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Stochastic quantum trajectories demonstrate the Quantum Zeno Effect in open spin 1/2, spin 1 and spin 3/2 systems

Published 21 Sep 2022 in quant-ph and cond-mat.stat-mech | (2209.10626v2)

Abstract: We investigate the Quantum Zeno Effect in spin 1/2, spin 1 and spin 3/2 open quantum systems undergoing Rabi oscillations, revealing unexplored features for the spin 1 and spin 3/2 systems. The systems interact with an environment designed to perform continuous measurements of an observable, driving the systems stochastically towards one of the eigenstates of the corresponding operator. The system-environment coupling constant represents the strength of the measurement. Stochastic quantum trajectories are generated by unravelling a Markovian Lindblad master equation using the quantum state diffusion formalism. These are regarded as a more appropriate representation of system behaviour than consideration of the averaged evolution since the latter can mask the effect of measurement. Complete positivity is maintained and thus the trajectories can be considered as physically meaningful. The Quantum Zeno Effect is investigated over a range of measurement strengths. Increasing the strength leads to greater system dwell in the vicinity of the eigenstates of the measured observable and lengthens the time taken by the system to return to that eigenstate,thus the Quantum Zeno Effect emerges. For very strong measurement, the Rabi oscillations resemble randomly occurring near-instantaneous jumps between eigenstates. The trajectories followed by the quantum system are heavily dependent on the measurement strength which other than slowing down and adding noise to the Rabi oscillations, changes the paths taken in spin phase space from a circular precession into elaborate figures-of-eight. For spin 1 and spin 3/2 systems, the measurement strength determines which eigenstates are explored and the Quantum Zeno Effect is stronger when the system dwells in the vicinity of certain eigenstates compared to others.

