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  • Open Access

Engineering active motion in quantum matter

Alexander P. Antonov1,*, Yuanjian Zheng1,*, Benno Liebchen2,†, and Hartmut Löwen1,‡

  • *These authors contributed equally to this work.
  • †Contact author: benno.liebchen@pkm.tu-darmstadt.de
  • ‡Contact author: hlowen@hhu.de
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Phys. Rev. Research 7, 033008 – Published 1 July, 2025

DOI: https://doi.org/10.1103/z3gm-32jn

Abstract

We introduce a framework for engineering active quantum matter that involves mimicking the role of self-propulsion through an external trapping potential that is moving along imposed trajectories traced by classical active dynamics. This approach in the presence of dissipation not only recovers essential dynamical behavior of classical activity, including the ballistic to diffusive crossover of its mean-square displacement, but also reveals additional features of activity that are of quantum origin. These quantum-active features are revealed in nondissipative systems, and manifest as novel exponents of the mean-square displacement at short timescales.

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References (96)

  1. M. Marchetti, J. Joanny, S. Ramaswamy, T. Liverpool, J. Prost, M. Rao, and R. A. Simha, Hydrodynamics of soft active matter, Rev. Mod. Phys. 85, 1143 (2013).
  2. S. Ramaswamy, The mechanics and statics of active matter, Annu. Rev. Condens. Matter Phys. 1, 323 (2010).
  3. G. Gompper, R. G. Winkler, T. Speck, A. Solon, C. Nardini, F. Peruani, H. Löwen, R. Golestanian, U. B. Kaupp, L. Alvarez et al., The 2020 motile active matter roadmap, J. Phys.: Condens. Matter 32, 193001 (2020).
  4. W. F. Paxton, K. C. Kistler, C. C. Olmeda, A. Sen, S. K. St. Angelo, Y. Cao, T. E. Mallouk, P. E. Lammert, and V. H. Crespi, Catalytic nanomotors: Autonomous movement of striped nanorods, J. Am. Chem. Soc. 126, 13424 (2004).
  5. C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, and G. Volpe, Active particles in complex and crowded environments, Rev. Mod. Phys. 88, 045006 (2016).
  6. J. R. Howse, R. A. Jones, A. J. Ryan, T. Gough, R. Vafabakhsh, and R. Golestanian, Self-motile colloidal particles: From directed propulsion to random walk, Phys. Rev. Lett. 99, 048102 (2007).
  7. R. Dreyfus, J. Baudry, M. L. Roper, M. Fermigier, H. A. Stone, and J. Bibette, Microscopic artificial swimmers, Nature (London) 437, 862 (2005).
  8. P. Tierno, R. Golestanian, I. Pagonabarraga, and F. Sagues, Magnetically actuated colloidal microswimmers, J. Phys. Chem. B 112, 16525 (2008).
  9. J. Deseigne, O. Dauchot, and H. Chaté, Collective motion of vibrated polar disks, Phys. Rev. Lett. 105, 098001 (2010).
  10. M. X. Lim, A. Souslov, V. Vitelli, and H. M. Jaeger, Cluster formation by acoustic forces and active fluctuations in levitated granular matter, Nat. Phys. 15, 460 (2019).
  11. F. Schmidt, B. Liebchen, H. Löwen, and G. Volpe, Light-controlled assembly of active colloidal molecules, J. Chem. Phys. 150, 094905 (2019).
  12. S. Saha, J. Agudo-Canalejo, and R. Golestanian, Scalar active mixtures: The nonreciprocal Cahn-Hilliard model, Phys. Rev. X 10, 041009 (2020).
  13. A. V. Ivlev, J. Bartnick, M. Heinen, C.-R. Du, V. Nosenko, and H. Löwen, Statistical mechanics where Newton's third law is broken, Phys. Rev. X 5, 011035 (2015).
  14. J. Grauer, F. Schmidt, J. Pineda, B. Midtvedt, H. Löwen, G. Volpe, and B. Liebchen, Active droploids, Nat. Commun. 12, 6005 (2021).
  15. P. Surówka, A. Souslov, F. Jülicher, and D. Banerjee, Odd Cosserat elasticity in active materials, Phys. Rev. E 108, 064609 (2023).
  16. R. Soto and R. Golestanian, Self-assembly of catalytically active colloidal molecules: Tailoring activity through surface chemistry, Phys. Rev. Lett. 112, 068301 (2014).
  17. R. Niu, A. Fischer, T. Palberg, and T. Speck, Dynamics of binary active clusters driven by ion-exchange particles, ACS Nano 12, 10932 (2018).
