Dipolar-coupled Nuclear Spins Research Articles

Floquet Dynamics in a One-Dimensional Chain in the Multipulse Spin Locking of Nuclear Magnetic Resonance

The dynamics of a one-dimensional chain that consists of 10–14 dipolar-coupled nuclear spins, is placed in an external magnetic field, and is irradiated by a periodic sequence of resonant π/n pulses (n is a natural number) with the same time delay 2τ between them has been studied. The numerical calculation has shown that thermodynamic equilibrium, which is determined by the common temperature of the Zeeman and dipole reservoirs, is established in the spin system at the average pulse field π/(2nτ) ∼ ωloc (where ωloc is the dipole frequency and n > 2) and times t ∼ ω loc −1 . The relaxation of the magnetization in the system irradiated by (π/2)x pulses at π/4τ ≫ πlocis due to a four-spin resonant process, and the relaxation rate is proportional to τ4.

The origin of negative cross-peaks in proton-spin diffusion spectrum of fully protonated solids at fast MAS: Coherent or incoherent effect?

Spin-diffusion (SD) is amongst the first methods proposed to spatially transfer polarization between dipolar-coupled nuclear spins. Lab-frame SD has proved particularly useful in structural characterization of a large variety of molecules. During SD, the rate of magnetization transfer between the two nuclei depends on the square of the dipolar coupling and the zero-quantum lineshape of the two spins. The relative sign of the diagonal and cross-peaks is determined by the spin part of the dipolar Hamiltonian. Practically, SD experiments are used in two ways: (a) SD transfer amongst only the protons (known as proton spin-diffusion or PSD) and b) SD amongst rare nuclei, coupled to a strong proton bath, known as proton driven spin-diffusion (PDSD). It is well established that the diagonal and cross-peaks have the same sign during SD based polarization transfer. 2D PSD experiments recorded on Histidine.HCl.H2O sample at fast magic angle spinning (MAS) show that some of the cross-peaks in the 2D spectrum are negative with respect to the diagonal peaks. Cross-relaxation due to stochastic motion is generally believed to give rise to such negative peaks. Herein, we use theoretical calculations, numerical simulations and experiments to show that the origin of the negative cross-peaks in PSD spectrum is due to coherent interactions. The origin of negative peaks can be specifically ascribed to a four spin, double-flip-double flop term, in the third-order Hamiltonian. These terms become the dominant terms at fast spinning when additional — conditions are satisfied.

Pulse control protocols for preserving coherence in dipolar-coupled nuclear spin baths

Coherence of solid state spin qubits is limited by decoherence and random fluctuations in the spin bath environment. Here we develop spin bath control sequences which simultaneously suppress the fluctuations arising from intrabath interactions and inhomogeneity. Experiments on neutral self-assembled quantum dots yield up to a five-fold increase in coherence of a bare nuclear spin bath. Numerical simulations agree with experiments and reveal emergent thermodynamic behaviour where fluctuations are ultimately caused by irreversible conversion of coherence into many-body quantum entanglement. Simulations show that for homogeneous spin baths our sequences are efficient with non-ideal control pulses, while inhomogeneous bath coherence is inherently limited even under ideal-pulse control, especially for strongly correlated spin-9/2 baths. These results highlight the limitations of self-assembled quantum dots and advantages of strain-free dots, where our sequences can be used to control the fluctuations of a homogeneous nuclear spin bath and potentially improve electron spin qubit coherence.

A DNP-hyperpolarized solid-state water NMR MASER: observation and qualitative analysis.

We present observations of an NMR MASER (microwave amplification by stimulated emission of radiation) of hyperpolarized 1H nuclei by dynamic nuclear polarization (DNP) at 1.2 K and in a magnetic field of 6.7 T. The sustained maser pulses originate from the interplay between radiation damping (RD) due to the large 1H magnetization, and the remagnetization to a negative value by the DNP process. NMR signals lasting for several tens of seconds are thus observed on an ensemble of dipolar-coupled nuclear spins. Magnetization dynamics are analyzed in terms of the combined Bloch-Maxwell and Provotorov (BMP) equations for RD and DNP. Insight into the long time evolution of the magnetization is provided by a theoretical analysis of this nonlinear dynamical system, and by fitting the NMR signal to a simplified version of the BMP equations.

QUANTUM SIMULATION. Localization-delocalization transition in the dynamics of dipolar-coupled nuclear spins.

Nonequilibrium dynamics of many-body systems are important in many scientific fields. Here, we report the experimental observation of a phase transition of the quantum coherent dynamics of a three-dimensional many-spin system with dipolar interactions. Using nuclear magnetic resonance (NMR) on a solid-state system of spins at room-temperature, we quench the interaction Hamiltonian to drive the evolution of the system. Depending on the quench strength, we then observe either localized or extended dynamics of the system coherence. We extract the critical exponents for the localized cluster size of correlated spins and diffusion coefficient around the phase transition separating the localized from the delocalized dynamical regime. These results show that NMR techniques are well suited to studying the nonequilibrium dynamics of complex many-body systems.

Communication: Long-lived states of nuclear spins in solids

We report an observation of extremely long-lived spin states in systems of dipolar-coupled nuclear spins in solids. The "suspended echo" experiment uses a simple stimulated echo pulse sequence and creates non-equilibrium states which live many orders of magnitude longer than the characteristic time of spin-spin dynamics T2. Large amounts of information can be encoded in such long-lived states and subsequently retrieved by an application of a single "reading" pulse.

Numerical simulation of free evolution in solid-state nuclear magnetic resonance using low-order correlations in Liouville space

The design of simulations of free evolution in dipolar-coupled nuclear-spin systems using low-order correlations in Liouville space (LCL) is discussed, and a computational scheme relying on the Suzuki-Trotter algorithm and involving minimal memory requirements is described. The unusual nature of the approximation introduced by Liouville-space reduction in a spinning solid is highlighted by considering the accuracy of LCL simulations at different spinning frequencies, the quasiequilibria achieved by spin systems in LCL simulations, and the growth of high-order coherences in the exact dynamics. In particular, it is shown that accurate LCL simulations of proton spin diffusion occur in a regime where the reduced space excludes the coherences that make the dominant contribution to ∥σ∥(2), the norm-squared of the density matrix.

Projection of a quantum state on eigenstates of average Hamiltonian

A scheme for projecting an arbitrary quantum state on eigenstates of average Hamiltonian is described. As an experimental example, projection on entangled Bell states, which are eigenstates of specially constructed average Hamiltonian, is demonstrated for a system of two dipolar-coupled nuclear spins. The results of a direct and time-reversed evolution are added to average out the coherences between different eigenstates and accomplish the projection.

Projective measurement in nuclear magnetic resonance

It is demonstrated that nuclear magnetic resonance experiments using pseudopure spin states can give possible outcomes of projective quantum measurement and probabilities of such outcomes. The physical system is a cluster of six dipolar-coupled nuclear spins of benzene in a liquid-crystalline matrix. For this system with the maximum total spin S=3, the results of measuring SX are presented for the cases when the state of the system is one of the eigenstates of SZ.

Resurrection of Schrödinger's cat

It is experimentally demonstrated that a quantum state, destroyed by uncontrollable natural decoherence, can be purified by using results of projective measurement and converted into a desired target pure state. The physical system is a cluster of seven dipolar-coupled nuclear spins of single-labelled 13C-benzene in liquid crystal. 13C spin plays the role of a device for measuring the protons' ‘cat’ state, a superposition of states with six spins up (alive) and six spins down (dead). Information about the state, stored in the 13C spin, is used to bring the protons' subsystem into the target alive state, while the excess entropy produced by decoherence is transferred to the ‘measuring device’, the 13C spin.

Quantification of homonuclear dipolar coupling networks from magic-angle spinning 1H NMR

Numerical simulations of magic-angle spinning (MAS) spectra of dipolar-coupled nuclear spins have been used to assess different approaches to the quantification of dipolar couplings from 1H solid-state NMR. Exploiting the translational symmetry of periodic spin systems allows extended networks with ‘realistic’ numbers of spins to be considered. The experimentally accessible parameter is shown to be the root-sum-square of the dipolar couplings to a given spin. The effectiveness of either fitting the resulting spinning sideband spectra to small spin system models, or using analyses based on moment expansions, has been examined. Fitting of the spinning sideband pattern is found to be considerably more robust with respect to experimental noise than frequency domain moment analysis. The influence of the MAS rate and system geometry on robustness of the quantification is analysed and discussed.

Twelve-spin “Schrödinger cat”

Pseudopure “cat” state, a superposition of quantum states with all spins up and all spins down, is experimentally demonstrated for a system of 12 dipolar-coupled nuclear spins of fully C13-labeled benzene molecule oriented in a liquid-crystalline matrix.

Experimental Demonstration of Quantum State Expansion in a Cluster of Dipolar-Coupled Nuclear Spins

It is experimentally demonstrated that an arbitrary quantum state of a single spin 1/2, a| upward arrow+b| downward arrow, can be converted into a superposition of the two ferromagnetic states of a spin cluster: a| upward arrow upward arrow... upward arrow upward arrow+b| downward arrow downward arrow... downward arrow downward arrow. The physical system is a cluster of seven dipolar-coupled nuclear spins of single-labeled 13C-benzene molecules in a liquid-crystalline matrix. In this complex system, the pseudopure ground state and the required controlled unitary transformations have been implemented. The experimental scheme can be considered as an explicit model of quantum measurement.

Pseudopure state of a twelve-spin system

Pseudopure states of a system of twelve interacting spins are experimentally demonstrated. The system is a cluster of dipolar-coupled nuclear spins of fully labeled (13)C(6)-benzene in a liquid crystalline matrix. At present, this is the largest and the most complex composite system where individual quantum states have been addressed.

Time-reversal of cross-polarization in nuclear magnetic resonance

It is demonstrated that the time evolution of the heteronuclear polarization-transfer process in a dipolar-coupled nuclear spin system can be reversed, leading to the observation of cross-polarization echoes. The cross-polarization echoes are induced by consecutive application of two pulse trains that produce effective Hamiltonians that differ only in sign. Cross-polarization echoes have been recorded for a powder sample of alanine. The time evolution of the spin system is consistent with both unitary quantum dynamics and with spin thermodynamics of two systems approaching a common spin temperature.

Nuclear magnetic resonance polarization and coherence echoes in static and rotating solids

The mechanisms of defocusing and refocusing of spin order in extended dipolar coupled nuclear spin systems are investigated by experiments on static and on rotating solids. It is demonstrated that polarization or coherence echoes are possible also under magic-angle sample spinning. The dipolar interactions, averaged by the spinning, are recovered by rotor-synchronized multiple-pulse sequences. By a simple modification of the pulse sequences, it is possible to reverse the sign of the effective dipolar Hamiltonian and to induce the refocusing of polarization or coherence. The creation of multiple-spin order in the course of polarization evolution or free precession is monitored by a modified echo experiment. Experimental results for a polycrystalline sample of calcium formate are presented.

Time-Reversal Experiments in Dipolar-Coupled Spin Systems

By applying a suitable sequence of strong rf fields, a system of dipolar-coupled nuclear spins can be made to behave as though the sign of the dipolar Hamiltonian had been reversed. The system then appears to develop backward in time, and states of nonequilibrium magnetization can be recovered in systems which would superficially appear to have decayed to equilibrium. This behavior is consistent with dynamical and thermodynamical principles, but shows that the spin-temperature hypothesis must be employed with caution. The theory of the timereversal phenomenon is discussed, including the practical limitations on the accuracy with which it can be achieved. Various echo experiments in the laboratory and in the rotating frame are reported. The application of repeated time reversals to the problem of high-resolution NMR in solids is discussed.