Experiment-friendly formulation of quantum backflow

Marek Miller1,2, Woo Chee Yuan1, Rainer Dumke1,3, and Tomasz Paterek1,4,5

1School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore
2Centre of New Technologies, University of Warsaw, Poland
3Centre for Quantum Technologies, National University of Singapore, Singapore
4MajuLab, International Joint Research Unit UMI 3654, CNRS, Universite Cote d'Azur, Sorbonne Universite, National University of Singapore, Nanyang Technological University, Singapore
5Institute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, Poland

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Quantum backflow is usually understood as a quantum interference phenomenon where probability current of a quantum particle points in the opposite direction to particle's momentum. Here, we quantify the amount of quantum backflow for arbitrary momentum distributions, paving the way towards its experimental verification. We give examples of backflow in gravitational and harmonic potential, and discuss experimental procedures required for the demonstration using atomic gravimeters. Such an experiment would show that the probability of finding a free falling particle above initial level could grow for suitably prepared quantum state with most momentum downwards.

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[1] A. Alberti, C. Robens, W. Alt, S. Brakhane, M. Karski, R. Reimann, A. Widera, and D. Meschede, ``Super-resolution microscopy of single atoms in optical lattices'' New J. Phys. 18, 053010 (2016).

[2] Go.R. Allcock ``The time of arrival in quantum mechanics I. Formal considerations'' Annals of Physics 53, 253–285 (1969).

[3] J. Ashfaque, J. Lynch, and P. Strange, ``Relativistic quantum backflow'' Physica Scripta (2019).

[4] M. Barbier ``Quantum backflow for many-particle systems'' Physical Review A 102, 023334 (2020).

[5] T.J. Beams, G. Peach, and I.B. Whittingham, ``Ultracold atomic collisions in tight harmonic traps: perturbation theory, ionization losses and application to metastable helium atoms'' Journal of Physics B: Atomic, Molecular and Optical Physics 37, 4561–4570 (2004).

[6] H. Bostelmann, D. Cadamuro, and Ga.f Lechner, ``Quantum backflow and scattering'' Physical Review A 96, 012112 (2017).

[7] A.J. Brackenand G.F. Melloy ``Probability backflow and a new dimensionless quantum number'' Journal of Physics A: Mathematical and General 27, 2197 (1994).

[8] M.A. De Gosson ``Symplectic geometry and quantum mechanics'' Springer Science & Business Media (2006).

[9] W. Dijkand F.M. Toyama ``Decay of a quasistable quantum system and quantum backflow'' Physical Review A 100, 052101 (2019).

[10] Y. Eliezer, T. Zacharias, and A. Bahabad, ``Observation of Optical Backflow'' Optica 7, 72 (2020).

[11] J.R. Ensher, D.S. Jin, M.R. Matthews, C.E. Wieman, and E.A. Cornell, ``Bose-Einstein Condensation in a Dilute Gas: Measurement of Energy and Ground-State Occupation'' Phys. Rev. lett. 77, 4984 (1996).

[12] T. Gericke, P. Würtz, D. Reitz, T. Langen, and H. Ott, ``High-resolution scanning electron microscopy of an ultracold quantum gas'' Nat. Phys. 4, 949–953 (2008).

[13] A. Goussev ``Equivalence between quantum backflow and classically forbidden probability flow in a diffraction-in-time problem'' Physical Review A 99, 043626 (2019).

[14] A. Goussev ``Probability backflow for correlated quantum states'' Physical Review Research 2, 033206 (2020).

[15] A. Goussev ``Quantum backflow in a ring'' arXiv preprint arXiv:2008.08022 (2020).

[16] J.J. Halliwell, E. Gillman, O. Lennon, M. Patel, and I. Ramirez, ``Quantum backflow states from eigenstates of the regularized current operator'' Journal of Physics A: Mathematical and Theoretical 46, 475303 (2013).

[17] J. Kijowski ``On the time operator in quantum mechanics and the Heisenberg uncertainty relation for energy and time'' Reports on Mathematical Physics 6, 361–386 (1974).

[18] J.R. Klauderand B.-S. Skagerstam ``Coherent States: Applications in Physics and Mathematical Physics'' World Scientific, Singapore (1985).

[19] M. McDonald, J. Trisnadi, K.-X. Yao, and C. Chin, ``Superresolution Microscopy of Cold Atoms in an Optical Lattice'' Phys. Rev. X 9, 021001 (2019).

[20] G.F. Melloyand A.J. Bracken ``Probability backflow for a Dirac particle'' Foundations of Physics 28, 505–514 (1998).

[21] G.F. Melloyand A.J. Bracken ``The velocity of probability transport in quantum mechanics'' Annals of Physics 7, 726–731 (1998).

[22] S..V Mousaviand S. Miret-Artés ``Dissipative quantum backflow'' The European Physical Journal Plus 135, 1–18 (2020).

[23] M. Palmero, E. Torrontegui, J.G. Muga, and M. Modugno, ``Detecting quantum backflow by the density of a Bose-Einstein condensate'' Physical Review A 87, 053618 (2013).

[24] M. Penz, Ge. Grübl, S. Kreidl, and P. Wagner, ``A new approach to quantum backflow'' Journal of Physics A: Mathematical and General 39, 423 (2005).

[25] H.-Y. Suand J.-L. Chen ``Quantum backflow in solutions to the Dirac equation of the spin-1 2 free particle'' Modern Physics Letters A 33, 1850186 (2018).

[26] G. Vandegrift ``Accelerating wave packet solution to Schrödinger’s equation'' American Journal of Physics 68, 576–577 (2000).

[27] A.H. Vasconcelos Jr ``Quantum backflow in the presence of a purely transmitting defect'' arXiv preprint arXiv:2007.07393 (2020).

[28] J.M. Yearsley, J.J. Halliwell, R. Hartshorn, and A. Whitby, ``Analytical examples, measurement models, and classical limit of quantum backflow'' Physical Review A 86, 042116 (2012).

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