Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
131 tokens/sec
GPT-4o
10 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

From integrability to chaos: the quantum-classical correspondence in a triple well bosonic model (2311.13189v2)

Published 22 Nov 2023 in quant-ph, nlin.CD, nlin.SI, and physics.class-ph

Abstract: In this work, we investigate the semiclassical limit of a simple bosonic quantum many-body system exhibiting both integrable and chaotic behavior. A classical Hamiltonian is derived using coherent states. The transition from regularity to chaos in classical dynamics is visualized through Poincar\'e sections. Classical trajectories in phase space closely resemble the projections of the Husimi functions of eigenstates with similar energy, even in chaotic cases. It is demonstrated that this correlation is more evident when projecting the eigenstates onto the Fock states. The analysis is carried out at a critical energy where the eigenstates are maximally delocalized in the Fock basis. Despite the imperfect delocalization, its influence is present in the classical and quantum properties under investigation. The study systematically establishes quantum-classical correspondence for a bosonic many-body system with more than two wells, even within the chaotic region.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (65)
  1. F. Haake, Quantum Signatures of Chaos. Berlin, Heidelberg: Springer-Verlag, 2010.
  2. M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics. New York, NY: Springer, 2013.
  3. M. C. Gutzwiller, “Periodic Orbits and Classical Quantization Conditions,” Journal of Mathematical Physics, vol. 12, pp. 343–358, 10 2003.
  4. R. Aurich, J. Bolte, and F. Steiner, “Universal signatures of quantum chaos,” Phys. Rev. Lett., vol. 73, pp. 1356–1359, Sep 1994.
  5. O. Bohigas, S. Tomsovic, and D. Ullmo, “Manifestations of classical phase space structures in quantum mechanics,” Physics Reports, vol. 223, no. 2, pp. 43–133, 1993.
  6. O. Bohigas, M. J. Giannoni, and C. Schmit, “Characterization of chaotic quantum spectra and universality of level fluctuation laws,” Phys. Rev. Lett., vol. 52, pp. 1–4, Jan 1984.
  7. P. Sěba, “Wave chaos in singular quantum billiard,” Phys. Rev. Lett., vol. 64, pp. 1855–1858, Apr 1990.
  8. C. Lozej, G. Casati, and T. Prosen, “Quantum chaos in triangular billiards,” Phys. Rev. Res., vol. 4, p. 013138, Feb 2022.
  9. R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev., vol. 93, pp. 99–110, Jan 1954.
  10. L. Bakemeier, A. Alvermann, and H. Fehske, “Dynamics of the dicke model close to the classical limit,” Phys. Rev. A, vol. 88, p. 043835, Oct 2013.
  11. S. Pilatowsky-Cameo, D. Villaseñor, M. A. Bastarrachea-Magnani, S. Lerma-Hernández, L. F. Santos, and J. G. Hirsch, “Quantum scarring in a spin-boson system: fundamental families of periodic orbits,” New Journal of Physics, vol. 23, p. 033045, mar 2021.
  12. C. Emary and T. Brandes, “Chaos and the quantum phase transition in the dicke model,” Phys. Rev. E, vol. 67, p. 066203, Jun 2003.
  13. M. A. Bastarrachea-Magnani, B. L. del Carpio, S. Lerma-Hernández, and J. G. Hirsch, “Chaos in the dicke model: quantum and semiclassical analysis,” Physica Scripta, vol. 90, p. 068015, may 2015.
  14. Q. Wang, “Quantum chaos in the extended dicke model,” Entropy, vol. 24, no. 10, 2022.
  15. T. Gorin and T. H. Seligman, “Signatures of the correlation hole in total and partial cross sections,” Phys. Rev. E, vol. 65, p. 026214, Jan 2002.
  16. E. J. Torres-Herrera and L. F. Santos, “Dynamical manifestations of quantum chaos: correlation hole and bulge,” Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 375, no. 2108, p. 20160434, 2017.
  17. L. F. Santos, F. Borgonovi, and F. M. Izrailev, “Onset of chaos and relaxation in isolated systems of interacting spins: Energy shell approach,” Phys. Rev. E, vol. 85, p. 036209, Mar 2012.
  18. J. French and S. Wong, “Validity of random matrix theories for many-particle systems,” Physics Letters B, vol. 33, no. 7, pp. 449–452, 1970.
  19. T. A. Brody, J. Flores, J. B. French, P. A. Mello, A. Pandey, and S. S. M. Wong, “Random-matrix physics: spectrum and strength fluctuations,” Rev. Mod. Phys., vol. 53, pp. 385–479, Jul 1981.
  20. L. F. Santos and M. Rigol, “Onset of quantum chaos in one-dimensional bosonic and fermionic systems and its relation to thermalization,” Phys. Rev. E, vol. 81, p. 036206, Mar 2010.
  21. R. Mondaini and M. Rigol, “Eigenstate thermalization in the two-dimensional transverse field ising model. ii. off-diagonal matrix elements of observables,” Phys. Rev. E, vol. 96, p. 012157, Jul 2017.
