Dipolar Coupled Spin System Research Articles

Intrinsic decoherence dynamics and dense coding in dipolar spin system

The quantum decoherence is an ineluctable process when a quantum system interacts with its surrounding environment. Milburn’s dynamical master equation, as a modified shape of the Schrödinger equation, is typically used to study the effects decoherence even without intervention of environment. We studied the temporal evolution of non-local correlations in a dipolar-coupled spin system under the influence of intrinsic decoherence. Primarily, the generation in correlations of Einstein–Podolsky–Rosen steering, measurement-induced non-locality and entanglement in an uncorrelated initial system state were studied. Also, the effect of the intrinsic decoherence on the quality of the dense coding capacity dynamics for the dipolar-coupled spin system was examined. Our results highlight that the initial system’s role in defining the quantum correlations’ robustness, and we also brought out the impacts of system’s parameters on the non-local correlations and the efficiency of dense coding process.

Partial lifting of degeneracy in the J1−J2−J3 Ising antiferromagnet on the kagome lattice

Motivated by dipolar-coupled artificial spin systems, we present a theoretical study of the classical $J_1-J_2-J_3$ Ising antiferromagnet on the kagome lattice. We establish the ground-state phase diagram of this model for $J_1 > |J_2|, |J_3|$ based on exact results for the ground-state energies. When all the couplings are antiferromagnetic, the model has three macroscopically degenerate ground-state phases, and using tensor networks, we can calculate the entropies of these phases and of their boundaries very accurately. In two cases, the entropy appears to be a fraction of that of the triangular lattice Ising antiferromagnet, and we provide analytical arguments to support this observation. We also notice that, surprisingly enough, the dipolar ground state is not a ground state of the truncated model, but of the model with smaller $J_3$ interactions, an indication of a very strong competition between low-energy states in this model.

Entropic Uncertainty for Two Coupled Dipole Spins Using Quantum Memory under the Dzyaloshinskii-Moriya Interaction.

In the thermodynamic equilibrium of dipolar-coupled spin systems under the influence of a Dzyaloshinskii–Moriya (D–M) interaction along the z-axis, the current study explores the quantum-memory-assisted entropic uncertainty relation (QMA-EUR), entropy mixedness and the concurrence two-spin entanglement. Quantum entanglement is reduced at increased temperature values, but inflation uncertainty and mixedness are enhanced. The considered quantum effects are stabilized to their stationary values at high temperatures. The two-spin entanglement is entirely repressed if the D–M interaction is disregarded, and the entropic uncertainty and entropy mixedness reach their maximum values for equal coupling rates. Rather than the concurrence, the entropy mixedness can be a proper indicator of the nature of the entropic uncertainty. The effect of model parameters (D–M coupling and dipole–dipole spin) on the quantum dynamic effects in thermal environment temperature is explored. The results reveal that the model parameters cause significant variations in the predicted QMA-EUR.

Continuous ground-state degeneracy of classical dipoles on regular lattices

Dipolar interactions are crucial in the modeling of many complex magnetic systems, such as the pyrochlores and artificial spin systems. Remarkably, many classical dipolar coupled spin systems exhibit a continuous ground-state degeneracy, which is unexpected as the Hamiltonian does not possess a continuous symmetry. In this paper, we explain, how such a finite point-symmetry leads to a continuous ground-state degeneracy of specific classical dipolar-coupled systems. This work, therefore, provides new insight into the theory of classical dipolar-coupled spin-systems and opens the way to understand more complex dipolar coupled systems.

Collective magnetism in an artificial 2D XY spin system

Two-dimensional magnetic systems with continuous spin degrees of freedom exhibit a rich spectrum of thermal behaviour due to the strong competition between fluctuations and correlations. When such systems incorporate coupling via the anisotropic dipolar interaction, a discrete symmetry emerges, which can be spontaneously broken leading to a low-temperature ordered phase. However, the experimental realisation of such two-dimensional spin systems in crystalline materials is difficult since the dipolar coupling is usually much weaker than the exchange interaction. Here we realise two-dimensional magnetostatically coupled XY spin systems with nanoscale thermally active magnetic discs placed on square lattices. Using low-energy muon-spin relaxation and soft X-ray scattering, we observe correlated dynamics at the critical temperature and the emergence of static long-range order at low temperatures, which is compatible with theoretical predictions for dipolar-coupled XY spin systems. Furthermore, by modifying the sample design, we demonstrate the possibility to tune the collective magnetic behaviour in thermally active artificial spin systems with continuous degrees of freedom.