  18. J. Toner and Y. Tu, Long-range order in a two-dimensional dynamical XY model: how birds fly together, Phys. Rev. Lett. 75, 4326 (1995).
  19. J. Toner and Y. Tu, Flocks, herds, and schools: A quantitative theory of flocking, Phys. Rev. E 58, 4828 (1998).
  20. V. Narayan, S. Ramaswamy, and N. Menon, Long-lived giant number fluctuations in a swarming granular nematic, Science 317, 105 (2007).
  21. M. E. Cates and J. Tailleur, Motility-induced phase separation, Annu. Rev. Condens. Matter Phys. 6, 219 (2015).
  22. I. Theurkauff, C. Cottin-Bizonne, J. Palacci, C. Ybert, and L. Bocquet, Dynamic clustering in active colloidal suspensions with chemical signaling, Phys. Rev. Lett. 108, 268303 (2012).
  23. J. Palacci, S. Sacanna, A. P. Steinberg, D. J. Pine, and P. M. Chaikin, Living crystals of light-activated colloidal surfers, Science 339, 936 (2013).
  24. I. Buttinoni, J. Bialké, F. Kümmel, H. Löwen, C. Bechinger, and T. Speck, Dynamical clustering and phase separation in suspensions of self-propelled colloidal particles, Phys. Rev. Lett. 110, 238301 (2013).
  25. F. Ginot, I. Theurkauff, F. Detcheverry, C. Ybert, and C. Cottin-Bizonne, Aggregation-fragmentation and individual dynamics of active clusters, Nat. Commun. 9, 696 (2018).
  26. G. M. Whitesides, Soft robotics, Angew. Chem. Int. Ed. 57, 4258 (2018).
  27. M. Leyman, F. Ogemark, J. Wehr, and G. Volpe, Tuning phototactic robots with sensorial delays, Phys. Rev. E 98, 052606 (2018).
  28. G. Vásárhelyi, C. Virágh, G. Somorjai, T. Nepusz, A. E. Eiben, and T. Vicsek, Optimized flocking of autonomous drones in Confined Environments, Sci. Robot. 3, eaat3536 (2018).
  29. N. A. M. Araújo, L. M. C. Janssen, T. Barois, G. Boffetta, I. Cohen, A. Corbetta, O. Dauchot, M. Dijkstra, W. M. Durham, A. Dussutour et al., Steering self-organisation through confinement, Soft Matter 19, 1695 (2023).
  30. S. J. Ebbens, Active colloids: Progress and challenges towards realising autonomous applications, Curr. Opin. Colloid Interface Sci. 21, 14 (2016).
  31. M. R. Shaebani, A. Wysocki, R. G. Winkler, G. Gompper, and H. Rieger, Computational models for active matter Nat. Rev. Phys. 2, 181 (2020).
  32. B. M. Mognetti, A. Saric, S. Angloletti-Uberti, A. Cacciuto, C. Valeriani, and D. Frenkel, Living clusters and crystals from low-density suspensions of active colloids, Phys. Rev. Lett. 111, 245702 (2013).
  33. M. E. Leunissen, C. G. Gristova, A.-P. Hynninen, C. P. Royall, A. I. Campbell, A. Imhof, M. Dijkstra, R. van Roij, and A. van Blaaderen, Ionic colloidal crystals of oppositely charged particles, Nature (London) 437, 235 (2005).
  34. S. H. L. Klapp, Collective dynamics of dipolar and multipolar colloids: From passive to active systems, Curr. Opin. Colloid Interface Sci. 21, 76 (2016).
  35. A. Ziepke, I. Maryshev, I. S. Aranson, and E. Frey, Multiscale organization in communicating active matter, Nat. Commun. 13, 6727 (2022).
  36. M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Observation of Bose-Einstein condensation in a dilute atomic vapor, Science 269, 198 (1995).
  37. C. C. Bradley, C. A. Sackett, J. J. Tollett, and R. G. Hulet, Bose-Einstein condensation of sodium atoms, Phys. Rev. Lett. 75, 1687 (1995).
  38. D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, Quantum dynamics of single trapped ions, Rev. Mod. Phys. 75, 281 (2003).
  39. Z. Hu and H. J. Kimble, Observation of a single atom in a magneto-optical trap, Opt. Lett. 19, 1888 (1994).
  40. I. Bloch, J. Dalibard, and W. Zwerger, Many-Body physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008).
  41. M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond, Adv. Phys. 56, 243 (2007).
  42. T. Langen, R. Geiger, and J. Schmiedmayer, Ultracold atoms out of equilibrium, Annu. Rev. Condens. Matter Phys. 6, 201 (2015).
  43. A. Polkovnikov, K. Sengupta, A. Silva, and M. Vengalattore, Colloquium: Nonequilibrium dynamics of closed interacting quantum systems, Rev. Mod. Phys. 83, 863 (2011).
