Hurry up and slow down!
Discovering faster adiabatic processes
Superadiabaticity in Magnetic Resonance,
M. Deschamps, G. Kervern, D. Massiot, G. Pintacuda, L. Emsley, and P. J. Grandinetti
While the scientist aims to understand Nature, it is the engineer who hopes to control it: wanting to keep a system under complete control while implementing some desired change. In classical and quantum mechanics, it is well known that implementing an adiabatic process is one of the simplest means for maintaining control while transforming a system. An adiabatic process can be visualized as one where the system is
held tightly and
slowly dragged by a controlling force from one state to the next. In a
perfect adiabatic process the controlling force is moved infinitely slowly with the system's trajectory locked to the controlling force's trajectory. In reality, the controlling force's motion occurs in a finite time and if it moves too quickly the system's trajectory can spiral away from the controlling force. Such departure of trajectories is traditionally seen as a loss of control.
Departure of the system's trajectory (orange) from the controlling force trajectory increases as the controlling force is moved more quickly along its trajectory. Image Credit: Gwendal Kervern
One field where adiabatic processes are often used is nuclear magnetic resonance (NMR) spectroscopy and magnetic resonance imaging (MRI). Surprisingly, since the beginning of NMR, there have been unsettling discrepancies between theoretical predictions and experimental observations of adiabatic processes. That is, processes that should not have been adiabatic according to theory are found experimentally to behave as if they were well within the adiabatic regime. This discrepancy has been brushed under the rug for decades, even though everyone knew that any meaningful disagreement between experiment and theory is nearly unheard of in NMR spectroscopy. Indeed, more generally, such discrepancies are not limited to magnetic resonance, but probably exist in nearly all theoretical applications of adiabatic processes, but may have been less noticeable.
In a collaboration with researchers from the CNRS in Orleans and the Universite de Lyon we have solved this puzzle. We have found that a surprisingly overlooked, but important work by Michael Berry (introduced as part of his seminal work on geometric phases), introducing the concept of superadiabaticity, must be invoked to obtain a proper treatment of the problem. In the traditional picture, any inertial forces that appear in the moving frame of the controlling force were considered
bad, in the sense that they were thought to cause loss of control. What we realized, however, is not all inertial forces will lead to loss of control. Some parts of the inertial forces can actually assist in
dragging the system between two states. Thus, when a system's trajectory fortuitously ends in the correct state even though it appeared to take a slightly different path than the controlling force's trajectory, the system may have been, all along, under the complete control of a
revised controlling force in a superadiabatic reference frame. Mathematically, this optimum superadiabatic frame is found by combining the controlling and inertial forces iteratively, creating new frames until a frame where the system's trajectory most closely follows the controlling force's trajectory is discovered. It is only in this optimum superadiabatic frame that the true adiabaticity (or superadiabaticity) of the process can be evaluated. This revelation and the mathematical algorithm for its discovery are particularly exciting as they open the road for new approaches for designing improved adiabatic processes in magnetic resonance as well as in other related fields.
• AIP Press Release by Jason Bardi.
• NSF Press Release, by Joshua A. Chamot.
• Ohio State University Press Release by Pam Frost Gorder.
• Science News coverage of this paper, by Patrick Barry.
• New Scientist coverage of this paper, by Flora Graham.
• Spectroscopy Now coverage of this paper, by David Bradley.