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arXiv:2604.27220

Multirate characterization of relaxation mechanisms for two nonequivalent nuclear spins 1/2 in a liquid using maximally entangled pseudo-pure quantum states

Georgiy Baroncha, Alexander Perepukhov, Boris V. Fine

quant-phcond-mat.mtrl-scicond-mat.othercond-mat.stat-mechSubmitted Apr 29, 2026• Announced May 1, 2026• 0 citations
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Abstract

Multirate characterization of spin responses in nuclear magnetic resonance (NMR) is a promising approach to fingerprinting complex molecules in the presence of multiple relaxation mechanisms. Here we present experimental and theoretical investigations simultaneously accessing 8 relaxation rates describing the density matrix of two adjacent non-equivalent nuclear spins 1/2 ($^1$H and $^{\ 13}$C) belonging to a molecule in a liquid. The selected nuclear pair is stable with respect to chemical exchange. Some of the rates are obtained from conventional measurements of inversion recovery and nuclear Overhauser effect, while other, less conventional ones, are extracted from the relaxation initialized by the maximally entangled pseudo-pure Bell states (Bell PPSs) of the spin pair. The Bell PPSs are created using a hereby introduced method based on a detuned Hartmann-Hahn double resonance condition. Microscopic theory behind the measured relaxation rates is presented, and its consistency is demonstrated by several parameter-free tests. In particular, it is shown both theoretically and experimentally, that the eigenmodes of the off-diagonal relaxation of the two-spin density matrix can be selectively initialized using Bell PPSs. Our multirate analysis suggests that the measured off-diagonal relaxation is partly due to an unconventional mechanism arising from very weak $J$-couplings of the spin pair with fluctuating distant nuclear spins. Furthermore, we identify a dimensionless ratio of diagonal relaxation rates, which is determined exclusively by intra-pair magnetic dipolar interaction and hence possesses a universal value for a broad class of nuclear spin pairs. This value is consistent with both our experiments and other experiments reported in the literature.

Comments
24 pages, 10 figures

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Multirate characterization of spin responses in nuclear magnetic resonance (NMR) is a promising approach to fingerprinting complex molecules in the presence of multiple relaxation mechanisms. Here we present experimental and theoretical investigations simultaneously accessing 8 relaxation rates describing the density matrix of two adjacent non-equivalent nuclear spins 1/2 (1^11H and  13^{\ 13} 13C) belonging to a molecule in a liquid. The selected nuclear pair is stable with respect to chemical exchange. Some of the rates are obtained from conventional measurements of inversion recovery and nuclear Overhauser effect, while other, less conventional ones, are extracted from the relaxation initialized by the maximally entangled pseudo-pure Bell states (Bell PPSs) of the spin pair. The Bell PPSs are created using a hereby introduced method based on a detuned Hartmann-Hahn double resonance condition. Microscopic theory behind the measured relaxation rates is presented, and its consistency is demonstrated by several parameter-free tests. In particular, it is shown both theoretically and experimentally, that the eigenmodes of the off-diagonal relaxation of the two-spin density matrix can be selectively initialized using Bell PPSs. Our multirate analysis suggests that the measured off-diagonal relaxation is partly due to an unconventional mechanism arising from very weak JJJ-couplings of the spin pair with fluctuating distant nuclear spins. Furthermore, we identify a dimensionless ratio of diagonal relaxation rates, which is determined exclusively by intra-pair magnetic dipolar interaction and hence possesses a universal value for a broad class of nuclear spin pairs. This value is consistent with both our experiments and other experiments reported in the literature.
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We investigate analytically and numerically the multiple-quantum (MQ) NMR dynamics in systems of nuclear spins 1∕21∕21∕2 coupled by the dipole-dipole interactions in the case of the dipolar ordered initial state. We suggest two different methods of MQ NMR. One of them is based on the measurement of the dipolar temperature in the quasiequilibrium state which is established after the time of order ${\ensuremath{\omega}}_{\mathit{loc}}^{\ensuremath{-}1}$ (${\ensuremath{\omega}}_{\mathit{loc}}$ is the dipolar local field) after the MQ NMR experiment. The other method uses an additional resonance ${(\ensuremath{\pi}∕4)}_{y}$ pulse after the preparation period of the standard MQ NMR experiment in solids. Many-spin clusters and correlations are created faster in such experiments than in the usual MQ NMR experiments and can be used for the investigation of many-spin dynamics of nuclear spins in solids.
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Quantum simulations, where controllable quantum systems are used to simulate other quantum systems, originally proposed by Richard Feynman, are one of the most remarkable applications of quantum information science. Compared to computation, quantum simulations require much less number of qubits for the m to be practical. In the work described in this thesis, we have performed a few quantum simulations of small quantum systems using Nuclear Magnetic Resonance(NMR) techniques. These simulations have been used to experimentally demonstrate the underlying interesting quantum protocols. All the experiments presented have been carried out using liquid-state or liquid crystal NMR. Numerical pulse optimization techniques have been utilized in some of the experiments, to achieve better control over the spin systems. The first chapter contains “Introduction” to quantum information processing, NMR, and numerical pulse optimization techniques. In chapter 2, we describe quantum simulation of a 3-spin Heisenberg-XY spin chain having only nearest neighbour interactions. Recently, spin chains having pre-engineered short-range interactions have been proposed to efficiently transfer quantum information between different parts of a quantum information processor. Other important proposals involving these spin chains include generating entangled states and universal quantum computation. However, such engineered interactions do not occur naturally in any system. In such a scenario, the experimental viability of these proposals can be tested by simulating the spin chains in other controllable quantum systems. In this work, we first theoretically study the time evolution of bipartite and tripartite entanglement measures for a 3-spin open ended XY spin chain. Then, by simulating the XY interactions in a 3-spin nuclear spin system, we experimentally generate, (i)a bipartite maximally(pseudo-)entangled state(Bell state) between end qubits, and(ii) multipartite(pseudo-)entangled states(Wand GHZ states),starting from separable pseudo-pure states. Bell state has been generated by using only the natural unitary evolution of the XY spin chain. W-state and GHZ-state have been generated by applying a single-qubit rotation to the second qubit, and a global rotation of all the three qubits respectively after the unitary evolution of the spin chain. In chapter 3, we simulate a 3-spin quantum transverse Ising spin system in a triangular configuration, and show that multipartite quantum correlations can be used to distinguish between the frustrated and non-frustrated regimes in the ground state of this spin system. The ground state of the spin system has been prepared by using adiabatic state preparation method. Gradient ascent pulse engineering technique has been utilized to efficiently realize the adiabatic evolution of the spin system. To analyse the experimental ground state of the system, we employ two different multipartite quantum correlation measures, generated from monogamy studies of bipartite quantum correlations. Chapter 4 contains a digital…
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