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Phys. Rev. A 65, 063405 (2002) [9 pages]

Control of a coupled two-spin system without hard pulses

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Viswanath Ramakrishna*
Department of Mathematical Sciences and Center for Signals, Systems and Communications, University of Texas at Dallas, P.O. Box 830688, Richardson, Texas 75083

Raimund J. Ober
Department of Electrical Engineering and Center for Signals, Systems and Communications, University of Texas at Dallas, P.O. Box 830688, Richardson, Texas 75083

Kathryn L. Flores
Department of Mathematical Sciences and Center for Signals, Systems and Communications, University of Texas at Dallas, P.O. Box 830688, Richardson, Texas 75083

Herschel Rabitz
Department of Chemistry, Frick Laboratories, Princeton University, Princeton, New Jersey 08544

Received 6 December 2000; revised 27 December 2001; published 6 June 2002

Constructive techniques for preparing a specific unitary generator from a coupled two-spin system, via bounded amplitude radio frequency selective single spin pulses, are presented. The frequency of any pulse in the sequence is one of the two Larmor frequencies, while the phase takes one of two values. The fact that the amplitude is bounded implies that the Larmor frequency separation between the two spins need not be large to maintain selectivity. In addition, the contribution of the J coupling term to single spin evolution is not neglected, but instead plays a crucial role. The procedure is based on a certain decomposition of SU(4) available in the literature. A method for determining the parameters entering this factorization, in terms of the entries of the target unitary generator, is also provided.

© 2002 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevA.65.063405
DOI:
10.1103/PhysRevA.65.063405
PACS:
32.80.Qk, 03.65.Ta

*Email address: vish@utdallas.edu

 
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