Abstract
In the present work, we have analysed the motion of a structured matter wave in the presence of a constant magnetic field under the influence of a time-dependent external force. We have introduced exact propagator kernels obtained from partial differential equations based on the Heisenberg equations of motion. The initial wave function is assumed to be a Gauss–Hermite wave function. For the evolved wave function, we have obtained and discussed the uncertainties, orbital angular momentum and the inertia tensor in the centre of mass frame of the density function. From the quantum interferometry of matter waves point of view, and also non-relativistic quantum electron microscopy, the results obtained here are important and more reliable than approximate methods like the axial approximation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R Jagannathan and S A Khan, Quantum mechanics of charged particle beam optics: Understanding devices from electron microscopes to particle accelerators (CRC Press, 2019)
H Larocque, I Kaminer, V Grillo, G Leuchs, M J Padgett, R W Boyd, M Segev and E Karimi, Contemp. Phys. 59, 126 (2018)
H Larocque, R Fickler, E Cohen, V Grillo, R E Dunin-Borkowski, G Leuchs and E Karimi, Phys. Rev. A 99, 023628 (2019)
M Arndt, A Ekers, W von Klitzing and H Ulbricht, New J. Phys. 14, 125006 (2012)
S Martellucci and M Santarsiero, Free and guided optical beams: International school of quantum electronics (World Scientific, 2004)
N Fukuda, T Takiya and M Han, Appl. Phys. Res. 10, 30 (2018)
S Khan and R Jagannathan, Physical Review E 51, 2510 (1995)
M G Minty and F Zimmermann, Measurement and control of charged particle beams (Springer Nature, 2003)
M Reiser, Theory and design of charged particle beams (John Wiley & Sons, 2008)
L Allen, M W Beijersbergen, R Spreeuw and J Woerdman, Phys. Rev. A 45, 8185 (1992)
K Y Bliokh, Y P Bliokh, S Savel’ev and F Nori, Phys. Rev. Lett. 99, 190404 (2007)
M Uchida and A Tonomura, Nature 464, 737 (2010)
J Harris, V Grillo, E Mafakheri, G C Gazzadi, S Frabboni, R W Boyd and E Karimi, Nature Phys. 11, 629 (2015)
V Grillo, G C Gazzadi, E Mafakheri, S Frabboni, E Karimi and R W Boyd, Phys. Rev. Lett. 114, 034801 (2015)
X Lü and S-J Chen, Commun. Nonlinear Sci. Numer. Simulat. 103, 105939 (2021)
Y-H Yin, X Lü and W-X Ma, Nonlinear Dynam. 108, 4181 (2022)
B Liu, X-E Zhang, B Wang and X Lü, Mod. Phys. Lett. B 36, 2250057 (2022)
X Lü and S-J Chen, Nonlinear Dynam. 103, 947 (2021)
A E Siegman, JOSA 63, 1093 (1973)
F Pampaloni and J Enderlein, arXiv preprint arXiv:physics/0410021 (2004)
G Zhou, Opt. Lett. 31, 2616 (2006)
P Kruit et al, Ultramicroscopy 164, 31 (2016)
W P Putnam and M F Yanik, Phys. Rev. A 80, 040902 (2009)
H Okamoto, Phys. Rev. A 106, 022605 (2022)
P Senthilkumaran, J Masajada and S Sato, Int. J. Opt. 2012, 517591 (2012)
R R Bommareddi, Technologies 2, 54 (2014)
J-F Schaff, T Langen and J Schmiedmayer, La Rivista del Nuovo Cimento 37, 509 (2014)
F Kheirandish, The Eur. Phys. J. Plus 133, 1 (2018)
V V Kotlyar, A A Kovalev and A P Porfirev, Opt. Lett. 42, 139 (2017)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Janjan, S., Kheirandish, F. Structured matter wave evolution in external time-dependent fields. Pramana - J Phys 97, 169 (2023). https://doi.org/10.1007/s12043-023-02662-6
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12043-023-02662-6