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Relaxation Optimized Polarization-Coherence Transfer in Ising Spin Chains

Dionisis Stefanatos, Navin Khaneja, Steffen J. Glaser

Published May 15, 2005• 0 citations
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Abstract

Experiments in coherent spectroscopy correspond to control of quantum-mechanical ensembles guiding them from initial to final target states. The control inputs (pulse sequences) that accomplish these transfers should be designed to minimize the effects of relaxation and to optimize the sensitivity of the experiments. For example in Nuclear Magnetic Resonance (NMR) spectroscopy, a question of fundamental importance is what is the maximum efficiency of polarization or coherence transfer between coupled spins in the presence of relaxation. Furthermore, what is the optimal pulse sequence which achieves this efficiency? This letter is a continuation of our previous work on the above problems. Here, we attempt to answer these questions for an Ising spin chain, under the presence of transverse relaxation. The methods presented in this paper are expected to find applications not only in coherent spectroscopy but also in quantum information processing.

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Experiments in coherent spectroscopy correspond to control of quantum-mechanical ensembles guiding them from initial to final target states. The control inputs (pulse sequences) that accomplish these transfers should be designed to minimize the effects of relaxation and to optimize the sensitivity of the experiments. For example in Nuclear Magnetic Resonance (NMR) spectroscopy, a question of fundamental importance is what is the maximum efficiency of polarization or coherence transfer between coupled spins in the presence of relaxation. Furthermore, what is the optimal pulse sequence which achieves this efficiency? This letter is a continuation of our previous work on the above problems. Here, we attempt to answer these questions for an Ising spin chain, under the presence of transverse relaxation. The methods presented in this paper are expected to find applications not only in coherent spectroscopy but also in quantum information processing.
Experiments in coherent spectroscopy correspond to control of quantum mechanical ensemble guiding them from initial to final target states. The control inputs (pulse sequences) that accomplish these transformations should be designed to minimize the effects of relaxation and to optimize the sensitivity of the experiments. For example in nuclear magnetic resonance (NMR) spectroscopy, a question of fundamental importance is what is the maximum efficiency of coherence or polarization transfer between two spins in the presence of relaxation. Furthermore what is the optimal pulse sequence which achieves this efficiency? This manuscript extends our previous work in the above problems. Here, we take into account both the longitudinal and the transverse relaxation mechanisms, thus generalizing our previous results, where the former had been neglected.
Experiments in coherent spectroscopy correspond to control of quantum mechanical ensembles guiding them from initial to final target states by unitary transformations. The control inputs (pulse sequences) that accomplish these unitary transformations should take as little time as possible so as to minimize the effects of relaxation and to optimize the sensitivity of the experiments. Here, we present a novel approach for efficient control of dynamics in spin chains of arbitrary length. The approach relies on creating certain three spin encoded states, which can be efficiently transferred through a spin chain. The methods presented are expected to find applications in control of spin dynamics in coherent spectroscopy and quantum information processing.
In this thesis, we study methods for optimal manipulation of coupled spin dynamics in the presence of relaxation. We use these methods to compute analytical upper bounds for the efficiency of coherence and polarization transfer between coupled nuclear spins in multidimensional nuclear magnetic resonance (NMR) experiments, under the presence of relaxation. We derive relaxation optimized pulse sequences which achieve or approach these bounds and maximize the sensitivity of the experiments. The two systems examined in detail in this thesis, arising in the context of protein NMR spectroscopy, are a coupled heteronuclear spin pair and an Ising spin chain. New schemes for coherence and polarization transfer are found, which yield substantial gains in transfer efficiency, compared to the traditionally used pulse sequences. From the standpoint of mathematical control theory, the problems arising in connection with optimal manipulation of dissipative quantum dynamics, motivate the study of a class of dissipative bilinear control systems and the computation of their reachable sets. For these systems we show that the optimal solution, corresponding to the maximization of transfer efficiency, and the reachable set can be found by solving a semidefinite program.
Experiments in coherent spectroscopy correspond to control of quantum mechanical ensembles guiding them from initial to final target states by unitary transformations. The control inputs (pulse sequences) that accomplish these unitary transformations should take as little time as possible so as to minimize the effects of relaxation and to optimize the sensitivity of the experiments. Here, we present a radically different and generally applicable approach to efficient control of dynamics in spin chains of arbitrary length. The approach relies on the creation of localized spin waves, ``spin solitons'', and efficient propagation of these soliton states through the spin chain. The methods presented are expected to find immediate applications in control of spin dynamics in coherent spectroscopy and quantum information processing.
We study multiple-spin coherence transfers in linear Ising spin chains with nearest-neighbor couplings. These constitute a model for efficient information transfers in future quantum computing devices and for many multidimensional experiments for the assignment of complex spectra in nuclear magnetic resonance spectroscopy. We complement prior analytic techniques for multiple-spin coherence transfers with a systematic numerical study where we obtain strong evidence that a certain analytically motivated family of restricted controls is sufficient for time optimality. In the case of a linear three-spin system, additional evidence suggests that prior analytic pulse sequences using this family of restricted controls are time optimal even for arbitrary local controls. In addition, we compare the pulse sequences for linear Ising spin chains to pulse sequences for more realistic spin systems with additional long-range couplings between nonadjacent spins. We experimentally implement the derived pulse sequences in three- and four-spin systems and demonstrate that they are applicable in realistic settings under relaxation and experimental imperfections---in particular---by deriving broadband pulse sequences which are robust with respect to frequency offsets.
In this paper, we develop methods for optimal manipulation of coupled spin dynamics in the presence of relaxation. These methods are used to compute analytical bounds for the optimal efficiency of coherence transfer between coupled nuclear spins in presence of longitudinal and transverse relaxation. We derive relaxation optimized pulse sequences which achieve these bounds and maximize the sensitivity of the experiments in spectroscopic applications. This paper is a continuation of our previous work. Here, we take into account both the longitudinal and the transverse relaxation mechanisms, thus generalizing our previous results, where the former had been neglected.