Floquet–Magnus expansion for general N-coupled spins systems in magic-angle spinning nuclear magnetic resonance spectra

In this paper we present a theoretical perturbative approach for describing the NMR spectrum of strongly dipolar-coupled spin systems under fast magic-angle spinning. Our treatment is based on two approaches: the Floquet approach and the Floquet–Magnus expansion. The Floquet approach is well known in the NMR community as a perturbative approach to get analytical approximations. Numerical procedures are based on step-by-step numerical integration of the corresponding differential equations. The Floquet–Magnus expansion is a perturbative approach of the Floquet theory. Furthermore, we address the “γ-encoding” effect using the Floquet–Magnus expansion approach. We show that the average over “γ” angle can be performed for any Hamiltonian with γ symmetry.

Efficient simulation of unitary operators by combining two numerical algorithms: An NMR simulation of the mirror-inversion propagator of anXYspin chain

We report an experimental quantum simulation of unitary dynamics of an XY spin chain with pre-engineered couplings. Using this simulation, we demonstrate the mirror inversion of quantum states, proposed by Albanese et al. [Phys. Rev. Lett. 93, 230502 (2004)]. The experiment is performed with a 5-qubit dipolar coupled spin system using nuclear magnetic resonance techniques. To perform quantum simulation we make use of the recently proposed unitary operator decomposition algorithm of Ajoy et al. [Phys. Rev. A 85, 030303 (2012)] along with numerical pulse optimization techniques. Further, using mirror inversion, we demonstrate that entangled states can be transferred from one end of the chain to the other end. The simulations are implemented with high experimental fidelity, which implies that these kind of simulations may be possible in larger systems.

Entanglement under equilibrium establishing in spin systems subjected to radiofrequency field

We study the entanglement evolution in a dipolar-coupled spin system irradiated by a radiofrequency (RF) field in quasi-equilibrium state characterized by a two-temperature density matrix. Process of the establishment of equilibrium is in the equalization of these temperatures. The method of the nonequilibrium statistical operator in a rotating frame is used to describe the evolution of the spin system. It is shown that the equilibrium establishment has nonexponential character, and the time needed for this establishment depends strongly on the RF field strength. Particularly, the weak RF irradiation increases the lifetime of entanglement. Temporal and temperature dependencies of the concurrence of spin pairs are obtained and discussed. It is shown that application of RF field increases the time of the equilibrium establishment (up to order of 1,000 times) and lifetime of the existence of entangled states (up to order of 1,000 times). Thus, with the help of RF irradiation, we can govern the relaxation process and control entanglement in the system. The obtained results can be used for analysis of more complex spin systems because dipole---dipole interaction decreases proportionally to inverse third power of the distance between the spins, and influence of far way spins can be negligible.

ZERO FIELD ENTANGLEMENT IN DIPOLAR COUPLING SPIN SYSTEM AT NEGATIVE TEMPERATURE

A dipolar coupled spin system can achieve internal thermodynamic equilibrium states at negative absolute temperature. We study analytically and numerically the temperature dependence of the concurrence in a dipolar coupled spin-1/2 system in both nonzero and zero fields and show that, at negative temperatures, entangled states can exist even in zero magnetic field.

