Optimal control of quantum systems with SU(1, 1) dynamical symmetry View Full Text


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Article Info

DATE

2015-08

AUTHORS

Wenbin Dong, Rebing Wu, Jianwu Wu, Chunwen Li, Tzyh-Jong Tarn

ABSTRACT

SU(1, 1) dynamical symmetry is of fundamental importance in analyzing unbounded quantum systems in theoretical and applied physics. In this paper, we study the control of generalized coherent states associated with quantum systems with SU(1, 1) dynamical symmetry. Based on a pseudo Riemannian metric on the SU(1, 1) group, we obtain necessary conditions for minimizing the field fluence of controls that steer the system to the desired final state. Further analyses show that the candidate optimal control solutions can be classified into normal and abnormal extremals. The abnormal extremals can only be constant functions when the control Hamiltonian is non-parabolic, while the normal extremals can be expressed by Weierstrass elliptic functions according to the parabolicity of the control Hamiltonian. As a special case, the optimal control solution that maximally squeezes a generalized coherent state is a sinusoidal field, which is consistent with what is used in the laboratory. More... »

PAGES

211-220

References to SciGraph publications

  • 1989. Elliptic Functions and Applications in NONE
  • 1972-09. Coherent states for arbitrary Lie group in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1997-07. SU(2) andSU(1,1) algebra eigenstates: A unified analytic approach to coherent and intelligent states in INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
  • 1978-08. Geometric methods for nonlinear optimal control problems in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1980. Group theory of the Morse potential in GROUP THEORETICAL METHODS IN PHYSICS
  • 1991. Representation of Lie Groups and Special Functions, Volume 1: Simplest Lie Groups, Special Functions and Integral Transforms in NONE
  • 2009-01. Control theory on lie groups in JOURNAL OF MATHEMATICAL SCIENCES
  • 2008-07. Conjugate Points in the Euler Elastic Problem in JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS
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    http://scigraph.springernature.com/pub.10.1007/s11768-015-4128-0

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    http://dx.doi.org/10.1007/s11768-015-4128-0

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