Multiple quantum NMR dynamics and relaxation in one-dimensional systems

Multiple quantum NMR dynamics and relaxation in one-dimensional systems by Dr. Edward Fel’dman.

When: February 21, 16:00

Where: MR-351 TPOC4  (Red building)


Multiple quantum (MQ) NMR dynamics is the foundation of MQ NMR spectroscopy [1], which is widely used to study nuclear spin distributions in solids. At the same time,  MQ NMR allows us to investigate decoherence of many-qubit coherent spin clusters since MQ NMR not only creates many-qubit coherent states but also permits the investigation of their relaxation under the action of a correlated spin reservoir [2]. One-dimensional spin systems open new possibilities for the investigation of decoherence, both theoretical and experimental, with MQ NMR methods. The point is that a consistent quantum mechanical theory of MQ NMR dynamics exists only for one-dimensional systems [3]. According to the developed theory [3], only MQ NMR coherences of the zeroth and plus/minus second orders arise in a one-dimensional spin chain initially prepared in the thermodynamic equilibrium state in the approximation of the nearest neighbor interactions.

        The relaxation of the MQ NMR coherences can be studied [2, 4] on the evolution period of the MQ NMR experiment [1]. This period begins immediately after the preparation period [1] and the density matrix at the end of that period can be used as the initial state in the relaxation process. The relaxation of the MQ NMR coherences is caused by the secular (with respect to the external magnetic field) dipole-dipole interactions (DDI). We obtained [5,6] the time-dependencies of the intensities of MQ NMR coherences of the zeroth and second orders on the lengths of the evolution period and the preparation period using the ZZ model, which neglects the flip-flop part of the DDI. The obtained theoretical results are in a good agreement with the experimental data which were obtained on the linear chain of 19F nuclei in a single crystal of calcium fluorapatite [5, 6]. We also calculated the second moments of the line shapes of MQ NMR coherences of the zeroth and second orders [7]. This allowed us to obtain semi-phenomenological formulae, describing the decay of MQ NMR coherences.

We showed that the second moment of the line shape of the MQ NMR coherence of the zeroth order does not depend on the flip-flop part of the DDI. The theoretical predictions agree with the obtained experimental data. It is shown that the relaxation of the MQ NMR coherence of the second order can be considered as a model of decoherence in many-qubit coherent clusters [8]. The dependence of the decoherence rate on the number of spins was also obtained. Dynamics and relaxation of  MQ NMR coherences  are investigated experimentally and theoretically at different orientations relative to the direction of the external magnetic field. Universal curves for dynamics and relaxation were obtained, which describe the experimental data for different orientations of the investigated sample. Those curves prove the dipolar nature of the observed relaxation process.


[1]J.Baum, M.Munowitz, A.N.Garroway, A.Pines, J.Chem.Phys. 83, 5, 2015-2025 (1985).
[2] G. Kaur, A. Ajoy, P. Cappellaro, New J. Phys. 15, 9, 093035 (2013).
[3] E.B.Fel’dman, Applied Magnetic Resonance 45, 8, 797-806 (2014).
[4] S.I.Doronin, E.B.Fel’dman, I.I.Maximov, J. Magn. Reson. 171, 37-42 (2004).
[5] G.A.Bochkin, E.B.Fel’dman, S.G.Vasil’ev, Z.Phys.Chem. 231, 3, 513-525 (2017).
[6] G.A.Bochkin, E.B.Fel’dman, S.G.Vasil’ev, V.I.Volkov, Chem. Phys.Lett. 680, 56-60 (2017).
[7] G.A.Bochkin, S.G.Vasil’ev, I.D.Lazarev, E.B.Fel’dman, JETP, 127, 3, 532-538 (2018).
[8] G.A.Bochkin, E.B.Fel’dman, S.G.Vasil’ev, V.I.Volkov, Appl.Magn.Reson.49, 1, 25-34 (2018).


Edward Feldman graduated from Moscow Institute of Physics and Technology in 1971 and obtained his Ph.D. in chemical physics (1976) at the Institute of Chemical Physics of RAS, focusing on problems of dynamics and thermodynamics of nuclear spin systems in solids. He worked out (with Professor B.N. Provotorov) the thermodynamic theory of multi-pulse NMR experiments.  E. Feldman investigated the convergence of the Magnus expansion in systems with periodically oscillating external fields. He obtained his Dr. Sci. degree in chemical physics in 1992 (Chernogolovka).

Since 1994 he works in the field of the theory of multiple quantum NMR in solids. He collaborated with Sherbrooke University (Canada) and the laboratory of Richard Ernst, Nobel Prizer in Chemistry,

(ETH, Zurich). Now he leads the theoretical department of the Institute of Problems of Chemical Physics, Chernogolovka. His current scientific interests are the theory of magnetic resonance and an application of the magnetic resonance methods to problems of quantum informatics.