Hurry up and slow down!
Discovering faster adiabatic processes
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 holding
and 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.
See also
•
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.
References and Related Resources from our Lab
Superadiabaticity in Magnetic Resonance,
M. Deschamps, G. Kervern, D. Massiot, G. Pintacuda, L. Emsley, and P. J. Grandinetti