Current Driven Magnetic Damping in Dipolar-Coupled Spin System

Magnetic damping of the spin, the decay rate from the initial spin state to the final state, can be controlled by the spin transfer torque. Such an active control of damping has given birth to novel phenomena like the current-driven magnetization reversal and the steady spin precession. The spintronic devices based on such phenomena generally consist of two separate spin layers, i.e., free and pinned layers. Here we report that the dipolar coupling between the two layers, which has been considered to give only marginal effects on the current driven spin dynamics, actually has a serious impact on it. The damping of the coupled spin system was greatly enhanced at a specific field, which could not be understood if the spin dynamics in each layer was considered separately. Our results give a way to control the magnetic damping of the dipolar coupled spin system through the external magnetic field.

Triple resonance, triple-quantum NMR studies of dipolar coupled spin systems

Multiple quantum-single quantum correlation experiments are employed for spectral simplification and determination of the relative signs of the couplings. In this study, we have demonstrated the excitation of three nuclei, triple quantum coherences and discussed the information obtainable from such experiments. The experiments have been carried out on doubly labeled acetonitrile and fluoroacetonitrile aligned in liquid crystalline media. The experiment is advantageous in providing many spectral parameters from a single experiment. The coherence pathways involved in the pulse sequence are described using product operators.

Demixing of severely overlapped 1H NMR resonances and interpretation of anomalous intensity pattern of dipolar coupled A3 spins in a weakly aligning medium

We report a single 13C spin edited selective proton–proton correlation experiment to decipher overcrowded 13C coupled proton NMR spectra of weakly dipolar coupled spin systems. The experiment unravels the masked 13C satellites in proton spectrum and permits the measurement of one bond carbon–proton residual dipolar couplings in I 3S and for each diastereotopic proton in I 2S groups. It also provides all the possible homonuclear proton–proton residual couplings which are otherwise difficult to extract from the broad and featureless one dimensional 1H spectrum, in addition to enantiodifferentiation in a chiral molecule. Employment of heteronuclear ( 13C) decoupling in the evolution period results in complete demixing of overlapped signals from enantiomers. The observed anomalous intensity pattern in strongly dipolar coupled methyl protons in methyl selective correlation experiment has been interpreted using polarization operator formalism.

Dipolar-coupling-mediated total correlation spectroscopy in solid-state 13C NMR: Selection of individual 13C– 13C dipolar interactions

Herein is described a useful approach in solid-state NMR, for selecting homonuclear 13C– 13C spin pairs in a multiple- 13C homonuclear dipolar coupled spin system. This method builds upon the zero-quantum (ZQ) dipolar recoupling method introduced by Levitt and coworkers (Marin-Montesinos et al., 2006 [30]) by extending the originally introduced one-dimensional (1D) experiment into a two-dimensional (2D) method with selective irradiation scheme, while moving the 13C– 13C mixing scheme from the transverse to the longitudinal mode, together with a dramatic improvement in the proton decoupling efficiency. Selective spin-pair recoupling experiments incorporating Gaussian and cosine-modulated Gaussian pulses for inverting specific spins were performed, demonstrating the ability to detect informative, simplified/individualized, long-range 13C– 13C homonuclear dipolar coupling interactions more accurately by removing less informative, stronger, short-range 13C– 13C interactions from 2D correlation spectra. The capability of this new approach was demonstrated experimentally on uniformly 13C–labeled Glutamine and a tripeptide sample, GAL.

Effective one-body dynamics in multiple-quantum NMR experiments

A suitable NMR experiment in a one-dimensional dipolar coupled spin system allows one to reduce the natural many-body dynamics into effective one-body dynamics. We verify this in a polycrystalline sample of hydroxyapatite (HAp) by monitoring the excitation of NMR many-body superposition states: the multiple-quantum coherences. The observed effective one-dimensionality of HAp relies on the quasi-one-dimensional structure of the dipolar coupled network that, as we show here, is dynamically enhanced by the quantum Zeno effect. Decoherence is also probed through a Loschmidt echo experiment, where the time reversal is implemented on the double-quantum Hamiltonian, ${\mathcal{H}}_{DQ}\ensuremath{\propto}{I}_{i}^{+}{I}_{j}^{+}+{I}_{i}^{\ensuremath{-}}{I}_{j}^{\ensuremath{-}}$. We contrast the decoherence of adamantane, a standard three-dimensional system, with that of HAp. While the first shows an abrupt Fermi-type decay, HAp presents a smooth exponential law.

