Optimal control of quantum systems with SU(1,1) dynamical symmetry
Wenbin DONG
Rebing WU
Jianwu WU
Chunwen LI
Tzyh-Jong TARN
摘要：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.
机标关键词：optimal controlnecessary conditionsRiemannian metriccoherent statesapplied physicsfinal stateused in
资助基金：the National Natural Science Foundation of China ()the National Natural Science Foundation of China (61374091)the National Natural Science Foundation of China (61134008)
论文发表日期：2015-01-01
在线出版日期：2025-08-15（本平台首次上网日期，不代表文献的发表时间）
页数：10( 211-220 )
英文信息