  44. M. Heyl, Dynamical quantum phase transitions: A review, Rep. Prog. Phys. 81, 054001 (2018).
  45. U. Schneider, L. Hackermüller, J. P. Ronzheimer, S. Will, S. Braun, T. Best, I. Bloch, E. Demler, S. Mandt, D. Rasch et al., Fermionic transport and out-of-equilibrium dynamics in a homogeneous Hubbard model with ultracold atoms, Nat. Phys. 8, 213 (2012).
  46. T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen, and O. Shochet, Novel type of phase transition in a system of self-driven particles, Phys. Rev. Lett. 75, 1226 (1995).
  47. H. M. López, J. Gachelin, C. Douarche, H. Auradou, and E. Clément, Turning bacteria suspensions into superfluids, Phys. Rev. Lett. 115, 028301 (2015).
  48. S. Guo, D. Samanta, Y. Peng, X. Xu, and X. Cheng, Symmetric shear banding and swarming vortices in bacterial superfluids, Proc. Natl. Acad. Sci. USA 115, 7212 (2018).
  49. M. te Vrugt, T. Frohoff-Hülsmann, E. Heifetz, U. Thiele, and R. Wittkowski, From a microscopic inertial active matter model to the Schrödinger equation, Nat. Commun. 14, 1302 (2023).
  50. K. Sone and Y. Ashida, Anomalous topological active matter, Phys. Rev. Lett. 123, 205502 (2019).
  51. B. Loewe, A. Souslov, and P. M. Goldbart, Flocking from a quantum Analogy: Spin–Orbit coupling in an active fluid, New J. Phys. 20, 013020 (2018).
  52. Y. Couder, and E. Fort, Single-Particle diffraction and interference at a macroscopic scale, Phys. Rev. Lett. 97, 154101 (2006).
  53. J. E. Avron, B. Gutkin, and D. H. Oaknin, Adiabatic swimming in an ideal quantum gas, Phys. Rev. Lett. 96, 130602 (2006).
  54. H. Saito, Can we swim in superfluids?: Numerical demonstration of self-propulsion in a Bose–Einstein condensate, J. Phys. Soc. Jpn. 84, 114001 (2015).
  55. V. Shukla, M. Brachet, and R. Pandit, Sticking transition in a minimal model for the collisions of active particles in quantum fluids, Phys. Rev. A 94, 041602(R) (2016).
  56. U. Giuriato and G. Krstulovic, Interaction between active particles and quantum vortices leading to Kelvin wave generation, Sci. Rep. 9, 4839 (2019).
  57. G. V. Kolmakov and I. S. Aranson, Superfluid swimmers, Phys. Rev. Res. 3, 013188 (2021).
  58. K. Adachi, K. Takasan, and K. Kawaguchi, Activity-induced phase transition in a quantum many-body system Phys. Rev. Res. 4, 013194 (2022).
  59. M. Yamagishi, N. Hatano, and H. Obuse, Defining a quantum active particle using non-Hermitian quantum walk, Sci. Rep. 14, 28648 (2024).
  60. A. S. Matsoukas-Roubeas, F. Roccati, J. Cornelius, Z. Xu, A. Chenu, and A. del Campo, Non-Hermitian Hamiltonian deformations in quantum mechanics, J. High Energy Phys. 01 (2023) 060.
  61. R. Khasseh, S. Wald, R. Moessner, C. A. Weber, and M. Heyl, Active quantum flocks, arXiv:2308.01603.
  62. I. Bloch, J. Dalibard, and S. Nascimbéne, Quantum simulations with ultracold quantum gases Nat. Phys. 8, 267 (2012).
  63. A. M. Kaufman and K.-K. Ni, Quantum science with optical tweezer arrays of ultracold atoms and molecules, Nat. Phys. 17, 1324 (2021).
  64. A. Browaeys and T. Lahaye, Many-body physics with individually controlled Rydberg atoms, Nat. Phys. 16, 132 (2020).
  65. F. Schäfer, T. Fukuhara, S. Sugawa, Y. Takasu, and Y. Takahashi, Tools for quantum simulation with ultracold atoms in optical lattices, Nat. Rev. Phys. 2, 411 (2020).
  66. G. Morigi, J. Eschner, C. Cormick, Y. Lin, D. Leibfried, and D. J. Wineland, Dissipative quantum control of a spin chain, Phys. Rev. Lett. 115, 200502 (2015).
  67. G. Pesce, P. H. Jones, O. M. Maragò, and G. Volpe, Optical tweezers: Theory and practice, Eur. Phys. J. Plus 135, 949 (2020).
  68. A. Ashkin, Acceleration and trapping of particles by radiation pressure, Phys. Rev. Lett. 24, 156 (1970).
  69. X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guery-Odelin, and J. G. Muga, Fast optimal frictionless atom cooling in harmonic traps: Shortcut to adiabaticity, Phys. Rev. Lett. 104, 063002 (2010).
