The NMR experiment is an undertaking in spin dynamics. Like all dynamical systems, the molecular system evolves in time under the action of control Hamiltonians. However, the molecular environment also affects the system, in undesirable or desirable ways, and there exist methods to track down, control, correct or utilize these affects in novel ways. In the Pines Lab, we explore different strategies to control and manipulate NMR coherences and polarizations.

The growing concern over the temporal limitations of fMRI has, over the past decade, given rise to a number of studies focused on demonstrating the feasibility of direct current imaging, with an emphasis on the detection of neuronal currents. The typical method for detecting small current-induced magnetic fields relies on imaging the phase shift caused by the field, a technique which has major limitations for oscillating or incoherent fields, since the phase shift will quickly average to zero. Recent studies¹ suggesting the importance of high gamma activity (80-150 Hz) in the brain emphasize the importance of developing an effective detection method for these currents.

Current work in the Pines lab has resulted in the development of a new method for detection of oscillating current-induced magnetic fields. This technique relies upon a resonant mechanism to produce saturation in spins near to a magnetic field. Nuclei are held in a transverse spin-lock which is applied at the Larmor frequency with power matched to the frequency of the oscillating current, causing a rotation of the magnetization around the z-axis and, after a storage pulse is applied, a corresponding depletion dependent on the spin-lock interval which can then be imaged through conventional means.

This resonant mechanism is fully compatible with oscillations in field strength and may be used to selectively image a desired frequency in a sample where several frequencies are present (shown in the 3D images at right for a sample with two loops of current at different frequencies). Furthermore, the lower limit of detectable magnetic field strength is only restricted by the relaxation properties of the sample and the duration of the current burst, allowing for the detection of sub-nT fields.

Currently we are investigating the use of decoupling techniques to increase the lifetime^1,2 of the singlet state produced by PASADENA. Under normal conditions the singlet state decays very rapidly, limiting the practical application of PASADENA for uses such as imaging or microfluidic NMR. It has been shown² that decoupling the protons of the singlet state remove some of the relaxation pathways, increasing the lifetime of the singlet state. The different composite pulse decoupling mechanisms also preserve the purity of the singlet state, allowing us to create pure initial states for quantum computation³. This technique can be used while performing hydrogenation with para-hydrogen in order to accumulate a larger amount of polarization over an extended period of time. Once optimized, this technique will be used for imaging and microfluidic NMR applications. These ideas are also linked to the concept of decoherence-free-subspaces and the lifetime enhancement of entangled states, used in quantum computation.

At the Pines Lab, we are developing a chemical means of recycling polarization derived from the PASADENA effect. We have an active collaboration with Robert Bergman’s Group in the Department of Chemistry, UCB, with whom we are investigating the possibility of polarization storage, intramolecular transfer to slowly relaxing nuclei and subsequent inter-molecular transfers to the solvent species by the SPINOE effect. One of the major hurdles in the practical implementation of NMR based quantum computers lies in the difficulty of resetting qubits (spins) in the spin computer. This resetting is important, for example, if we want to replenish the system with a fresh supply of error correction qubits which can be used to implement fault tolerance. The resetting operation can also markedly lower the spin temperature of an already cold molecule, the so-called algorithmic cooling procedure⁴. Importantly the PASADENA-SPINOE effect is expected to reach departures from equilibrium magnetization in the solvent. Unlike the DNP, this pre-polarization method works without elaborate set-ups for microwave irradiation and does not require freezing the sample. This is currently work under progress. In this context, we are also using gradient ascent pulse design methods for determining optimal polarization compression sequences.

Coherent light is used for controlling energy transfer and conversion mechanisms in several biochemical processes such as photosynthesis. The outcome of a process can be fed back into the input through a feedback loop, adaptively shaping the input laser pulse⁵. At the Pines Lab, we have applied a similar adaptive control method to achieve broadband inversion of spins in solution. Output from the spectrum is matched against a fitness function which is fed back into a genetic evolution program which searches for an improved pulse profile. This is a general method which does not rely on knowing the details of the system, i.e. the Hamiltonian. That is it can be applied to any problem where an appropriate fitness parameter can be assigned. And in combination with computer simulations it provides a robust method for correcting for pulse miscalibrations and unaccounted experimental parameters (e.g. relaxation, inhomogeneity of the sample, RF power fluctuations, etc.). Results from this project will appear soon.