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References (43)
  1. A. Degasperis, L. Fonda, and G. C. Ghirardi, Does the lifetime of an unstable system depend on the measuring apparatus?, Il Nuovo Cimento A 21, 471 (1974).
  2. B. Misra and E. C. G. Sudarshan, The Zeno’s paradox in quantum theory, Journal of Mathematical Physics 18, 756 (1977).
  3. A. Peres and A. Ron, Incomplete “collapse” and partial quantum Zeno effect, Physical Review A 42, 5720 (1990).
  4. Y.-H. Chen and T. A. Brun, Continuous quantum error detection and suppression with pairwise local interactions, Physical Review Research 2, 043093 (2020).
  5. N. V. Leppenen and D. S. Smirnov, Optical measurement of electron spins in quantum dots: Quantum Zeno effects (2022), arxiv:2202.13994 [cond-mat, physics:quant-ph] .
  6. S. Patsch, S. Maniscalco, and C. P. Koch, Simulation of open-quantum-system dynamics using the quantum Zeno effect, Physical Review Research 2, 023133 (2020).
  7. T. Norsen, Foundations of Quantum Mechanics: An Exploration of the Physical Meaning of Quantum Theory (Springer, Cham, Switzerland, 2017).
  8. K. Jacobs, Quantum Measurement Theory and Its Applications (Cambridge University Press, Cambridge, 2014).
  9. A. N. Jordan, Watching the wavefunction collapse, Nature 502, 177 (2013).
  10. C. Presilla, R. Onofrio, and U. Tambini, Measurement Quantum Mechanics and Experiments on Quantum Zeno Effect, Annals of Physics 248, 95 (1996).
  11. K. Snizhko, P. Kumar, and A. Romito, Quantum Zeno effect appears in stages, Physical Review Research 2, 033512 (2020).
  12. I. de Vega and D. Alonso, Dynamics of non-Markovian open quantum systems, Reviews of Modern Physics 89, 015001 (2017).
  13. C. W. Gardiner, A. S. Parkins, and P. Zoller, Wave-function quantum stochastic differential equations and quantum-jump simulation methods, Physical Review A 46, 4363 (1992).
  14. C. Gneiting, A. V. Rozhkov, and F. Nori, Jump-time unraveling of Markovian open quantum systems, Physical Review A 104, 062212 (2021).
  15. I. Percival, Quantum State Diffusion (Cambridge University Press, Cambridge, 1998).
  16. M. Bauer, D. Bernard, and A. Tilloy, Computing the rates of measurement-induced quantum jumps, Journal of Physics A: Mathematical and Theoretical 48, 25FT02 (2015).
  17. T. P. Spiller, The Zeno effect: Measurement versus decoherence, Physics Letters A 192, 163 (1994).
  18. R. Penrose, On the Gravitization of Quantum Mechanics 1: Quantum State Reduction, Foundations of Physics 44, 557 (2014).
  19. G. C. Ghirardi, A. Rimini, and T. Weber, Unified dynamics for microscopic and macroscopic systems, Physical Review D 34, 470 (1986).
  20. D. Bohm, A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. I, Physical Review 85, 166 (1952).
  21. H. Everett, "Relative State" Formulation of Quantum Mechanics, Reviews of Modern Physics 29, 454 (1957).
  22. M. F. Pusey, J. Barrett, and T. Rudolph, On the reality of the quantum state, Nature Physics 8, 475 (2012).
  23. O. Lombardi and D. Dieks, Modal Interpretations of Quantum Mechanics, in The Stanford Encyclopedia of Philosophy, edited by E. N. Zalta (Metaphysics Research Lab, Stanford University, 2021) winter 2021 ed.
  24. A. Petersen, The Philosophy of Niels Bohr, Bulletin of the Atomic Scientists 19, 8 (1963).
  25. C. A. Fuchs, N. D. Mermin, and R. Schack, An introduction to QBism with an application to the locality of quantum mechanics, American Journal of Physics 82, 749 (2014).
  26. I. Pitowsky, Quantum mechanics as a theory of probability (2005), arxiv:quant-ph/0510095 .
  27. R. Healey, Quantum Theory: A Pragmatist Approach, The British Journal for the Philosophy of Science 63, 729 (2012).
  28. S. Kochen and E. P. Specker, The Problem of Hidden Variables in Quantum Mechanics, Journal of Mathematics and Mechanics 17, 59 (1967), 24902153 .
  29. C. Brukner and A. Zeilinger, Information and fundamental elements of the structure of quantum theory (2002), arxiv:quant-ph/0212084 .
  30. N. D. Mermin, Annotated Interview with a QBist in the Making (2013), arxiv:1301.6551 [physics, physics:quant-ph] .
  31. C. Rovelli, Helgoland (Penguin Books, London, 2021).
  32. T. Maudlin, Philosophy of Physics: Quantum Theory, Princeton Foundations of Contemporary Philosophy (Princeton University Press, Princeton, 2019).
  33. M. S. Leifer, Is the quantum state real? An extended review of ψ𝜓\psiitalic_ψ-ontology theorems, Quanta 3, 67 (2014), arxiv:1409.1570 .
  34. H. M. Wiseman, Quantum trajectories and quantum measurement theory, Quantum and Semiclassical Optics: Journal of the European Optical Society Part B 8, 205 (1996).
  35. J. Gambetta and H. M. Wiseman, Interpretation of non-Markovian stochastic Schrödinger equations as a hidden-variable theory, Physical Review A 68, 062104 (2003).
  36. H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2007).
  37. C. L. Clarke, Irreversibility Measures in a Quantum Setting, Doctoral, UCL (University College London) (2022).
  38. K. Itô, Stochastic integral, Proceedings of the Imperial Academy 20, 519 (1944).
  39. D. Aerts and M. Sassoli de Bianchi, The extended Bloch representation of quantum mechanics and the hidden-measurement solution to the measurement problem, Annals of Physics 351, 975 (2014).
  40. I. Lukach and Ya.A. Smorodinskij, On algebra of Gell-Mann’s matrices for SU(3) group, Yadernaya Fizika 27, 1694 (1978).
  41. P. E. Kloeden and E. Platen, Stochastic Differential Equations, in Numerical Solution of Stochastic Differential Equations, Applications of Mathematics, edited by P. E. Kloeden and E. Platen (Springer, Berlin, Heidelberg, 1992) pp. 103–160.
  42. https://drive.google.com/file/d/ 1xcBIlHtQ-pseZNxMxSvL-PG60BxXxLNH/view? usp=sharing Movie of spin 1 dynamics with measurement strength 3. (a).
  43. https://drive.google.com/file/d/ 1sNncxc19eDs8ZXe5Pt66LE_fIHOMlT_v/view?usp= sharing Movie of spin 3/2 dynamics with measurement strength 1. (b).
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