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.
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 |
Archive Staff Only
![]() |
View Item |