An example of a collaborative research project between the Pines group and colleagues in Applied Mathematics and Engineering involves the development and implementation of an approach to iterative control of nuclear spins. Since nuclear spins play a central role in nuclear magnetic resonance (NMR) spectroscopy and magnetic resonance imaging (MRI), control of nuclear spins is tantamount to control of the parameters that determine the features and information content of NMR spectra and MRI images.

Consider, in general schematic terms, the control of a system, taking it from a given initial state to a desired final state under the action of a control propagator P(control):

The system may be a robot, a vehicle or spacecraft, a molecule, or, as in the case of our research, a system of nuclear spins.

Traditional differential control involves the feedback adjustment of the parameters of an evolving system as it deviates from its prescribed trajectory. Such control necessitates the comparison of the evolving trajectory with the prescribed one, i.e. it is necessary to "see where you're going." In contrast, for the novel iterative schemes, the propagator P(control) that induces the desired trajectory is made to be the stable fixed point, in "propagator space," of an iterative map F:

thereby ensuring that any deviant initial propagator P(0) resulting from errors or perturbations will converge to P(control) under iterative application of the map F:

In such iterative sequences it is not necessary to "see where you're going." Instead of tailored differential control for each member of an ensemble that may experience different errors, the same control sequence can be applied "blindly" to the whole ensemble. Of course , there is a price to pay for this "broadband" privilege--the trajectory from initial to final state may be considerably longer and more complex, but convergence to the desired final state with predetermined precision is assured. Clearly there are circumstances in which differential control is more appropriate, and there are others where iterative control is superior. The situation of nuclear spins often fall into the latter category because they involve large ensembles with broad ranges of possible control parameters and errors.

Iterative sequences derived form the mathematical models have been implemented in NMR and MRI by our group. Instruments thus enhanced have made it possible to achieve precise and selective control of the states of nuclear spins. On the microscopic scale, for example, it is now possible, by iterative decoupling sequences, to eliminate the effects of spin-spin interactions, thereby simplifying the NMR spectra and making it possible to determine the structures of molecules in solution and in materials.

On the macroscopic scale, iterative excitation in MRI makes it possible to elicit and to selectively enhance or suppress signals from particular regions of the images of organisms, thereby providing spatially selective biomedical information.

The iterative maps associated with these sequences often have fractal basin images.

In recent years, NMR has emerged, beyond its role as a diagnostic analytical tool for molecules, materials and organisms, as a potentially powerful environment for the implementation of Quantum Information Processing (QIP). The nuclear spins are, after all, quantum systems with a natural binary basis, the two quantum states "up" and "down" in a magnetic field. The spins can function therefore as "qubits" whose entangled quantum states are manipulated in quantum logic gates by means of delicately controlled radiofrequency pulses, as in Multiple-Quantum NMR spectroscopy.

Advantage of quantum computing over classical computing is foreseen because the quantum algorithms involve the participation of all qubits at the same time, "in parallel." This is a uniquely quantum phenomenon akin to capitalizing on the simultaneous existence of the alive and dead quantum “Schroedinger cat." Iterative control schemes under development should make it possible to overcome the effects of "decoherence"

thus allowing the implementation of extended quantum computation algorithms even in the presence of imperfect quantum logic gates and interactions with the environment.

[1] Canolty, R. T. et al. Science 313, 1626-1628 (2006)
[2] Caravetta, M. And Levitt, M J. Am. Chem. Soc. 126, 6228-6229 (2001)
[3] Anwar, M. et al. Phys. Rev.Lett. 93, 040501 (2004)
[4] Baugh, J. et al. Nature 438, 470 (2005)
[5] Herek, J. et al. Nature 417, 533 (2002)