Two-spin System Research Articles

Hyperfine-Enhanced Gyroscope Based on Solid-State Spins.

Solid-state platforms based on electronuclear spin systems are attractive candidates for rotation sensing due to their excellent sensitivity, stability, and compact size, compatible with industrial applications. Conventional spin-based gyroscopes measure the accumulated phase of a nuclear spin superposition state to extract the rotation rate and thus suffer from spin dephasing. Here, we propose a gyroscope protocol based on a two-spin system that includes a spin intrinsically tied to the host material, while the other spin is isolated. The rotation rate is then extracted by measuring the relative rotation angle between the two spins starting from their population states, robust against spin dephasing. In particular, the relative rotation rate between the two spins can be enhanced by their hyperfine coupling by more than an order of magnitude, further boosting the achievable sensitivity. The ultimate sensitivity of the gyroscope is limited by the lifetime of the spin system and compatible with a broad dynamic range, even in the presence of magnetic noise or control errors due to initialization and qubit manipulations. Our result enables precise measurement of slow rotations and exploration of fundamental physics.

Lindblad Relaxation of Multiple Quantum NMR Coherence in Two-Spin Systems

Lindblad Relaxation of Multiple Quantum NMR Coherence in Two-Spin Systems

Selective Transition Enhancement in a g-Engineered Diradical.

A diradical with engineered g-asymmetry was synthesized by grafting a nitroxide radical onto the [Y(Pc)2]⋅ radical platform. Various spectroscopic techniques and computational studies revealed that the electronic structures of the two spin systems remained minimally affected within the diradical system. Fluid-solution Electron Paramagnetic Resonance (EPR) experiments revealed a weak exchange coupling with |J| ~ 0.014 cm-1, subsequently rationalized by CAS-SCF calculations. Frozen solution continuous-wave (CW) EPR experiments showed a complicated and power-dependent spectrum that eluded analysis using the point-dipole model. Pulse EPR manipulations with varying microwave powers, or under varying magnetic fields, demonstrated that different resonances could be selectively enhanced or suppressed, based on their different tipping angles. In particular, Field-Swept Echo-Detected (FSED) spectra revealed absorptions of MW power-dependent intensities, while Field-Swept Spin Nutation (FSSN) experiments revealed two distinct Rabi frequencies. This study introduces a methodology to synthesize and characterize g-asymmetric two-spin systems, of interest in the implementation of spin-based CNOT gates.

Dissipative dynamics of multiple-quantum NMR coherences in two-spin systems

Multiple-quantum (MQ) NMR experiments were performed at a special orientation of a hambergite (Be2BO3OH) single crystal, which consists of alternating zigzag proton chains. At the chosen orientation, one of the dipolar coupling constants in the chain becomes zero and the system becomes a set of well-isolated dipolar coupled spin pairs. The relaxation of the spin pairs in the MQ NMR experiment was studied on the basis of the Lindblad equation. Fermi’s golden rule was used to investigate the relaxation mechanism. The agreement of the calculated relaxation time with the experimental value (125 μs) suggests that the dipole–dipole interactions with protons surrounding the pair are responsible for the relaxation of MQ coherences.

Anisotropy-assisted thermodynamic advantage of a local-spin quantum thermal machine.

We study quantum Otto thermal machines with a two-spin working system coupled by anisotropic interaction. Depending on the choice of different parameters, the quantum Otto cycle can function as different thermal machines, including a heat engine, refrigerator, accelerator, and heater. We aim to investigate how the anisotropy plays a fundamental role in the performance of the quantum Otto engine (QOE) operating in different timescales. We find that while the engine's efficiency increases with the increase in anisotropy for the quasistatic operation, quantum internal friction and incomplete thermalization degrade the performance in a finite-time cycle. Further, we study the quantum heat engine (QHE) with one of the spins (local spin) as the working system. We show that the efficiency of such an engine can surpass the standard quantum Otto limit, along with maximum power, thanks to the anisotropy. This can be attributed to quantum interference effects. We demonstrate that the enhanced performance of a local-spin QHE originates from the same interference effects, as in a measurement-based QOE for their finite-time operation.

Dynamics of quantum coherence and nonlocality of a two-spin system in the chemical compass.

