Jae-Seung Lee
Postdoctoral Fellow
Department of Chemistry
Kent State University
Kent OH 44242-0001 USA
Phone: +1 330 672 9402
Fax: +1 330 672 3816
E-mail: jlee2 [at] kent [dot] edu
My current research interests are engineered quantum dynamics, including the development of useful theoretical models for nano and quantum devices and their experimental demonstration with nuclear magnetic resonance (NMR), and NMR spectroscopy, with a focus on development of new solid-state NMR techniques.
Engineered Quantum Dynamics
Research on nano and quantum devices is one of emerging fields in science and technology. Those devices require quantum control of small systems consisting of electrons, photons, spins, and so on. NMR has been a leading testbed for realizing basic ideas of quantum information processing (QIP) on small quantum systems consisting of up to twelve nuclear spins [1]. In QIP, the information is manipulated with quantum mechanical laws to efficiently solve computationally hard problems. The investigation of new quantum dynamics and its experimental demonstration with NMR would facilitate the development of practical devices exploiting such dynamics and will also generate new ideas for spectroscopic techniques.
One of examples of my study is the mechanism of amplification in quantum mechanics. Since quantum dynamics is governed by linear equations of motion, classical mechanisms of amplification based on non-linear dynamics do not work. As we have found, quantum mechanics offers another alternatives for converting a small perturbation into a big change in observable values: amplified detection and measurement using entangled states [2] and "quantum domino" [3].
In the model of amplified detection and measurement, small local perturbation changes a wave function of the entire system in a coherent way, and this change can be converted into macroscopically distinguishable states by a unitary transformation. I demonstrated these ideas with a system of seven nuclear spins 1/2, where six spins were prepared in a cat state, a superposition of all six spins up and all six spins down, and played a role of quantum amplifier to detect and measure the existence and state of the 7th spin.
In the study of "quantum domino" dynamics, a more efficient way has been proposed to bring a given system to macroscopically distinguishable states. In a 1D Ising chain with nearest-neighbor interactions subject to a weak resonant transverse field, a stimulated wave of flipped spins can be triggered by a flip of a single spin. I analytically solved the dynamic problem and showed that both the maximum coefficient of amplification and the time of operation increase linearly with the size of the chain, which means this scheme may provide one of the fastest methods to measure the state of a single spin. We have also demonstrated experimental realization of this quantum domino dynamics using a linear chain of four nuclear spins.
To extend capabilities of coherent control in NMR, I have developed several experimental techniques, which allow us to manipulate individual quantum states of a strongly-coupled spin system. A strongly-coupled spin system is attractive for QIP because it provides a complex coupling network enabling faster quantum operations, but individual addressability, which is normally required by QIP, is lost. Pseudopure ground and cat states, amplified detection and measurement, resurrection of Schrodinger cat, projective measurement, and adiabatic transfer of coherence have been demonstrated by manipulating individual quantum states of six, seven, and twelve spins 1/2 [4].
As ongoing research projects on engineered quantum dynamics, I study the dynamics of a system of several qubits interacting with environment. The results of this work will help understanding the environmental effects, like decoherence, and will be useful in developing new methods of quantum control. I also work on increasing the size of a quantum system that could be coherently manipulated.
New NMR Spectroscopic Techniques
NMR spectroscopy is one of the major analytic tools in chemistry. Today, the problems of determining structures of large molecules stimulate enormous progresses in NMR spectroscopic methods. In many cases, NMR structures suggested by current techniques are not unique, which formulates a demand for more accurate and precise methods. As we have shown, solid-state NMR of static powdered samples allows us to measure inter-nuclear distances with unprecedented accuracy. I have developed a new adiabatic cross-polarization technique, which is more efficient than any of the existing methods, and measured distances between hetero-nuclear spins in static powdered samples with better accuracy than ever done before. Development of new spectroscopic methods requires understanding of spin dynamics and also efficient methods of coherent control for spin systems. Therefore, this research is closely related to my study of quantum dynamics. The ultimate goal of this research would be development of more accurate and universal techniques for NMR spectroscopy.
Enhancing NMR signals from rare nuclei is very desirable. As an example, carbon or nitrogen nuclei can give important information on molecular structures, but their NMR signals are weak due to their small gyromagnetic ratios and low natural abundance. In order to increase the signal sensitivity, methods of cross-polarization have been used, wherein the nuclear spin polarization is transferred from abundant nuclei with high gyromagnetic ratio, such as protons, to rare nuclei with lower gyromagnetic ratio, such as carbons or nitrogens. Usual enhancement factor is given by the ratio of gyromagnetic ratios between abundant and rare nuclei. I demonstrated that the signals of rare nuclei can be dramatically increased beyond the ratio of gyromagnetic ratios in liquid crystals and static solids by adiabatic demagnetization-remagnetization process [5]. In this technique, the Zeeman order of abundant nuclei is first converted into the dipolar order, and then, into the Zeeman order of rare nuclei. This NMR signal enhancement was a key ingredient needed to accurately measure the 13C-15N distances in organic solids.
For the measurement of distances between heteronuclei, I have used a scheme minimizing a perturbation of a spin system together with new adiabatic cross-polarization and efficient proton decoupling sequences [6]. The experiments were done with a conventional liquid state NMR probe and labeled glycine molecules in static powder samples, and the distances between 13C and 15N nuclei in a glycine molecule was obtained directly from dipolar spectra. The precision for the 13C - 15N distances was close to that obtained in neutron-scattering experiments. In order to get even better precision, several experimental improvements are being investigated, including new probe design, temperature-dependent experiment, cryogenic experiment, and so on. At the same time, the extension of the method for other pairs of hetero-nuclei is being pursued.
As ongoing research projects on new NMR methods, I am developing the theoretical framework for the adiabatic cross-polarization that will help optimizing the process and increasing its efficiency. For the distance measurement, experiments for homo-nuclear pairs of 13C spins and pairs of 13C and 2H spins will be performed and analyzed in the near future.
References
[1] J.-S. Lee and A. K. Khitrin, "Pseudopure state in a twelve-spin system," J. Chem. Phys. 122, 041101 (2005); J.-S. Lee and A. K. Khitrin, "Twelve-spin Schrodinger cat," Appl. Phys. Lett. 87, 204109 (2005).
[2] J.-S. Lee and A. K. Khitrin, "Quantum amplifier: Measurement with entangled spins," J. Chem. Phys. 121, 3949-3952 (2004); J.-S. Lee and A. K. Khitrin, "Experimental Demonstration of Quantum State Expansion in a Cluster of Dipolar-Coupled Nuclear Spins," Phys. Rev. Lett. 94, 150504 (2005).
[3] J.-S. Lee and A. K. Khitrin, "Stimulated wave of polarization in a one-dimensional Ising chain," Phys. Rev. A 71, 062338 (2005); J.-S. Lee, T. Adams and A. K. Khitrin, "Experimental demonstration of stimulated polarization wave in a chain of nuclear spins," New J. Phys. 9, 83 (2007).
[4] J.-S. Lee and A. K. Khitrin, "NMR quantum toys," Concepts Magn. Reson. Part A 30A, 194-217 (2007).
[5] J.-S. Lee and A. K. Khitrin, "Adiabatic cross-polarization via intermediate dipolar-ordered state," J. Magn. Reson. 177, 152 (2005).
[6] J.-S. Lee and A. K. Khitrin, "Accurate measurement of 13C - 15N distances with solid-state NMR," J. Chem. Phys. 124, 144508 (2006).
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