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Wavefunction collapse driven by non-Hermitian disturbance (2404.16445v1)

Published 25 Apr 2024 in quant-ph and cond-mat.other

Abstract: In the context of the measurement problem, we propose to model the interaction between a quantum particle and an "apparatus" through a non-Hermitian Hamiltonian term. We simulate the time evolution of a normalized quantum state split into two spin components (via a Stern-Gerlach experiment) and that undergoes a wave-function collapse driven by a non-Hermitian Hatano-Nelson Hamiltonian. We further analyze how the strength and other parameters of the non-Hermitian perturbation influence the time-to-collapse of the wave function obtained under a Schr\"{o}dinger-type evolution. We finally discuss a thought experiment where manipulation of the apparatus could challenge standard quantum mechanics predictions.

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References (42)
  1. A. Einstein, B. Podolsky,  and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777 (1935).
  2. N. Bohr, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 48, 696 (1935).
  3. J. S. Bell, “On the einstein podolsky rosen paradox,” Physics Physique Fizika 1, 195 (1964).
  4. E. P. Wigner, “Review of the quantum-mechanical measurement problem,” in Science, Computers, and the Information Onslaught, edited by D. M. Kerr, K. Braithwaite, N. Metropolis, D. H. Sharp,  and G.-C. Rota (Academic Press, 1984) pp. 63–82.
  5. F. Laloë, “Do we really understand quantum mechanics? Strange correlations, paradoxes, and theorems,” American Journal of Physics 69, 655 (2001).
  6. J. S. Bell and A. Aspect, Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy, 2nd ed. (Cambridge University Press, 2004).
  7. J. Bell, “Against ‘measurement’,” Physics World 3, 33 (1990).
  8. N. D. Mermin, “Hidden variables and the two theorems of john bell,” Rev. Mod. Phys. 65, 803 (1993).
  9. J. R. Hance and S. Hossenfelder, “What does it take to solve the measurement problem?” Journal of Physics Communications 6, 102001 (2022).
  10. N. Ormrod, V. Vilasini,  and J. Barrett, “Which theories have a measurement problem?”  (2023), arXiv:2303.03353 [quant-ph] .
  11. G. C. Ghirardi, A. Rimini,  and T. Weber, “Unified dynamics for microscopic and macroscopic systems,” Physical Review D 34, 470 (1986).
  12. G. C. Ghirardi, P. Pearle,  and A. Rimini, “Markov processes in hilbert space and continuous spontaneous localization of systems of identical particles,” Phys. Rev. A 42, 78 (1990).
  13. A. Bassi and G. Ghirardi, “Dynamical reduction models,” Physics Reports 379, 257 (2003).
  14. P. Pearle, “Combining stochastic dynamical state-vector reduction with spontaneous localization,” Physical Review A 39, 2277 (1989).
  15. F. Laloë, “Quantum collapse dynamics with attractive densities,” Physical Review A 99, 052111 (2019).
  16. L. Diósi, “Models for universal reduction of macroscopic quantum fluctuations,” Phys. Rev. A 40, 1165 (1989).
  17. R. Penrose, “On gravity’s role in quantum state reduction,” General Relativity and Gravitation 28, 581 (1996).
  18. A. Bassi, K. Lochan, S. Satin, T. P. Singh,  and H. Ulbricht, “Models of wave-function collapse, underlying theories, and experimental tests,” Rev. Mod. Phys. 85, 471 (2013).
  19. F. Laloë, “A model of quantum collapse induced by gravity,” The European Physical Journal D 74, 25 (2020).
  20. F. Laloë, “Gravitational quantum collapse in dilute systems,” Comptes Rendus. Physique 23, 27 (2022).
  21. S. Donadi, K. Piscicchia, C. Curceanu, L. Diósi, M. Laubenstein,  and A. Bassi, “Underground test of gravity-related wave function collapse,” Nature Physics 17, 74 (2021).