In this paper a system consisting of two electron spins has been prepared initially in a singlet state using the chemical compass model is considered. It is assumed that each electron spin interacts symmetrically and/or asymmetrically with its respective private nuclear environment in the presence of an external magnetic field. We discussed the effect of the interaction parameters and the external magnetic field on some quantifiers of quantum correlations as entanglement, coherence, Bell inequality, as well as the steerability inequality. It is shown that within a certain range of external magnetic fields, the quantum coherence and entanglement behave similarly. The Bell and the steerable inequalities predicted a similar behavior for symmetric and asymmetric interactions. Moreover, as one increases the external magnetic field, the lower bounds of both inequalities have improved. The usefulness of using the spin state as quantum channel to teleport a two-qubit system has examined where the Bell inequality could be above its classical bounds by controlling the interaction parameters. It is shown that by tuning the coupling parameters the fidelity of the teleported state exceeds the classical bounds, as well as the long-lived stationary fidelity could be achieved during the interaction time.

Resonant tunneling and quantum interference of a two-spin system in silicon tunnel FETs

We investigated the resonant tunneling of a two-spin system through the double quantum dots in Al–N-implanted silicon tunnel FETs (TFETs) by electrical-transport measurements and Landau–Zener–Stückelberg–Majorana interferometry with and without magnetic fields. Our experimental results revealed the coexistence of spin-conserving and spin-flip tunneling channels in the two-spin system in non-zero magnetic fields. Additionally, we obtained the spin-conserving/spin-flip tunneling rates of the two-spin system through the double quantum dots in the TFET. These findings will improve our understanding of the two-spin system in silicon TFET qubits and may facilitate the coherent control of quantum states through all-electric manipulation.

Comparative study of quantum Otto and Carnot engines powered by a spin working substance.

Quantum Otto and Carnot engines have recently been receiving attention due to their ability to achieve high efficiencies and powers based on the laws of quantum mechanics. This paper discusses the theory, progress, and possible applications of quantum Otto and Carnot engines, such as energy production, cooling, and nanoscale technologies. In particular, we investigate a two-spin Heisenberg system that works as a substance in quantum Otto and Carnot cycles while exposed to an external magnetic field with both Dzyaloshinsky-Moriya and dipole-dipole interactions. The four stages of engine cycles are subject to analysis with respect to the heat exchanges that occur between the hot and cold reservoirs, alongside the work done during each stage. The operating conditions of the heat engine, refrigerator, thermal accelerator, and heater are all achieved. Moreover, our results demonstrate that the laws of thermodynamics are strictly upheld and the Carnot cycle produces more useful work than that of the Otto cycle.

Selective filtration of NMR signals arising from weakly- and strongly-coupled spin systems

Nuclear magnetic resonance (NMR) spectroscopy is a powerful technique for analyzing chemical and biological systems. However, in complex solutions with similar molecular components, NMR signals can overlap, making it challenging to distinguish and quantify individual species. In this paper, we introduce new spectral editing sequences that exploit the differences in nuclear spin interactions (J-couplings) between weakly- and strongly-coupled two-spin systems. These sequences selectively attenuate or nullify undesired spin magnetization while they preserve the desired signals, resulting in simplified NMR spectra and potentially facilitating single-species imaging applications. We demonstrate the effectiveness of our approach using a 31P spectral filtration method on a model system of nicotinamide dinucleotide (NAD), which exists in oxidized (NAD+) and reduced (NADH) forms. The presented sequences are robust to field inhomogeneity, do not require additional sub-spectra, and retain a significant portion of the original signal.

A fundamental lower bound of the cost for bit reset

A general measurement process, involving a unitary operation on the composite system and a projective measurement on one of the subsystems, is proposed. The average entropy change of the composite system due to the measurement induced irreversibility is evaluated and found to be positive by applying the quantum-trajectory approach. This leads to an inequality associated with the fundamental lower bound on the thermodynamic energy cost for information erasure. We show that the lower bound is determined by the cost for erasing information and the relative entropy. A two-spin system is adopted to verify the validity of the findings. The results provide a deeper understanding of the performance of measurement and control systems.

Thermal Uhlmann phase in a locally driven two-spin system

Thermal Uhlmann phase in a locally driven two-spin system

Measurement-based quantum Otto engine with a two-spin system coupled by anisotropic interaction: Enhanced efficiency at finite times.