  70. O. Abah, J. Roßnagel, G. Jacob, S. Deffner, F. Schmidt-Kaler, K. Singer, and E. Lutz, Single-Ion heat engine at maximum power, Phys. Rev. Lett. 109, 203006 (2012).
  71. J. Roßnagel, O. Abah, F. Schmidt-Kaler, K. Singer, and E. Lutz, Nanoscale heat engine beyond the carnot limit, Phys. Rev. Lett. 112, 030602 (2014).
  72. S. Sabhapandit and S. N. Majumdar, Noninteracting particles in a harmonic trap with a stochastically driven center, J. Phys. A: Math. Theor. 57, 335003 (2024).
  73. G. E. Uhlenbeck and L. S. Ornstein, 1930, On the theory of the Brownian motion, Phys. Rev. 36, 823 (1930).
  74. P. Romanczuk, M. Bär, W. Ebeling, B. Lindner, and L. Schimansky-Geier, Active Brownian particles, Eur. Phys. J. Spec. Top. 202, 1 (2012).
  75. L. Bonilla, Active Ornstein-Uhlenbeck particles, Phys. Rev. E 100, 022601 (2019).
  76. À. Rivas and S. F. Huelga, Open Quantum Systems: An Introduction (Springer, Berlin, 2011).
  77. B. G. Englert and G. Morigi, Five Lectures on Dissipative Master Equations. Coherent Evolution in Noisy Environments, Lecture Notes in Physics, Vol 611 (Springer, Berlin, 2002).
  78. A. P. Antonov, S. Lee, B. Liebchen, and H. Löwen, J. Melles, Y. Tuchkov, and M. te Vrugt (unpublished).
  79. See Supplemental Material at http://link.aps.org/supplemental/10.1103/z3gm-32jn for details of analytical calculations and numerical method, which includes Refs. [90, 91, 92, 93, 94, 95, 96].
  80. G. H. P. Nguyen, R. Wittmann, and H. Löwen, Active Ornstein–Uhlenbeck model for self-propelled particles with inertia, J. Phys.: Condens. Matter 34, 035101 (2022).
  81. R. Veyron, J.-P. Gérent, G. Baclet, V. Mancois, P. Bouyer, and S. Bernon, In situ subwavelength microscopy of ultracold atoms using dressed excited states, PRX Quantum 5, 030349 (2024).
  82. A. Solon, M. Cates, and J. Tailleur, Active brownian particles and run-and-tumble particles: A comparative study, Eur. Phys. J. Spec. Top. 224, 1231 (2015).
  83. M. E. Cates and J. Tailleur, When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation, Europhys. Lett. 101, 20010 (2013).
  84. E. Frey and K. Kroy, Brownian motion: A paradigm of soft matter and biological physics, Ann. Phys. (Leipzig) 517, 20 (2005).
  85. M. Hyrkäs, V. Apaja, and M. Manninen, Many-particle dynamics of bosons and fermions in quasi-one-dimensional flat-band lattices, Phys. Rev. A 87, 023614 (2013).
  86. J. W. Abraham, K. Balzer, D. Hochstuhl, and M. Bonitz, Quantum breathing mode of trapped systems in one and two dimensions, Phys. Rev. B 86, 125112 (2012).
  87. Y. Zheng and D. Poletti, Quantum statistics and the performance of engine cycles, Phys. Rev. E 92, 012110 (2015).
  88. N. M. Myers and S. Deffner, Bosons outperform fermions: The thermodynamic advantage of symmetry, Phys. Rev. E 101, 012110 (2020).
  89. M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms, Nature (London) 415, 39 (2002).
  90. D. J. Griffiths and D. F. Schroeter, Introduction to Quantum Mechanics, 3rd ed. (Cambridge University Press, Cambridge, 2018).
  91. C. W. Gardiner and P. Zoller, Quantum Noise (Springer, Berlin, 2000).
  92. H. P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002).
  93. D. Manzano, A short introduction to the Lindblad master equation, AIP Adv. 10, 025106 (2020).
  94. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes, The Art of Scientific Computing, 3rd ed. (Cambridge University Press, Cambridge, 2007).
  95. D. Martin, J. O'Byrne, M. E. Cates, É. Fodor, C. Nardini, J. Tailleur, and F. van Wijland, Statistical mechanics of active Ornstein-Uhlenbeck particles, Phys. Rev. E 103, 032607 (2021).
  96. L. Comtet, Advanced Combinatorics (Springer, Dordrecht, 1974).

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Phys. Rev. Research 7, 033008– Published 1 July, 2025
  • Received 7 April 2024
  • Revised 19 February 2025
  • Accepted 9 June 2025
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