收稿日期: 2010-11-26
修回日期: 2010-12-27
网络出版日期: 2012-01-15
基金资助
Supported by the National Key Basic Research Program (2009CB929601), the National Science Foundation of China (61074050), and the undergraduate innovation fund of USTC
States transfer of open quantum systems with single control field
Received date: 2010-11-26
Revised date: 2010-12-27
Online published: 2012-01-15
Supported by
Supported by the National Key Basic Research Program (2009CB929601), the National Science Foundation of China (61074050), and the undergraduate innovation fund of USTC
杨洁 , 丛爽 . 单个控制场下开放量子系统的状态转移[J]. 中国科学院大学学报, 2012 , 29(1) : 17 -26 . DOI: 10.7523/j.issn.2095-6134.2012.1.003
Dynamical model of open quantum systems in a matrix form is transformed into the model in a vector form using Liouville super-operator. Given a dynamical model of a dissipative quantum system in the presence of a time-dependent external control field, we achieve an improved optimal control law with the squared error between density matrices of system state and target state as the performance index. The states transfer experiment on a spin 1/2 particle system is carried out. Under the proposed optimal control, eigenstates, pure states, and mixed states are taken as initial and target states of the system, respectively. Detailed comparative analyses are given.
[1] Zwolak M P. Dynamics and simulation of open quantum systems . California Institute of Technology, June 2007.
[2] Ferrante A, Pavon M, Raccanelli G. Control of quantum systems using model-based feedback strategies //15th International Symposium on Mathematical Theory of Networks and Systems. Indiana, MA6, 2002: 1-9.
[3] Ferrante A, Pavon M, Raccanelli G. Driving the propagator of a spin system: A feedback approach //Proceedings of the 41th IEEE Conference on Decision and Control. Las Vegas, 2002, 1(11): 46-50.
[4] Hekman K A, Singhose W E. A feedback control system for suppressing crane oscillations with on-off motors
[J]. International Journal of Control, Automation, and Systems, 2007, 5(3): 223-233.
[5] Roloff R, Wenin M, Pötz W. Optimal control for open quantum systems: qubits and quantum gates
[J]. Journal of Computational and Theoretical Nanoscience, 2009, 6(8): 1837-1863.
[6] Wang Q F. Quantum optimal control of nuclei in the presence of perturbation in electric field
[J]. IEEE transactions on Automation Control, 2009, 3(9): 1175-1182.
[7] Mirrahimi M, Rouchon P, Turinici G. Lyapunov control of bilinear Schrödinger equations
[J]. Automatica, 2005, 41(11): 1987-1994.
[8] Kuang S, Cong S. Lyapunov control methods of closed quantum systems
[J]. Automatica, 2008, 44(1): 98-108.
[9] D'Alessandro D, Dahleh M. Optimal control of two-level quantum systems
[J]. IEEE Transactions on Automation Control, 2001, 46(6): 866-876.
[10] Rice S A, Zhao M. Optical control of molecular dynamics
[M]. New York:Wiley, 2000.
[11] Shapiro M, Brumer P. Principles of the quantum control of molecular processes
[M]. New York:Wiley, 2003.
[12] Kormann K, Holmgren S, Karlsson H O. A fourier-coefficient based solution of an optimal control problem in quantum chemistry . Technical Report, Department of Information Technology, Uppsala University, 2009.
[13] Rabitz H, de Vivie-Riedle R, Motzkus M, et al. Quantum optimally controlled transition landscapes
[J]. Science, 2000, 288(5467): 824-828.
[14] Khaneja N, Reiss T, Luy B, et al. Optimal control of spin dynamics in the presence of relaxation
[J]. Journal of Magnetic Resonance, 2003, 162:311-319.
[15] Grivopoulos S. Optimal control of quantum systems . ME, University of California at Santa Barbara, 2005.
[16] Yang J, Cong S. Optimal control of open quantum systems based on Liouville superoperator form //System Simulation Technology and Applications. Hefei: University of Science & Technology of China Press, 2008: 837-843 (in Chinese). 杨洁,丛爽.基于Liouville超算符变换的开放量子系统最优控制 //2008年系统仿真技术及应用学术会议论文集.合肥:中国科学技术大学出版社,2008:837-843.
[17] Yang J, Cong S. Performance comparison of two control methods of quantum systems //2009 Chinese Automation Conference. Hangzhou, 2009, T2B: 1-10 (in Chinese). 杨洁,丛爽. 基于量子系统仿真实验的两种控制方法的性能对比研究 //2009中国自动化大会暨两化融合高峰会议论文集.杭州,2009,T2B:1-10.
/
| 〈 |
|
〉 |
