The quantum theory of the Penning trap

Crimin, F. , Garraway, B.M. and Verdú, J. (2017) The quantum theory of the Penning trap. Journal of Modern Optics, 65(4), pp. 427-440. (doi: 10.1080/09500340.2017.1393570)

Abstract

We present the quantum theory of the Penning trap in terms of individual x and y radial modes of the motion of a single charged particle in the trap, and demonstrate how the conventional rotating frame used to examine these individual dynamics fails in the quantum regime. In solving the radial Hamiltonian in the {x,y} basis, we show how canonical transformation of the variables must take place after quantization, in order that these separate motions can be consistently tracked. This is in contrast to previous work. The results of the discussion lend themselves to a fully quantum treatment of mode coupling in the trap, leading to an avoided crossing between the coupled energy levels of the system. Exploiting the algebraic structure of the problem allows employment of a dressed-atom formalism within quantum Penning trap theory, and future applications resulting from this are proposed.

• Item Type: Articles
• Additional Information: This work was supported by the UK Engineering and Physical Sciences Research Council [grant number EP/K503198/1].
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Crimin, Dr Frances
• Authors: Crimin, F., Garraway, B.M., and Verdú, J.
• College/School: College of Science and Engineering > School of Physics and Astronomy
• Journal Name: Journal of Modern Optics
• Publisher: Taylor & Francis
• ISSN: 0950-0340
• ISSN (Online): 1362-3044
• Published Online: 28 November 2017
• Copyright Holders: Copyright © 2017 The Authors
• First Published: First published in Journal of Modern Optics 65(4): 427-440
• Publisher Policy: Reproduced under a Creative Commons License