Understand
We show that we can achieve global density-operator controllability for most N-dimensional bilinear Hamiltonian control systems with general fixed couplings using a single, locally-acting actuator that modulates one energy-level transition.
- Controllability depends upon the position of the actuator and relies on the absence of either decompositions into non-interacting subgroups or symmetries restricting the dynamics to a subgroup of SU(N).
- These results are applied to spin-chain systems and used to explicitly construct control sequences for a single binary-valued switch actuator.
Built on
V. Jurdjevic and H. J. Sussmann, J. Diff. Eq. 12
1972
Earlier work this paper cites.
G. M. Huang, T. J. Tarn, and J. W. Clark, J. Math. Phys. 24
1983
Earlier work this paper cites.
V. Ramakrishna, M. V. Salapaka, M. Dahleh, H. Rabitz, and A. Peirce, Phys. Rev. A 51
1995
Earlier work this paper cites.
B. E. Kane, Nature 393
1998
Earlier work this paper cites.
J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, SIAM Journal of Optimization 9
1998
Earlier work this paper cites.
S. G. Schirmer, M. D. Girardeau, and J. V. Leahy, Phys. Rev. A 61
2000
Earlier work this paper cites.
Similar
F. Albertini and D. D’Alessandro, http://arxiv.org/abs/quant-ph/0106128 (2001)
2001
Cited alongside, same era.
S. G. Schirmer, H. Fu, and A. I. Solomon, Phys. Rev. A 63
2001
Cited alongside, same era.
G. Turinici and H. Rabitz, Chem. Phys. 267
2001
Cited alongside, same era.
H. Fu, S. G. Schirmer, and A. I. Solomon, J. Phys. A 34
2001
Cited alongside, same era.
S. G. Schirmer, J. V. Leahy, and A. I. Solomon, J. Phys. A 35
2002
Cited alongside, same era.
C. Altafini, J. Math. Phys. 43
2002
Cited alongside, same era.
Then
S. G. Schirmer, I. C. H. Pullen, and A. I. Solomon, J. Phys. A 35
2002
Later among the works it cites.
S. G. Schirmer, I. C. H. Pullen, and A. I. Solomon, in Hamiltonian and Lagrangian Methods in Nonlinear Control
2003
Later among the works it cites.
Y. Ohtsuki, G. Turinici, and H. Rabitz, J. Chem. Phys. 120
2004
Later among the works it cites.
S. G. Schirmer, I. C. H. Pullen, and A. I. Solomon, J. Optics B 7
2005
Later among the works it cites.
N. Khaneja, T. Reiss, C. Kehlet, T. Schulte-Herbrueggen, and S. J. Glaser, J. Mag. Resonance 172
2005
Later among the works it cites.
H. C. Fu, H. Dong, X. F. Liu, and C. P. Sun, Physical Review A (Atomic, Molecular, and Optical Physics) 75
2007
Later among the works it cites.
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