  22. I. J. Arnquist, F. T. Avignone, A. S. Barabash, C. J. Barton, K. H. Bhimani, E. Blalock, B. Bos, M. Busch, M. Buuck, T. S. Caldwell, Y.-D. Chan, C. D. Christofferson, P.-H. Chu, M. L. Clark, C. Cuesta, J. A. Detwiler, Y. Efremenko, H. Ejiri, S. R. Elliott, G. K. Giovanetti, M. P. Green, J. Gruszko, I. S. Guinn, V. E. Guiseppe, C. R. Haufe, R. Henning, D. Hervas Aguilar, E. W. Hoppe, A. Hostiuc, I. Kim, R. T. Kouzes, T. E. Lannen V., A. Li, A. M. Lopez, J. M. López-Castaño, E. L. Martin, R. D. Martin, R. Massarczyk, S. J. Meijer, T. K. Oli, G. Othman, L. S. Paudel, W. Pettus, A. W. P. Poon, D. C. Radford, A. L. Reine, K. Rielage, N. W. Ruof, D. Tedeschi, R. L. Varner, S. Vasilyev, J. F. Wilkerson, C. Wiseman, W. Xu, C.-H. Yu,  and B. X. Zhu (Majorana Collaboration), “Search for spontaneous radiation from wave function collapse in the majorana demonstrator,” Phys. Rev. Lett. 129, 080401 (2022).
  23. S. Donadi, L. Ferialdi,  and A. Bassi, “Collapse dynamics are diffusive,” Phys. Rev. Lett. 130, 230202 (2023).
  24. N. Hatano and D. R. Nelson, “Vortex pinning and non-hermitian quantum mechanics,” Phys. Rev. B 56, 8651 (1997).
  25. N. Hatano and D. R. Nelson, “Non-hermitian delocalization and eigenfunctions,” Phys. Rev. B 58, 8384 (1998).
  26. N. Hatano and D. R. Nelson, “Localization transitions in non-hermitian quantum mechanics,” Phys. Rev. Lett. 77, 570 (1996).
  27. T. Orito and K.-I. Imura, “Entanglement dynamics in the many-body hatano-nelson model,” Phys. Rev. B 108, 214308 (2023).
  28. T. Orito and K.-I. Imura, “Unusual wave-packet spreading and entanglement dynamics in non-hermitian disordered many-body systems,” Phys. Rev. B 105, 024303 (2022).
  29. Y. Takane, S. Kobayashi,  and K.-I. Imura, “Probability conservation and localization in a one-dimensional non-hermitian system,” Journal of the Physical Society of Japan 92, 104705 (2023).
  30. F. Laloë, W. J. Mullin,  and P. Pearle, “Heating of trapped ultracold atoms by collapse dynamics,” Phys. Rev. A 90, 052119 (2014).
  31. S. Machluf, Y. Japha,  and R. Folman, “Coherent stern–gerlach momentum splitting on an atom chip,” Nature Communications 4, 2424 (2013).
  32. Y. Margalit, O. Dobkowski, Z. Zhou, O. Amit, Y. Japha, S. Moukouri, D. Rohrlich, A. Mazumdar, S. Bose, C. Henkel,  and R. Folman, “Realization of a complete stern-gerlach interferometer: Toward a test of quantum gravity,” Science Advances 7, eabg2879 (2021), https://www.science.org/doi/pdf/10.1126/sciadv.abg2879 .
  33. M. Keil, S. Machluf, Y. Margalit, Z. Zhou, O. Amit, O. Dobkowski, Y. Japha, S. Moukouri, D. Rohrlich, Z. Binstock, Y. Bar-Haim, M. Givon, D. Groswasser, Y. Meir,  and R. Folman, “Stern-gerlach interferometry with the atom chip,” in Molecular Beams in Physics and Chemistry: From Otto Stern’s Pioneering Exploits to Present-Day Feats, edited by B. Friedrich and H. Schmidt-Böcking (Springer International Publishing, Cham, 2021) pp. 263–301.
  34. Y. Japha and R. Folman, “Quantum uncertainty limit for stern-gerlach interferometry with massive objects,” Phys. Rev. Lett. 130, 113602 (2023).
  35. A. Aspect, P. Grangier,  and G. Roger, “Experimental realization of einstein-podolsky-rosen-bohm gedankenexperiment: A new violation of bell’s inequalities,” Phys. Rev. Lett. 49, 91 (1982a).
  36. A. Aspect, J. Dalibard,  and G. Roger, “Experimental test of bell’s inequalities using time-varying analyzers,” Phys. Rev. Lett. 49, 1804 (1982b).
  37. W. D. Heiss, “The physics of exceptional points,” Journal of Physics A: Mathematical and Theoretical 45, 444016 (2012).
  38. I. Rotter and J. P. Bird, “A review of progress in the physics of open quantum systems: theory and experiment,” Reports on Progress in Physics 78, 114001 (2015).
  39. L. E. F. Foa Torres, “Perspective on topological states of non-hermitian lattices,” Journal of Physics: Materials 3, 014002 (2020).
  40. L. J. Fernández-Alcázar and H. M. Pastawski, “Decoherent time-dependent transport beyond the Landauer-B\”uttiker formulation: A quantum-drift alternative to quantum jumps,” Physical Review A 91, 022117 (2015).
  41. G. Singh, R. K. Singh,  and S. Banerjee, “Embedding of a non-hermitian hamiltonian to emulate the von neumann measurement scheme,” Journal of Physics A: Mathematical and Theoretical 57, 035301 (2023a).
  42. G. Singh, R. K. Singh,  and S. Banerjee, “Emulating the measurement postulates of quantum mechanics via non-hermitian hamiltonian,”  (2023b), arXiv:2302.01898 [quant-ph] .
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