Morigi, J. Phys. B: At. Mol. Opt. Phys. 46, 224001 (2013).
https://doi.org/10.1088/0953-4075/46/22/224001

[15] T. Pudlik, H. Hennig, D. Witthaut, and D. K. Campbell, Phys. Rev. A 88, 063606 (2013).
https://doi.org/10.1103/PhysRevA.88.063606

[16] T. Grujic, S. R. Clark, D. Jaksch, and D. G. Angelakis, Phys. Rev. A 87, 053846 (2013).
https://doi.org/10.1103/PhysRevA.87.053846

[17] B. Cao, K. W. Mahmud, and M. Hafezi, Phys. Rev. A 94, 063805 (2016).
https://doi.org/10.1103/PhysRevA.94.063805

[18] W. Casteels and C. Ciuti, Phys. Rev. A 95, 013812 (2017).
https://doi.org/10.1103/PhysRevA.95.013812

[19] W. Casteels and M. Wouters, Phys. Rev. A 95, 043833 (2017).
https://doi.org/10.1103/PhysRevA.95.043833

[20] C. Noh and D. G. Angelakis, Rep. Prog. Phys 80, 016401 (2017).
https://doi.org/10.1088/0034-4885/80/1/016401

[21] D. E. Chang, L. Jiang, A. V. Gorshkov, and H. J. Kimble, New J. Phys. 14, 063003 (2012).
https://doi.org/10.1088/1367-2630/14/6/063003

[22] A. Metelmann and A. A. Clerk, Phys. Rev. X 5, 021025 (2015).
https://doi.org/10.1103/PhysRevX.5.021025

[23] T. Yamamoto, K. Inomata, M. Watanabe, K. Matsuba, T. Miyazaki, W. D. Oliver, Y. Nakamura, and J. S. Tsai, Appl. Phys. Lett. 93, 042510 (2008).
https://doi.org/10.1063/1.2964182

[24] P. Krantz, A. Bengtsson, M. Simoen, S. Gustavsson, V. Shumeiko, W. D. Oliver, C. M. Wilson, P. Delsing, and J. Bylander, Nat. Comm. 7, 11417 EP (2016).
https://doi.org/10.1038/ncomms11417

[25] J. Y. Mutus, T. C. White, R. Barends, 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, K. M. Sundqvist, A. N. Cleland, and J. M. Martinis, Appl. Phys. Lett. 104, 263513 (2014).
https://doi.org/10.1063/1.4886408

[26] G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, Nature 495, 205 EP (2013).
https://doi.org/10.1038/nature11902

[27] K. M. Sliwa, M. Hatridge, A. Narla, S. Shankar, L. Frunzio, R. J. Schoelkopf, and M. H. Devoret, Phys. Rev. X 5, 041020 (2015).
https://doi.org/10.1103/PhysRevX.5.041020

[28] F. Lecocq, L. Ranzani, G. A. Peterson, K. Cicak, R. W. Simmonds, J. D. Teufel, and J. Aumentado, Phys. Rev. Applied 7, 024028 (2017).
https://doi.org/10.1103/PhysRevApplied.7.024028

[29] F. Lecocq, J. B. Clark, R. W. Simmonds, J. Aumentado, and J. D. Teufel, Phys. Rev. Lett. 116, 043601 (2016).
https://doi.org/10.1103/PhysRevLett.116.043601

[30] J. I. Cirac, A. S. Parkins, R. Blatt, and P. Zoller, Phys. Rev. Lett. 70, 556 (1993).
https://doi.org/10.1103/PhysRevLett.70.556

[31] P. Rabl, A. Shnirman, and P. Zoller, Phys. Rev. B 70, 205304 (2004).
https://doi.org/10.1103/PhysRevB.70.205304

[32] A. Kronwald, F. Marquardt, and A. A. Clerk, Phys. Rev. A 88, 063833 (2013).
https://doi.org/10.1103/PhysRevA.88.063833

[33] E. E. Wollman, C. U. Lei, A. J. Weinstein, J. Suh, A. Kronwald, F. Marquardt, A. A. Clerk, and K. C. Schwab, Science 349, 952 (2015).
https://doi.org/10.1126/science.aac5138

[34] F. Lecocq, J. B. Clark, R. W. Simmonds, J. Aumentado, and J. D. Teufel, Phys. Rev. X 5, 041037 (2015).
https://doi.org/10.1103/PhysRevX.5.041037

[35] J.-M. Pirkkalainen, E. Damskägg, M. Brandt, F. Massel, and M. A. Sillanpää, Phys. Rev. Lett. 115, 243601 (2015).
https://doi.org/10.1103/PhysRevLett.115.243601

[36] D. Kienzler, H.-Y. Lo, B. Keitch, L. de Clercq, F. Leupold, F. Lindenfelser, M. Marinelli, V. Negnevitsky, and J. P. Home, Science 347, 53 (2015).
https://doi.org/10.1126/science.1261033

[37] J. K. Asbóth, P. Adam, M. Koniorczyk, and J. Janszky, Eur. Phys. J. B 30, 403 (2004).
https://doi.org/10.1140/epjd/e2004-00094-2

[38] K. Fang, J. Luo, A. Metelmann, M. H. Matheny, F. Marquardt, A. A. Clerk, and O. Painter, Nature Physics 13, 465 EP (2017).
https://doi.org/10.1038/nphys4009

[39] H. Goto, Phys. Rev. A 93, 050301 (2016a).
https://doi.org/10.1103/PhysRevA.93.050301

[40] H. Goto, Sci. Rep. 6, 21686 (2016b).
https://doi.org/10.1038/srep21686

[41] F. Minganti, N. Bartolo, J. Lolli, W. Casteels, and C. Ciuti, Sci. Rep. 6, 26987 (2016).
https://doi.org/10.1038/srep26987

[42] S. Puri, S. Boutin, and A. Blais, npj Quant. Inf. 3, 18 (2017).
https://doi.org/10.1038/s41534-017-0019-1

[43] P. D. Drummond and D. F. Walls, J. Phys. A: Math. Gen. 13, 725 (1980).
https://doi.org/10.1088/0305-4470/13/2/034

[44] K. Stannigel, P. Rabl, and P. Zoller, New J. Phys. 14, 063014 (2012).
https://doi.org/10.1088/1367-2630/14/6/063014

[45] M. Reagor, H. Paik, G. Catelani, L. Sun, C. Axline, E. Holland, I. M. Pop, N. A. Masluk, T. Brecht, L. Frunzio, M. H. Devoret, L. Glazman, and R. J. Schoelkopf, Appl. Phys. Lett. 102, 192604 (2013).
https://doi.org/10.1063/1.4807015

[46] M. Reagor, W. Pfaff, C. Axline, R. W. Heeres, N. Ofek, K. Sliwa, E. Holland, C. Wang, J. Blumoff, K. Chou, M. J. Hatridge, L. Frunzio, M. H. Devoret, L. Jiang, and R. J. Schoelkopf, Phys. Rev. B 94, 014506 (2016).
https://doi.org/10.1103/PhysRevB.94.014506

[47] V. E. Manucharyan, J. Koch, L. I. Glazman, and M. H. Devoret, Science 326, 113 (2009).
https://doi.org/10.1126/science.1175552

[48] S. M. Girvin, in Quantum Machines: Measurement and Control of Engineered Quantum Systems: Lecture Notes of the Les Houches Summer School, edited by M. Devoret, R. J. Schoelkopf, B. Huard, and L. F. Cugliandolo (Oxford University Press, 2014) Chap. 3.
https://doi.org/10.1093/acprof:oso/9780199681181.001.0001

[49] J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Phys. Rev. A 76, 042319 (2007).
https://doi.org/10.1103/PhysRevA.76.042319

[50] G. Zhu, D. G. Ferguson, V. E. Manucharyan, and J. Koch, Phys. Rev. B 87, 024510 (2013).
https://doi.org/10.1103/PhysRevB.87.024510

[51] N. E. Frattini, U. Vool, S. Shankar, A. Narla, K. M. Sliwa, and M. H. Devoret, Appl. Phys. Lett. 110, 222603 (2017).
https://doi.org/10.1063/1.4984142

[52] W. Zhang, W. Huang, M. E. Gershenson, and M. T. Bell, Phys. Rev. Applied 8, 051001 (2017).
https://doi.org/10.1103/PhysRevApplied.8.051001

Cited by

[1] Tobias Graß, "Excitations and correlations in the driven-dissipative Bose-Hubbard model", Physical Review A 99 4, 043607 (2019).

[2] Fabrizio Minganti, Vincenzo Macrì, Alessio Settineri, Salvatore Savasta, and Franco Nori, "Dissipative state transfer and Maxwell's demon in single quantum trajectories: Excitation transfer between two noninteracting qubits via unbalanced dissipation rates", Physical Review A 103 5, 052201 (2021).

[3] Zheng-Yang Zhou, Clemens Gneiting, J. Q. You, and Franco Nori, "Frustration Elimination and Excited State Search in Coherent Ising Machines", Physical Review Letters 134 9, 090401 (2025).

[4] S.O. Mundhada, A. Grimm, J. Venkatraman, Z.K. Minev, S. Touzard, N.E. Frattini, V.V. Sivak, K. Sliwa, P. Reinhold, S. Shankar, M. Mirrahimi, and M.H. Devoret, "Experimental Implementation of a Raman-Assisted Eight-Wave Mixing Process", Physical Review Applied 12 5, 054051 (2019).

[5] Zheng-Yang Zhou, Clemens Gneiting, J. Q. You, and Franco Nori, "Generating and detecting entangled cat states in dissipatively coupled degenerate optical parametric oscillators", Physical Review A 104 1, 013715 (2021).

[6] R. Dassonneville, R. Assouly, T. Peronnin, A.A. Clerk, A. Bienfait, and B. Huard, "Dissipative Stabilization of Squeezing Beyond 3 dB in a Microwave Mode", PRX Quantum 2 2, 020323 (2021).

[7] Tomasz Linowski, Clemens Gneiting, and Łukasz Rudnicki, "Stabilizing entanglement in two-mode Gaussian states", Physical Review A 102 4, 042405 (2020).

[8] S. Kannan, M. Rohith, and C. Sudheesh, "Nonlinear dynamics of superposition of wavepackets", The European Physical Journal Plus 137 4, 471 (2022).

[9] Muhammad Fuady Emzir, Matthew J. Woolley, and Ian R. Petersen, "Stability analysis of quantum systems: A Lyapunov criterion and an invariance principle", Automatica 146, 110660 (2022).

[10] Iacopo Carusotto, Andrew A. Houck, Alicia J. Kollár, Pedram Roushan, David I. Schuster, and Jonathan Simon, "Photonic materials in circuit quantum electrodynamics", Nature Physics 16 3, 268 (2020).

[11] Yuan Zhou, Ying Li, Jing-Wei Wang, Xing-Chen Wang, Peng Xie, Dong Lü, Xin-Ke Li, and Hong-Tao Ren, "Robust scheme for high-fidelity generation of mesoscopic entangled cat state", Physica Scripta 98 6, 065108 (2023).

[12] Aashish Clerk, "Introduction to quantum non-reciprocal interactions: from non-Hermitian Hamiltonians to quantum master equations and quantum feedforward schemes", SciPost Physics Lecture Notes 44 (2022).

[13] Subhanka Mal, Anushree Dey, Kingshuk Adhikary, and Bimalendu Deb, "Dynamic structure factor of a driven-dissipative Bose–Hubbard model", New Journal of Physics 27 11, 114509 (2025).

[14] Łukasz Rudnicki and Clemens Gneiting, "Stabilizable Gaussian states", Physical Review A 98 3, 032120 (2018).

[15] Tomasz Linowski, Łukasz Rudnicki, and Clemens Gneiting, "Spectral stabilizability", Physical Review A 107 4, 042218 (2023).

[16] Jia-Wen Yu, Yiming Yu, Ke-Xiong Yan, Jun-Hao Lin, Jie Song, Ye-Hong Chen, and Yan Xia, "Critical states preparation in light-matter systems with deep reinforcement learning", Physical Review Research 8 3, 033063 (2026).

[17] Petr Zapletal, Andreas Nunnenkamp, and Matteo Brunelli, "Stabilization of Multimode Schrödinger Cat States Via Normal-Mode Dissipation Engineering", PRX Quantum 3 1, 010301 (2022).

[18] Timo Hillmann and Fernando Quijandría, "Quantum error correction with dissipatively stabilized squeezed-cat qubits", Physical Review A 107 3, 032423 (2023).

[19] Themistoklis K. Mavrogordatos, "Decoherence of Schrödinger cat states in light of wave/particle duality", Comptes Rendus. Physique 27 G1, 17 (2026).

[20] José Lebreuilly, Camille Aron, and Christophe Mora, "Stabilizing Arrays of Photonic Cat States via Spontaneous Symmetry Breaking", Physical Review Letters 122 12, 120402 (2019).

[21] Iacopo Carusotto, "How to exploit driving and dissipation to stabilize and manipulate quantum many-body states", Comptes Rendus. Physique 26 G1, 533 (2025).

[22] Niels Lörch, Yaxing Zhang, Christoph Bruder, and M. I. Dykman, "Quantum state preparation for coupled period tripling oscillators", Physical Review Research 1 2, 023023 (2019).

[23] Zhi-Rong Zhong, Xin-Jie Huang, Zhen-Biao Yang, Li-Tuo Shen, and Shi-Biao Zheng, "Generation and stabilization of entangled coherent states for the vibrational modes of a trapped ion", Physical Review A 98 3, 032311 (2018).

[24] Ivan Rojkov, Matteo Simoni, Elias Zapusek, Florentin Reiter, and Jonathan Home, "Stabilization of Cat-State Manifolds Using Nonlinear Reservoir Engineering", Physical Review X 16 1, 011056 (2026).

[25] David Roberts, Andrew Lingenfelter, and A.A. Clerk, "Hidden Time-Reversal Symmetry, Quantum Detailed Balance and Exact Solutions of Driven-Dissipative Quantum Systems", PRX Quantum 2 2, 020336 (2021).

[26] Patrick M. Harrington, Erich J. Mueller, and Kater W. Murch, "Engineered dissipation for quantum information science", Nature Reviews Physics 4 10, 660 (2022).

[27] Martin Koppenhöfer, Christoph Bruder, and Niels Lörch, "Heralded dissipative preparation of nonclassical states in a Kerr oscillator", Physical Review Research 2 1, 013071 (2020).

[28] Peter McConnell, Oussama Houhou, Matteo Brunelli, and Alessandro Ferraro, "Unconditional Wigner-negative mechanical entanglement with linear-and-quadratic optomechanical interactions", Physical Review A 109 3, 033508 (2024).

[29] Hayato Goto and Taro Kanao, "Chaos in coupled Kerr-nonlinear parametric oscillators", Physical Review Research 3 4, 043196 (2021).

[30] Sangil Kwon, Shohei Watabe, and Jaw-Shen Tsai, "Autonomous quantum error correction in a four-photon Kerr parametric oscillator", npj Quantum Information 8 1, 40 (2022).

[31] Th. K. Mavrogordatos, "Decoherence of Schrödinger cat states in light of wave/particle duality", arXiv:2501.12328, (2025).

[32] S. Zhao and A. Metelmann, "Dissipative preparation and stabilization of d-mode multinomial cat states", arXiv:2607.03302, (2026).

The above citations are from Crossref's cited-by service (last updated successfully 2026-08-09 21:11:52) and SAO/NASA ADS (last updated successfully 2026-08-09 21:11:54). The list may be incomplete as not all publishers provide suitable and complete citation data.

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.