posted on 2017-03-01, 09:35authored byJ.F. Ralph, Kurt Jacobs, Mark Everitt
A fundamental requirement for the emergence of classical behavior from an underlying quantum description is that certain observed quantum systems make a transition to chaotic dynamics as their action is increased relative to
ℏ. While experiments have demonstrated some aspects of this transition, the emergence of quantum trajectories with a positive Lyapunov exponent has never been observed directly. Here, we remove a major obstacle to achieving this goal by showing that, for the Duffing oscillator, the transition to a positive Lyapunov exponent can be resolved clearly from observed trajectories even with measurement efficiencies as low as 20%. We also find that the positive Lyapunov exponent is robust to highly mixed, low-purity states and to variations in the parameters of the system.
Funding
J.F.R. would like to thank the US Army Research Laboratories (Contract No. W911NF-16-2-0067).
History
School
Science
Department
Physics
Published in
Physical Review A
Volume
95
Issue
1
Citation
RALPH, J.F., JACOBS, K. and EVERITT, M.J., 2017. Observing quantum chaos with noisy measurements and highly mixed states. Physical Review A, 95 (1), 012135.
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/
Acceptance date
2017-01-06
Publication date
2017-01-26
Notes
This paper was accepted for publication in the journal Physical Review A and is available at http://dx.doi.org/10.1103/PhysRevA.95.012135.