  22. L. F. Santos, F. Pérez-Bernal, and E. J. Torres-Herrera, “Speck of chaos,” Phys. Rev. Res., vol. 2, p. 043034, Oct 2020.
  23. K. W. Wilsmann, L. H. Ymai, A. P. Tonel, J. Links, and A. Foerster, “Control of tunneling in an atomtronic switching device,” Commun Phys, vol. 1, p. 91, Dec 2018.
  24. K. Wittmann W., E. R. Castro, A. Foerster, and L. F. Santos, “Interacting bosons in a triple well: Preface of many-body quantum chaos,” Phys. Rev. E, vol. 105, p. 034204, Mar 2022.
  25. G. Nakerst and M. Haque, “Chaos in the three-site bose-hubbard model: Classical versus quantum,” Phys. Rev. E, vol. 107, p. 024210, Feb 2023.
  26. L. H. Ymai, A. P. Tonel, A. Foerster, and J. Links, “Quantum integrable multi-well tunneling models,” J. Phys. A Math. Theor., vol. 50, no. 26, p. 264001, 2017.
  27. A. J. Leggett, “Bose-einstein condensation in the alkali gases: Some fundamental concepts,” Rev. Mod. Phys., vol. 73, pp. 307–356, Apr 2001.
  28. I. Bloch, J. Dalibard, and W. Zwerger, “Many-body physics with ultracold gases,” Rev. Mod. Phys., vol. 80, pp. 885–964, Jul 2008.
  29. T. F. Viscondi and K. Furuya, “Dynamics of a bose–einstein condensate in a symmetric triple-well trap,” Journal of Physics A: Mathematical and Theoretical, vol. 44, p. 175301, mar 2011.
  30. L. Cao, I. Brouzos, S. Zöllner, and P. Schmelcher, “Interaction-driven interband tunneling of bosons in the triple well,” New Journal of Physics, vol. 13, p. 033032, mar 2011.
  31. G. M. Koutentakis, S. I. Mistakidis, and P. Schmelcher, “Quench-induced resonant tunneling mechanisms of bosons in an optical lattice with harmonic confinement,” Phys. Rev. A, vol. 95, p. 013617, Jan 2017.
  32. I. Bloch, “Ultracold quantum gases in optical lattices,” Nat Phys, vol. 1, pp. 23–30, Oct 2005.
  33. M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, “Boson localization and the superfluid-insulator transition,” Phys. Rev. B, vol. 40, pp. 546–570, Jul 1989.
  34. C. Kollath, G. Roux, G. Biroli, and A. M. Läuchli, “Statistical properties of the spectrum of the extended bose–hubbard model,” Journal of Statistical Mechanics: Theory and Experiment, vol. 2010, p. P08011, aug 2010.
  35. S. Dutta, M. C. Tsatsos, S. Basu, and A. U. J. Lode, “Management of the correlations of ultracoldbosons in triple wells,” New Journal of Physics, vol. 21, p. 053044, may 2019.
  36. N. Oelkers and J. Links, “Ground-state properties of the attractive one-dimensional bose-hubbard model,” Phys. Rev. B, vol. 75, p. 115119, Mar 2007.
  37. Q. Guo, X. Chen, and B. Wu, “Tunneling dynamics and band structures of three weakly coupled bose-einstein condensates,” Opt. Express, vol. 22, pp. 19219–19234, Aug 2014.
  38. A. R. Kolovsky and A. Buchleitner, “Quantum chaos in the bose-hubbard model,” Europhysics Letters, vol. 68, p. 632, nov 2004.
  39. T. Choy and F. Haldane, “Failure of bethe-ansatz solutions of generalisations of the hubbard chain to arbitrary permutation symmetry,” Physics Letters A, vol. 90, no. 1, pp. 83–84, 1982.
  40. A. I. Streltsov, K. Sakmann, O. E. Alon, and L. S. Cederbaum, “Accurate multi-boson long-time dynamics in triple-well periodic traps,” Phys. Rev. A, vol. 83, p. 043604, Apr 2011.
  41. T. Lahaye, T. Pfau, and L. Santos, “Mesoscopic ensembles of polar bosons in triple-well potentials,” Phys. Rev. Lett., vol. 104, p. 170404, Apr 2010.
  42. P. Buonsante, R. Franzosi, and V. Penna, “Control of unstable macroscopic oscillations in the dynamics of three coupled bose condensates,” Journal of Physics A: Mathematical and Theoretical, vol. 42, p. 285307, jun 2009.
  43. A. Foerster and E. Ragoucy, “Exactly solvable models in atomic and molecular physics,” Nuclear Physics B, vol. 777, no. 3, pp. 373–403, 2007.
  44. A. P. Tonel, L. H. Ymai, K. W. W., A. Foerster, and J. Links, “Entangled states of dipolar bosons generated in a triple-well potential,” SciPost Phys. Core, vol. 2, p. 3, 2020.
