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Dipolar optimal control of entangled current states

Héctor Briongos-Merino1,2,*, Felipe Isaule3, Bruno Juliá-Díaz1,2, and Montserrat Guilleumas1,2

  • *Contact author: hbriongos@fqa.ub.edu
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Phys. Rev. Research 8, 033121 – Published 28 July, 2026

DOI: https://doi.org/10.1103/yt2c-1qh7

Abstract

Quantum state control is a fundamental tool for quantum technologies. In this work, we propose and analyze the use of quantum optimal control to exploit the dipolar interaction of ultracold atoms on a lattice ring, focusing on the generation of selected states with entangled circulation. This scheme requires time-dependent control over the orientation of the magnetic field, a technique that is feasible in ultracold atom laboratories. The system's evolution is driven by just two independent control functions. We describe the symmetry constraints of this approach and numerically test them using the extended Bose-Hubbard model. We find that the proposed control can engineer entangled current states with perfect fidelity across a wide range of systems, and that in the remaining cases, the theoretical upper bounds for fidelity are reached.

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References (62)

  1. E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lundgren, and D. Preda, A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem, Science 292, 472 (2001).
  2. X. Chen, B. Zeng, Z.-C. Gu, B. Yoshida, and I. L. Chuang, Gapped two-body Hamiltonian whose unique ground state is universal for one-way quantum computation, Phys. Rev. Lett. 102, 220501 (2009).
  3. A. S. Sørensen, E. Altman, M. Gullans, J. V. Porto, M. D. Lukin, and E. Demler, Adiabatic preparation of many-body states in optical lattices, Phys. Rev. A 81, 061603(R) (2010).
  4. M. Ljubotina, B. Roos, D. A. Abanin, and M. Serbyn, Optimal steering of matrix product states and quantum many-body scars, PRX Quantum 3, 030343 (2022).
  5. C. Lin, Y. Ma, and D. Sels, Optimal control for quantum metrology via Pontryagin's principle, Phys. Rev. A 103, 052607 (2021).
  6. D. S. Grün, K. Wittmann W., L. H. Ymai, J. Links, and A. Foerster, Protocol designs for NOON states, Commun. Phys. 5, 36 (2022).
  7. C. Jarzynski, Generating shortcuts to adiabaticity in quantum and classical dynamics, Phys. Rev. A 88, 040101(R) (2013).
  8. L. C. Venuti, T. Albash, M. Marvian, D. Lidar, and P. Zanardi, Relaxation versus adiabatic quantum steady-state preparation, Phys. Rev. A 95, 042302 (2017).
  9. T. Hatomura, Shortcuts to adiabaticity: Theoretical framework, relations between different methods, and versatile approximations, J. Phys. B: At. Mol. Opt. Phys. 57, 102001 (2024).
  10. F. Albertini and D. D'Alessandro, Notions of controllability for quantum mechanical systems, in Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228) (IEEE, Orlando, FL, USA, 2001), Vol. 2, pp. 1589–1594.
  11. D. Dong and I. R. Petersen, Quantum control theory and applications: A survey, IET Control Theory Appl. 4, 2651 (2010).
  12. S. J. Glaser, U. Boscain, T. Calarco, C. P. Koch, W. Köckenberger, R. Kosloff, I. Kuprov, B. Luy, S. Schirmer, T. Schulte-Herbrüggen, D. Sugny, and F. K. Wilhelm, Training Schrödinger's cat: Quantum optimal control, Eur. Phys. J. D 69, 279 (2015).
  13. D. D'Alessandro, Introduction to Quantum Control and Dynamics, 2nd ed. (Chapman and Hall/CRC, New York, 2021).
  14. C. P. Koch, U. Boscain, T. Calarco, G. Dirr, S. Filipp, S. J. Glaser, R. Kosloff, S. Montangero, T. Schulte-Herbrüggen, D. Sugny, and F. K. Wilhelm, Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe, EPJ Quantum Technol. 9, 19 (2022).
  15. O. Morandi, Optimal control of entanglement in atom pairs with dipole-dipole interaction by quantum phase space formalism, Phys. Lett. A 502, 129390 (2024).
  16. L.-N. Wu, X. Li, N. Goldman, and B. Wang, Optimal control for preparing fractional quantum Hall states in optical lattices, Phys. Rev. B 111, 235111 (2025).
  17. T. Haug, R. Dumke, L.-C. Kwek, C. Miniatura, and L. Amico, Machine-learning engineering of quantum currents, Phys. Rev. Res. 3, 013034 (2021).
  18. F. Perciavalle, D. Rossini, J. Polo, O. Morsch, and L. Amico, Quantum superpositions of current states in Rydberg-atom networks, Phys. Rev. Res. 6, 043025 (2024).
  19. S. Machnes, U. Sander, S. J. Glaser, P. de Fouquières, A. Gruslys, S. Schirmer, and T. Schulte-Herbrüggen, Comparing, optimizing, and benchmarking quantum-control algorithms in a unifying programming framework, Phys. Rev. A 84, 022305 (2011).
  20. N. Khaneja, T. Reiss, C. Kehlet, T. Schulte-Herbrüggen, and S. J. Glaser, Optimal control of coupled spin dynamics: Design of NMR pulse sequences by gradient ascent algorithms, J. Magn. Reson. 172, 296 (2005).
  21. M. M. Müller, R. S. Said, F. Jelezko, T. Calarco, and S. Montangero, One decade of quantum optimal control in the chopped random basis, Rep. Prog. Phys. 85, 076001 (2022).
  22. D. M. Reich, M. Ndong, and C. P. Koch, Monotonically convergent optimization in quantum control using Krotov's method, J. Chem. Phys. 136, 104103 (2012).
  23. G. Carleo, I. Cirac, K. Cranmer, L. Daudet, M. Schuld, N. Tishby, L. Vogt-Maranto, and L. Zdeborová, Machine learning and the physical sciences, Rev. Mod. Phys. 91, 045002 (2019).
  24. A. Norambuena, M. Mattheakis, F. J. González, and R. Coto, Physics-informed neural networks for quantum control, Phys. Rev. Lett. 132, 010801 (2024).
  25. L. Amico, M. Boshier, G. Birkl, A. Minguzzi, C. Miniatura, L.-C. Kwek, D. Aghamalyan, V. Ahufinger, D. Anderson, N. Andrei et al., Roadmap on atomtronics: State of the art and perspective, AVS Quantum Sci. 3, 039201 (2021).
  26. L. Amico, D. Anderson, M. Boshier, J.-P. Brantut, L.-C. Kwek, A. Minguzzi, and W. von Klitzing, Colloquium: Atomtronic circuits: From many-body physics to quantum technologies, Rev. Mod. Phys. 94, 041001 (2022).
  27. M. Lu, N. Q. Burdick, S. H. Youn, and B. L. Lev, Strongly dipolar Bose-Einstein condensate of dysprosium, Phys. Rev. Lett. 107, 190401 (2011).
  28. Y. Tang, N. Q. Burdick, K. Baumann, and B. L. Lev, Bose–Einstein condensation of Dy162 and Dy160, New J. Phys. 17, 045006 (2015).
  29. K. Aikawa, A. Frisch, M. Mark, S. Baier, A. Rietzler, R. Grimm, and F. Ferlaino, Bose-Einstein condensation of erbium, Phys. Rev. Lett. 108, 210401 (2012).
  30. A. Griesmaier, J. Werner, S. Hensler, J. Stuhler, and T. Pfau, Bose-Einstein condensation of chromium, Phys. Rev. Lett. 94, 160401 (2005).
  31. Y. Miyazawa, R. Inoue, H. Matsui, G. Nomura, and M. Kozuma, Bose-Einstein condensation of europium, Phys. Rev. Lett. 129, 223401 (2022).
  32. J. L. Bohn, A. M. Rey, and J. Ye, Cold molecules: Progress in quantum engineering of chemistry and quantum matter, Science 357, 1002 (2017).
  33. T. Langen, G. Valtolina, D. Wang, and J. Ye, Quantum state manipulation and cooling of ultracold molecules, Nat. Phys. 20, 702 (2024).
  34. N. Bigagli, W. Yuan, S. Zhang, B. Bulatovic, T. Karman, I. Stevenson, and S. Will, Observation of Bose–Einstein condensation of dipolar molecules, Nature (London) 631, 289 (2024).
  35. A. Gallemí, M. Guilleumas, R. Mayol, and A. Sanpera, Role of anisotropy in dipolar bosons in triple-well potentials, Phys. Rev. A 88, 063645 (2013).
  36. M. Rovirola, H. Briongos-Merino, B. Juliá-Díaz, and M. Guilleumas, Ultracold dipolar bosons trapped in atomtronic circuits, Phys. Rev. A 109, 063331 (2024).
  37. L. H. Ymai and A. P. Tonel, Tunneling control of dipolar bosons in triple-well circuits via dipole polarization orientation and quantum sensing application, Phys. Rev. A 112, 013302 (2025).
  38. H. Briongos-Merino, F. Isaule, M. Guilleumas, and B. Juliá-Díaz, Dipolar magnetostirring protocol for three-well atomtronic circuits, SciPost Phys. 19, 059 (2025).
  39. L. Klaus, T. Bland, E. Poli, C. Politi, G. Lamporesi, E. Casotti, R. N. Bisset, M. J. Mark, and F. Ferlaino, Observation of vortices and vortex stripes in a dipolar condensate, Nat. Phys. 18, 1453 (2022).
  40. S. B. Prasad, T. Bland, B. C. Mulkerin, N. G. Parker, and A. M. Martin, Vortex lattice formation in dipolar Bose-Einstein condensates via rotation of the polarization, Phys. Rev. A 100, 023625 (2019).
  41. S. B. Prasad, B. C. Mulkerin, and A. M. Martin, Arbitrary-angle rotation of the polarization of a dipolar Bose-Einstein condensate, Phys. Rev. A 103, 033322 (2021).
  42. T. Bland, G. Lamporesi, M. J. Mark, and F. Ferlaino, Vortices in dipolar Bose-Einstein condensates, C. R. Phys. 24, 133 (2023).
  43. T. L. Gustavson, P. Bouyer, and M. A. Kasevich, Precision rotation measurements with an atom interferometer gyroscope, Phys. Rev. Lett. 78, 2046 (1997).
  44. G. Pelegrí, J. Mompart, and V. Ahufinger, Quantum sensing using imbalanced counter-rotating Bose–Einstein condensate modes, New J. Phys. 20, 103001 (2018).
  45. J. E. Mooij and C. J. P. M. Harmans, Phase-slip flux qubits, New J. Phys. 7, 219 (2005).
  46. V. Ramakrishna, M. V. Salapaka, M. Dahleh, H. Rabitz, and A. Peirce, Controllability of molecular systems, Phys. Rev. A 51, 960 (1995).
  47. S. G. Schirmer, H. Fu, and A. I. Solomon, Complete controllability of quantum systems, Phys. Rev. A 63, 063410 (2001).
  48. V. Jurdjevic and H. J. Sussmann, Control systems on Lie groups, J. Differ. Equations 12, 313 (1972).
  49. G. Turinici and H. Rabitz, Quantum wavefunction controllability, Chem. Phys. 267, 1 (2001).
  50. R. Chakrabarti and H. Rabitz, Quantum control landscapes, Int. Rev. Phys. Chem. 26, 671 (2007).
  51. H. Fu, S. G. Schirmer, and A. I. Solomon, Complete controllability of finite-level quantum systems, J. Phys. A: Math. Gen. 34, 1679 (2001).
  52. R. Zeier and T. Schulte-Herbrüggen, Symmetry principles in quantum systems theory, J. Math. Phys. 52, 113510 (2011).
  53. M. H. Goerz, S. C. Carrasco, and V. S. Malinovsky, Quantum optimal control via semi-automatic differentiation, Quantum 6, 871 (2022).
  54. S. Baier, M. J. Mark, D. Petter, K. Aikawa, L. Chomaz, Z. Cai, M. Baranov, P. Zoller, and F. Ferlaino, Extended Bose-Hubbard models with ultracold magnetic atoms, Science 352, 201 (2016).
  55. L. Su, A. Douglas, M. Szurek, R. Groth, S. F. Ozturk, A. Krahn, A. H. Hébert, G. A. Phelps, S. Ebadi, S. Dickerson, F. Ferlaino, O. Marković, and M. Greiner, Dipolar quantum solids emerging in a Hubbard quantum simulator, Nature (London) 622, 724 (2023).
  56. Y. Tang, W. Kao, K.-Y. Li, and B. L. Lev, Tuning the dipole-dipole interaction in a quantum gas with a rotating magnetic field, Phys. Rev. Lett. 120, 230401 (2018).
  57. H. Briongos-Merino, Data for: Dipolar optimal control of quantum states - State preparation [Data set], Zenodo, 2025, https://doi.org/10.5281/zenodo.18661208.
  58. F. Ninio, A simple proof of the Perron-Frobenius theorem for positive symmetric matrices, J. Phys. A: Math. Gen. 9, 1281 (1976).
  59. S. Deffner and E. Lutz, Energy–time uncertainty relation for driven quantum systems, J. Phys. A: Math. Theor. 46, 335302 (2013).
  60. M. Okuyama and M. Ohzeki, Comment on ‘Energy-time uncertainty relation for driven quantum systems', J. Phys. A: Math. Theor. 51, 318001 (2018).
  61. A. Carlini, A. Hosoya, T. Koike, and Y. Okudaira, Time-optimal quantum evolution, Phys. Rev. Lett. 96, 060503 (2006).
  62. P. J. Jones and P. Kok, Geometric derivation of the quantum speed limit, Phys. Rev. A 82, 022107 (2010).

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Phys. Rev. Research 8, 033121– Published 28 July, 2026
  • Received 11 August 2025
  • Accepted 29 June 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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