We have studied the performance of a measurement-based quantum Otto engine (QOE) in a working system of two spins coupled by Heisenberg anisotropic interaction. A nonselective quantum measurement fuels the engine. We have calculated thermodynamic quantities of the cycle in terms of the transition probabilities between the instantaneous energy eigenstates, and also between the instantaneous energy eigenstates and the basis states of the measurement, when the unitary stages of the cycle operate for a finite time τ. The efficiency attains a large value in the limit of τ→0 and then gradually reaches the adiabatic value in a long-time limit τ→∞. For finite values of τ and for anisotropic interaction, an oscillatory behavior of the efficiency of the engine is observed. This oscillation can be interpreted in terms of interference between the relevant transition amplitudes in the unitary stages of the engine cycle. Therefore, for a suitable choice of timing of the unitary processes in the short time regime, the engine can have a higher work output and less heat absorption, such that it works more efficiently than a quasistatic engine. In the case of an always-on heat bath, in a very short time, the bath has a negligible effect on its performance.

Dynamic nuclear polarization with trityl radicals

Despite the expanding applications of dynamic nuclear polarization (DNP) to problems in biological and materials science, there remain unresolved questions concerning DNP mechanisms. In this paper, we investigate the Zeeman DNP frequency profiles obtained with trityl radicals, OX063 and its partially deuterated analog OX071, in two commonly used glassing matrices based on glycerol and dimethyl sulfoxide (DMSO). When microwave irradiation is applied in the neighborhood of the narrow EPR transition, we observe a dispersive shape in the 1H Zeeman field and the effects are larger in DMSO than in glycerol. With the help of direct DNP observations on 13C and 2H nuclei, we investigate the origin of this dispersive field profile. In particular, we observe a weak nuclear Overhauser effect between 1H and 13C in the sample, which, when irradiating at the positive 1H solid effect (SE) condition, results in a negative enhancement of 13C spins. This observation is not consistent with thermal mixing (TM) being the mechanism responsible for the dispersive shape in the 1H DNP Zeeman frequency profile. Instead, we propose a new mechanism, resonant mixing, involving mixing of nuclear and electron spin states in a simple two-spin system without invoking electron–electron dipolar interactions.

Correction to: The Intrinsic Decoherence Effects on Nonclassical Correlations in a Dipole-Dipole Two-Spin System with Dzyaloshinsky-Moriya Interaction

Correction to: The Intrinsic Decoherence Effects on Nonclassical Correlations in a Dipole-Dipole Two-Spin System with Dzyaloshinsky-Moriya Interaction

An analytical treatment of electron spectral saturation for dynamic nuclear polarization NMR of rotating solids.

Saturation of electron magnetization by microwave irradiation under magic-angle spinning (MAS) is studied theoretically. The saturation is essential for dynamic nuclear polarization (DNP) enhancement of nuclear magnetic resonance signals. For a spin with a large g-anisotropy and a long T1 relative to the rotor period, the sample rotation distributes saturation to the whole powder sample spectrum. Analytical expressions for the saturation and frequency profiles are obtained. For a pair of coupled electrons such as those in bis-nitroxides, which are commonly used for MAS DNP, an el-er model (where el and er stand for electrons on the left and the right, respectively, in their spectral positions) is introduced to simplify the analysis of a coupled two-spin system under MAS. For such a system, strong electron couplings exchange magnetization during dipolar/J rotor events when the two electron frequencies cross each other. The exchange is equivalent to a swap of the el and er electrons. This allows for the treatment of a coupled spin pair as two independent spins such that an analytical solution can be obtained for the steady-state magnetization and the difference between the two electrons. The theoretical study with its analytical result provides a simple physical picture of electron saturation under MAS and of how radical properties and experimental parameters affect cross-effect DNP. The effects of depolarization and the extension to more coupled electron spins are also discussed using this approach.

The Intrinsic Decoherence Effects on Nonclassical Correlations in a Dipole-Dipole Two-Spin System with Dzyaloshinsky-Moriya Interaction

The Intrinsic Decoherence Effects on Nonclassical Correlations in a Dipole-Dipole Two-Spin System with Dzyaloshinsky-Moriya Interaction

Visualization of dynamics in coupled multi-spin systems.

