Optimal control of coupled spin dynamics under cross-correlated relaxation

2004 ◽  
Author(s):  
N. Khaneja ◽  
S. Glaser
Keyword(s):  
Optimal Control ◽  
Spin Dynamics

Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms

2005 ◽  
Vol 172 (2) ◽  
pp. 296-305 ◽  
Author(s):  
Navin Khaneja ◽  
Timo Reiss ◽  
Cindie Kehlet ◽  
Thomas Schulte-Herbrüggen ◽  
Steffen J. Glaser
Keyword(s):  
Optimal Control ◽  
Spin Dynamics ◽  
Pulse Sequences ◽  
Gradient Ascent

scholarly journals Spin Dynamics: A Paradigm for Time Optimal Control on Compact Lie Groups

2006 ◽  
Vol 35 (3) ◽  
pp. 443-474 ◽  
Author(s):  
G. Dirr ◽  
U. helmke ◽  
K. Hüper ◽  
M. Kleinsteuber ◽  
Y. Liu
Keyword(s):  
Optimal Control ◽  
Lie Groups ◽  
Spin Dynamics ◽  
Time Optimal Control ◽  
Compact Lie Groups ◽  
Time Optimal

scholarly journals Cone separation, quadratic control systems and control of spin dynamics in the presence of decoherence

2017 ◽  
Vol 375 (2088) ◽  
pp. 20160214
Author(s):  
Navin Khaneja
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Spin Dynamics ◽  
Resonance Spectroscopy ◽  
Control Problems ◽  
State Variables ◽  
Systems And Control ◽  
Time Optimal ◽  
Optimal Efficiency ◽  
And Control

In this paper, we study some control problems related to the control of coupled spin dynamics in the presence of relaxation and decoherence in nuclear magnetic resonance spectroscopy. The decoherence is modelled through a master equation. We study some model problems, whereby, through an appropriate choice of state variables, the system is reduced to a control system, where the state enters linearly and controls quadratically. We study this quadratic control system. Study of this system gives us explicit bounds on how close a coupled spin system can be driven to its target state and how much coherence and polarization can be transferred between coupled spins. Optimal control for the quadratic control system can be understood as the separation of closed cones, and we show how the derived results on optimal efficiency can be interpreted in this formulation. Finally, we study some finite-time optimal control problems for the quadratic control system. This article is part of the themed issue ‘Horizons of cybernetical physics’.

scholarly journals Connection between Inverse Engineering and Optimal Control in Shortcuts to Adiabaticity

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 84
Author(s):  
Qi Zhang ◽  
Xi Chen ◽  
David Guéry-Odelin
Keyword(s):  
Optimal Control ◽  
Quantum Control ◽  
Cold Atoms ◽  
Spin Dynamics ◽  
Harmonic Trap ◽  
High Fidelity ◽  
Physical Constraints ◽  
Atomic Transport ◽  
Shortcuts To Adiabaticity ◽  
Very High

We consider fast high-fidelity quantum control by using a shortcut to adiabaticity (STA) technique and optimal control theory (OCT). Three specific examples, including expansion of cold atoms from the harmonic trap, atomic transport by moving harmonic trap, and spin dynamics in the presence of dissipation, are explicitly detailed. Using OCT as a qualitative guide, we demonstrate how STA protocols designed from inverse engineering method can approach with very high precision optimal solutions built about physical constraints, by a proper choice of the interpolation function and with a very reduced number of adjustable parameters.

scholarly journals Optimal control of spin dynamics in the presence of relaxation

2003 ◽  
Vol 162 (2) ◽  
pp. 311-319 ◽  
Author(s):  
Navin Khaneja ◽  
Timo Reiss ◽  
Burkhard Luy ◽  
Steffen J. Glaser
Keyword(s):  
Optimal Control ◽  
Spin Dynamics
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