Spin State Selective Detection of Single Quantum Transitions Using Multiple Quantum Coherence: Simplifying the Analyses of Complex NMR Spectra

NMR spectra of molecules oriented in liquid-crystalline matrix provide information on the structure and orientation of the molecules. Thermotropic liquid crystals used as an orienting media result in the spectra of spins that are generally strongly coupled. The number of allowed transitions increases rapidly with the increase in the number of interacting spins. Furthermore, the number of single quantum transitions required for analysis is highly redundant. In the present study, we have demonstrated that it is possible to separate the subspectra of a homonuclear dipolar coupled spin system on the basis of the spin states of the coupled heteronuclei by multiple quantum (MQ)-single quantum (SQ) correlation experiments. This significantly reduces the number of redundant transitions, thereby simplifying the analysis of the complex spectrum. The methodology has been demonstrated on the doubly 13C labeled acetonitrile aligned in the liquid-crystal matrix and has been applied to analyze the complex spectrum of an oriented six spin system.

Selective coherence transfers in homonuclear dipolar coupled spin systems

Controlling the dynamics of a dipolar coupled spin system is critical to the development of solid-state spin-based quantum information processors. Such control remains challenging, as every spin is coupled to a large number of surrounding spins. Here we demonstrate that in an ensemble of spin pairs it is possible to decouple the weaker interactions (weak coupling ${\ensuremath{\omega}}_{D}^{w}$) between different pairs and extend the coherence lifetimes within the two-spin system from $19\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}11.1\phantom{\rule{0.3em}{0ex}}\mathrm{ms}$, a factor of 580. This is achieved without decoupling the stronger interaction (strong coupling ${\ensuremath{\omega}}_{D}^{S}$) between the two spins within a pair. An amplitude modulated rf field is applied on resonance with the Larmor frequency of the spins, with amplitude ${\ensuremath{\omega}}_{1}$, and frequency of the modulation matched to the strong coupling. The spin pairs appear isolated from each other in the regime where the rf power satisfies ${\ensuremath{\omega}}_{D}^{w}⪡{\ensuremath{\omega}}_{1}⪡{\ensuremath{\omega}}_{D}^{S}$.

Site-disordered glassy systems

A theory for phase transitions capable of describing competing interactions in dipolar coupled spin systems and clustered metal alloys is discussed. A variational solution is used to minimise the free energy in order to determine phase boundaries. Results show spin glass transitions and re-entrant behaviour in two and three dimensions.

Coherent Response Signals of Dipolar-coupled Spin Systems

Recently, it has been demonstrated that long pulses of a weak radio-frequency field can generate long-lived coherent NMR signals in bulk liquid crystals, which are systems of dipolar-coupled spins with unresolved conventional spectra. Here we describe this phenomenon in more detail and present results of new experimental investigations and computer simulations. It is shown that such response signals can also be excited when the initial spin state of a system corresponds to dipolar ordering. In addition, results of the application of weak pulses on liquid crystalline systems with heteronuclear dipolar couplings are presented, and the role of overlapping peaks is explored.

Site-disordered glassy systems

A theory for phase transitions capable of describing competing interactions in dipolar coupled spin systems and clustered metal alloys is discussed. A variational solution is used to minimise the free energy in order to determine phase boundaries. Results show spin glass transitions and re-entrant behaviour in two and three dimensions.

Pulse error compensating symmetric magic-echo trains

We present improved line-narrowing sequences for dipolar coupled spin systems, based on a train of magic-echoes which are compensated for the effects of finite pulse widths and utilize symmetry properties of supercycles. Sequences are introduced for spectroscopy and imaging by proper choice of a phase alternating scheme. Using a 16 pulse time-suspension magic-echo cycle, the highest level of line-narrowing achieved was 2.7 Hz for the [100] direction of a single crystal of calcium fluoride, a reduction in linewidth by 4 orders of magnitude.