Since the dawn of quantum mechanics, ways to visualize spins and their interactions have attracted the attention of researchers and philosophers of science. In this work we present a generalized measurement-based 3D-visualization approach for describing dynamics in strongly coupled spin ensembles. The approach brings together angular momentum probability surfaces (AMPS), Husimi functions, and DROPS (discrete representations of operators for spin systems) and finds particular utility when the total angular momentum basis is used for describing Hamiltonians. We show that, depending on the choice of a generalized measurement operator, the plotted surfaces either represent probabilities of finding the maximal projection of an angular momentum along any direction in space or represent measurable coherences between the states with different total angular momenta. Such effects are difficult to grasp by looking at (time-dependent) numerical values of density-matrix elements. The approach is complete in a sense that there is one-to-one correspondence between the plotted surfaces and the density matrix. Three examples of nuclear spin dynamics in two-spin systems are visualized: (i)a zero- to ultralow-field (ZULF) nuclear magnetic resonance (NMR) experiment in the presence of a magnetic field applied perpendicularly to the sensitive axis of the detector, (ii)interplay between chemical exchange and spin dynamics during high-field signal amplification by reversible exchange (SABRE), and (iii)a high-field spin-lock-induced crossing (SLIC) sequence, with the initial state being the singlet state between two spins. The presented visualization technique facilitates intuitive understanding of spin dynamics during complex experiments as exemplified here by the considered cases. Temporal sequences ("the movies") of such surfaces show phenomena like interconversion of spin order between the coupled spins and are particularly relevant in ZULF NMR.

Intrinsic decoherence effects on nonclassical correlations in a symmetric spin–orbit model

Nonclassical correlations dynamics of local quantum Fisher information, trace-norm measurement-induced nonlocality, and log-negativity are investigated in a symmetric spin–orbit model. This model is described by a Heisenberg XYZ two-spin system exposed to the magnetic field and Kaplan–Shekhtman–Entin-Wohlman–Aharony (KSEA) interaction under the intrinsic decoherence effects. To evaluate the resourcefulness of this model for the generation and preservation of quantum correlations, we consider two qubits that are initially prepared in two different states, namely uncorrelated and maximally correlated states. The magnetic field is discovered to be effective at generating and preserving nonclassical correlations. Besides, we find that the KSEA interaction can alter the generation, preservation, and revival features of nonclassical correlations in the two-qubit system. However, the bipartite nonclassical correlations become extremely fragile when intrinsic decoherence effects appear.

Robust thermal correlations induced by spin–orbit interactions

In this work, we demonstrate that the thermal nonclassical correlations can enhance and become more stable under the magnetic field and second-order spin–orbit interaction effect. Also, we show that the local quantum uncertainty measure can reveal purely quantum correlations beyond other quantifiers of correlations. Our analytical model describes a Heisenberg XYZ two-spin system with an inhomogeneous magnetic field and spin–orbit interaction. A special emphasis is devoted to local quantum uncertainty, concurrence, and Bell-nonlocality measures to investigate the correlations of the bipartite-system at the equilibrium temperature. Our results indicate that temperature, magnetic field, and magnetic field inhomogeneity with DMI and Kaplan–Shekhtman–Entin-Wohlman–Aharony (KSEA) exchanges all play a role in determining the degree of correlation between the quantum spins to some extent. The KSEA interaction greatly enhances the quantum correlation in the system whereas quantum quantifiers are more stable under the influence of the external magnetic field, especially when inhomogeneous and homogeneous magnetic field are near to zero. Furthermore, these findings suggest that the thermal LQU captures a stronger quantum correlation than the Bell-nonlocality and entanglement measures.

Quantum state preparation by adiabatic evolution with custom gates

Quantum state preparation by adiabatic evolution is currently rendered ineffective by the long implementation times of the underlying quantum circuits, comparable to the decoherence time of present and near-term quantum devices. These implementation times can be significantly reduced by realizing these circuits with custom gates. Using classical computing, we model the output of a realistic two-qubit processor implementing the adiabatic evolution of a two-spin system by means of custom gates. This modeled output is then compared with the results of quantum simulations solving the same problem on IBM Quantum (IBMQ) systems. When used to emulate the behavior of the IBMQ quantum circuit, our realistic model yields state fidelities ranging from 65% to 85%, similar to the actual performance of a diverse set of IBMQ devices. When we reduced the implementation time by using custom gates, however, the loss of fidelity was reduced by at least a factor of 4, allowing us to accurately extract the energy of the target state. This improvement is enough to render adiabatic evolution useful for quantum state preparation for small systems or as a preconditioner for other state preparation methods.