Delocalized long-lived states (LLSs) and collective zero-quantum long-lived coherences (LLCs) in aliphatic chains provide a promising route for preserving nuclear spin order with lifetimes that exceed the conventional
T1 and
T2 relaxation times, respectively. Their extended lifetimes make them attractive for applications including hyperpolarization storage, ligand-observed drug screening based on the loss of longevity upon binding to a target protein, and quantum information processing exploiting the collective properties of many-body spin systems. Although LLSs and LLCs have been observed experimentally in methylene networks, their origin and general structure in chains of arbitrary length have remained unclear. Here we show that these relaxation-protected modes follow directly from Redfield relaxation theory. Specifically, we construct the long-lived subspace, i.e., the zero-eigenvalue subspace of the relaxation superoperator associated with the dominant intra-pair dipole--dipole relaxation mechanism. The long-lived subspace contains
2N−1 independent non-trivial operators, which excludes the identity operator, where
N>1 is the number of
−CH2− groups in the chain. In achiral molecules, conservation of the global intra-pair permutation parity restricts experimental access to at most
2N−2 of these operators, whereas in chiral molecules this parity is not conserved, making up to
2N−1 long-lived operators accessible. We further develop a general framework for constructing both LLSs and LLCs in aliphatic chains containing an arbitrary number of
−CH2− groups in achiral molecules, and illustrate the approach explicitly for chains with
N=2, 3, and 4 methylene groups.
Algorithmic cooling methods manipulate an open quantum system in order to lower its temperature below that of the environment. We achieve significant cooling of an ensemble of nuclear spin-pair systems by exploiting the long-lived nuclear singlet state, which is an antisymmetric quantum superposition of the “up” and “down” Zeeman states. The effect is demonstrated by nuclear magnetic resonance experiments on a molecular system containing a coupled pair of near-equivalent 13C nuclei. The populations of the system are subjected to a repeating sequence of cyclic permutations separated by relaxation intervals. The long-lived nuclear singlet order is pumped well beyond the unitary limit. The pumped singlet order is converted into nuclear magnetization which is enhanced by 21% relative to its thermal equilibrium value.
We analyze the symmetry properties of the dipolar Hamiltonian as the main relaxation mechanism responsible for the observed NMR spectra of long-lived states of methyl groups. Long-lived states exhibit relaxation times that are considerably longer than the spin–lattice relaxation time,
T1 . The analysis is complementary to previous studies and provides insight into the relaxation mechanism of long-lived states by focusing exclusively on the symmetry of the spin Hamiltonian. Our study shows that the dipole–dipole coupling between protons of a methyl group and between the protons and an external spin are both symmetry breaking interactions that can lead to relaxation pathways that transform the polarization from symmetry order to Zeeman order. The net contribution of the internal dipolar interaction to the NMR observation of long-lived states is zero. Our calculation is in good agreement with the reported features of the observed spectra and previous theoretical studies.
Abstract Long-lived coherences, emerging under periodic pulse driving in the disordered ensembles of strongly interacting spins, offer immense advantages for future quantum technologies, but the physical origin and the key properties of this phenomenon remain poorly understood. We theoretically investigate this effect in ensembles of different dimensionality, and predict existence of the long-lived coherences in all such systems, from two-dimensional to infinite-dimensional (where every spin is coupled to all others with similar strength), which are of particular importance for quantum sensing and quantum information processing. We explore the transition from two to infinite dimensions, and show that the long-time coherence dynamics in all dimensionalities is qualitatively similar, although the short-time behavior is drastically different, exhibiting dimensionality-dependent singularity. Our study establishes the common physical origin of the long-lived coherences in different dimensionalities, and suggests that this effect is a generic feature of the strongly coupled spin systems with positional disorder. Our results lay out foundation for utilizing the long-lived coherences in a range of application, from quantum sensing with two-dimensional spin ensembles, to quantum information processing with the infinitely-dimensional spin systems in the cavity-QED settings.
The effect of spin permutation symmetry on the maximum achievable efficiency of coherence transfer between pairs of Hermitian or non-Hermitian spin operators is investigated. It is shown that spin permutation symmetry may tighten significantly the quantum mechanical bounds hitherto known to apply for coherence transfer processes. This feature is demonstrated for the heteronuclear coherence transfer processes S x → F x , S - → F - and 2F z S x → F x , 2F z S - → F - (F = Σ n i=1 I i ) in I2S and I3S (n = 2,3) spin-1/2 systems. The bounds arising from permutation symmetry apply for non-selective multidimensional NMR experiments.
The quantum dynamics of spin systems is often treated by a differential equation known as the master equation, which describes the trajectories of spin observables such as magnetization components, spin state populations, and coherences between spin states. The master equation describes how a perturbed spin system returns to a state of thermal equilibrium with a finite-temperature environment. The conventional master equation, which has the form of an inhomogeneous differential equation, applies to cases where the spin system remains close to thermal equilibrium, which is well satisfied for a wide variety of magnetic resonance experiments conducted on thermally polarized spin systems at ordinary temperatures. However, the conventional inhomogeneous master equation may fail in the case of hyperpolarized spin systems, when the spin state populations deviate strongly from thermal equilibrium, and in general where there is a high degree of nuclear spin order. We highlight a simple case in which the inhomogeneous master equation clearly fails, and propose an alternative master equation based on Lindblad superoperators which avoids most of the deficiencies of previous proposals. We discuss the strengths and limitations of the various formulations of the master equation, in the context of spin systems which are far from thermal equilibrium. The method is applied to several problems in nuclear magnetic resonance and to spin-isomer conversion.