UCL Discovery Stage
UCL home » Library Services » Electronic resources » UCL Discovery Stage

The reachable set of single-mode quadratic Hamiltonians

Shackerley-Bennett, U; Pitchford, A; Genoni, MG; Serafini, A; Burgarth, DK; (2017) The reachable set of single-mode quadratic Hamiltonians. Journal of Physics A: Mathematical and Theoretical , 50 , Article 155203. 10.1088/1751-8121/aa6243. Green open access

[thumbnail of 1605.09688 (1).pdf]
Preview
Text
1605.09688 (1).pdf - Accepted Version

Download (2MB) | Preview

Abstract

Open-loop controllability in quantum mechanics refers to finding conditions on time-varying Hamiltonians such that a full group of unitary transformations can be enacted with them. For compact groups controllability is well understood and is dealt with using the Lie algebra rank criterion. Gaussian systems, however, evolve under Hamiltonians generating the non-compact symplectic group, rendering the rank criterion necessary but no longer sufficient. In this setting it is possible to satisfy the rank criterion without the ability to enact all symplectic transformations. We refer to such systems as 'unstable' and explore the set of symplectic transformations that remain reachable. We provide a partial analytical characterisation for the reachable set of a single-mode unstable system. From this it is proven that no orthogonal-symplectic operations ('energy-preserving' or 'passive' in the literature) may be reached with such controls. We then apply numerical optimal control algorithms to demonstrate a complete characterisation of the set in specific cases. These results suggest approaches to the long-standing open problem of controllability in n modes.

Type: Article
Title: The reachable set of single-mode quadratic Hamiltonians
Open access status: An open access version is available from UCL Discovery
DOI: 10.1088/1751-8121/aa6243
Publisher version: http://doi.org/10.1088/1751-8121/aa6243
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Physics and Astronomy
URI: https://discovery-pp.ucl.ac.uk/id/eprint/10060487
Downloads since deposit
2,240Downloads
Download activity - last month
Download activity - last 12 months
Downloads by country - last 12 months

Archive Staff Only

View Item View Item