  45. G. Nakerst and M. Haque, “Eigenstate thermalization scaling in approaching the classical limit,” Phys. Rev. E, vol. 103, p. 042109, Apr 2021.
  46. M. Rautenberg and M. Gärttner, “Classical and quantum chaos in a three-mode bosonic system,” Phys. Rev. A, vol. 101, p. 053604, May 2020.
  47. S. Ray, D. Cohen, and A. Vardi, “Chaos-induced breakdown of bose-hubbard modeling,” Phys. Rev. A, vol. 101, p. 013624, Jan 2020.
  48. S. Bera, R. Roy, A. Gammal, B. Chakrabarti, and B. Chatterjee, “Probing relaxation dynamics of a few strongly correlated bosons in a 1d triple well optical lattice,” Journal of Physics B: Atomic, Molecular and Optical Physics, vol. 52, p. 215303, oct 2019.
  49. A. Richaud and V. Penna, “Phase separation can be stronger than chaos,” New Journal of Physics, vol. 20, p. 105008, oct 2018.
  50. M. A. Garcia-March, S. van Frank, M. Bonneau, J. Schmiedmayer, M. Lewenstein, and L. F. Santos, “Relaxation, chaos, and thermalization in a three-mode model of a bose–einstein condensate,” New Journal of Physics, vol. 20, p. 113039, nov 2018.
  51. L. Guo, L. Du, C. Yin, Y. Zhang, and S. Chen, “Dynamical evolutions in non-hermitian triple-well systems with a complex potential,” Phys. Rev. A, vol. 97, p. 032109, Mar 2018.
  52. G. McCormack, R. Nath, and W. Li, “Hyperchaos in a bose-hubbard chain with rydberg-dressed interactions,” Photonics, vol. 8, no. 12, 2021.
  53. T. Yan, M. Collins, R. Nath, and W. Li, “Signatures of quantum chaos of rydberg-dressed bosons in a triple-well potential,” Atoms, vol. 11, no. 6, 2023.
  54. C. B. Dağ, S. I. Mistakidis, A. Chan, and H. R. Sadeghpour, “Many-body quantum chaos in stroboscopically-driven cold atoms,” Commun Phys, vol. 6, p. 136, Jun 2023.
  55. K. W. W., L. H. Ymai, B. H. C. Barros, J. Links, and A. Foerster, “Controlling entanglement in a triple-well system of dipolar atoms,” Phys. Rev. A, vol. 108, p. 033313, Sep 2023.
  56. A. P. Tonel, J. Links, and A. Foerster, “Quantum dynamics of a model for two Josephson-coupled Bose–Einstein condensates,” Journal of Physics A: Mathematical and General, vol. 38, p. 1235, jan 2005.
  57. J. Links, A. Foerster, A. Tonel, and G. Santos, “The two-site Bose-Hubbard model,” Ann. Henri Poincaré, vol. 7, p. 1591, 2006.
  58. E. R. Castro, J. Chávez-Carlos, I. Roditi, L. F. Santos, and J. G. Hirsch, “Quantum-classical correspondence of a system of interacting bosons in a triple-well potential,” Quantum, vol. 5, p. 563, Oct. 2021.
  59. L. F. Santos, M. Távora, and F. Pérez-Bernal, “Excited-state quantum phase transitions in many-body systems with infinite-range interaction: Localization, dynamics, and bifurcation,” Phys. Rev. A, vol. 94, p. 012113, Jul 2016.
  60. J. A. Pérez-Hernández and L. Benet, “Perezhz/taylorintegration.jl:,” 10.5281/zenodo.2562352, vol. v0.4.1,, 2019.
  61. W. Kirkby, Y. Yee, K. Shi, and D. H. J. O’Dell, “Caustics in quantum many-body dynamics,” Phys. Rev. Res., vol. 4, p. 013105, Feb 2022.
  62. i. c. v. Lozej, D. Lukman, and M. Robnik, “Effects of stickiness in the classical and quantum ergodic lemon billiard,” Phys. Rev. E, vol. 103, p. 012204, Jan 2021.
  63. S. Pilatowsky-Cameo, D. Villaseñor, M. A. Bastarrachea-Magnani, S. Lerma-Hernández, L. F. Santos, and J. G. Hirsch, “Ubiquitous quantum scarring does not prevent ergodicity,” Nature Communications, vol. 12, p. 852, Feb 2021.
  64. D. S. Grün, L. H. Ymai, K. Wittmann W., A. P. Tonel, A. Foerster, and J. Links, “Integrable atomtronic interferometry,” Phys. Rev. Lett., vol. 129, p. 020401, Jul 2022.
  65. D. S. Grün, K. Wittmann W., L. H. Ymai, J. Links, and A. Foerster, “Protocol designs for NOON states,” Commun. Phys., vol. 5, no. 1, p. 36, 2022.
Citations (1)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets