Spin Pairs Research Articles

Non-local spin entanglement in a fermionic chain

An effective two-spin density matrix (TSDM) for a pair of spin-$1/2$ degree of freedom, residing at a distance of $R$ in a spinful Fermi sea, can be obtained from the two-electron density matrix following the framework prescribed in Phys. Rev. A 69, 054305 (2004). We note that the single spin density matrix (SSDM) obtained from this TSDM for generic spin-degenerate systems of free fermions is always pinned to the maximally mixed state $i.e.$ $(1/2) \ \mathbb{I}$, independent of the distance $R$ while the TSDM confirms to the form for the set of maximally entangled mixed state (the so called "X-state") at finite $R$. The X-state reduces to a pure state (a singlet) in the $R\rightarrow 0$ limit while it saturates to an X-state with largest allowed value of von-Neumann entropy of $2 \ln2$ as $R \rightarrow \infty$ independent of the value of chemical potential. However, once an external magnetic field is applied to lift the spin-degeneracy, we find that the von-Neumann entropy of SSDM becomes a function of the distance $R$ between the two spins. We also show that the von-Neumann entropy of TSDM in the $R\rightarrow \infty$ limit becomes a function of the chemical potential and it saturate to $2 \ln2$ only when the band in completely filled unlike the spin-degenerate case. Finally we extend our study to include spin-orbit coupling and show that it does effect these asymptotic results. Our findings are in sharp contrast with previous works which were based on continuum models owing to physics which stem from the lattice model.

Magnetic-Field Dependence of LC-Photo-CIDNP in the Presence of Target Molecules Carrying a Quasi-Isolated Spin Pair.

NMR spectroscopy is well known for its superb resolution, especially at high applied magnetic field. However, the sensitivity of this technique is very low. Liquid-state low-concentration photo-chemically-induced dynamic nuclear polarization (LC-photo-CIDNP) is a promising emerging methodology capable of enhancing NMR sensitivity in solution. LC-photo-CIDNP works well on solvent-exposed Trp and Tyr residues, either in isolation or within proteins. This study explores the magnetic-field dependence of the LC-photo-CIDNP experienced by two tryptophan isotopologs in solution upon in situ LED-mediated optical irradiation. Out of the two uniformly 13C,15N-labeled Trp (Trp-U-13C,15N) and Trp-α-13C-β,β,2,4,5,6,7-d7 species employed here, only the latter bears a quasi-isolated 1Hα-13Cα spin pair. Computer simulations of the predicted polarization due to geminate recombination of both species display a roughly bell-shaped field dependence. However, while Trp-U-13C,15N is predicted to show a maximum at ca. 500 MHz (11.7 T) and a fairly weak field dependence, Trp-α-13C-β,β,2,4,5,6,7-d7 is expected to display a much sharper field dependence accompanied by a dramatic polarization increase at lower field (ca. 200 MHz, 4.7 T). Experimental LC-photo-CIDNP studies on both Trp isotopologs at 1μM concentration, performed at selected fields, are consistent with the theoretical predictions. In summary, this study highlights the prominent field-dependence of LC-photo-CIDNP enhancements () experienced by Trp isotopologs bearing a quasi-isolated spin pair.

Nanosheet fabrication from magnon thermal conductivity cuprates for the advanced thermal management

Spin-chain–spin-ladder cuprates, such as La5Ca9Cu24O41, have notable electronic and thermal properties because of their unique electron spin arrangement. Among them, magnon thermal conductivity, which originates from the excitation of paired electron spins, is promising for the advanced thermal management applications that enable dynamic control of heat flow. This is because of its high, anisotropic thermal conductivity at room temperature and its dynamic controllability. In this study, we report nanosheet fabrications from polycrystalline La5Ca9Cu24O41 to enhance the control width. We obtained that the nanosheets with a thickness of about 3 nm are obtained via immersion of the polycrystals in a NaOH aqueous solution. We propose the exfoliation model based on the chemical reaction between the (La/Ca)2Cu2O3 subsystem and NaOH solution. The nanosheet fabrications can also lead to new research development on spin-ladder system and other strongly correlated cuprates.

Spin Entropy.

Two types of randomness are associated with a mixed quantum state: the uncertainty in the probability coefficients of the constituent pure states and the uncertainty in the value of each observable captured by the Born’s rule probabilities. Entropy is a quantification of randomness, and we propose a spin-entropy for the observables of spin pure states based on the phase space of a spin as described by the geometric quantization method, and we also expand it to mixed quantum states. This proposed entropy overcomes the limitations of previously-proposed entropies such as von Neumann entropy which only quantifies the randomness of specifying the quantum state. As an example of a limitation, previously-proposed entropies are higher for Bell entangled spin states than for disentangled spin states, even though the spin observables are less constrained for a disentangled pair of spins than for an entangled pair. The proposed spin-entropy accurately quantifies the randomness of a quantum state, it never reaches zero value, and it is lower for entangled states than for disentangled states.

Non-iterative method for constructing valence antibonding molecular orbitals and a molecule-adapted minimum basis.

While bonding molecular orbitals exhibit constructive interference relative to atomic orbitals, antibonding orbitals show destructive interference. When full localization of occupied orbitals into bonds is possible, bonding and antibonding orbitals exist in 1:1 correspondence with each other. Antibonding orbitals play an important role in chemistry because they are frontier orbitals that determine orbital interactions, as well as much of the response of the bonding orbital to perturbations. In this work, we present an efficient method to construct antibonding orbitals by finding the orbital that yields the maximum opposite spin pair correlation amplitude in second order perturbation theory (AB2) and compare it with other techniques with increasing basis set size. We conclude the AB2 antibonding orbitals are a more robust alternative to the Sano orbitals as initial guesses for valence bond calculations due to having a useful basis set limit. The AB2 orbitals are also useful for efficiently constructing an active space, and they work as good initial guesses for valence excited states. In addition, when combined with the localized occupied orbitals, and relocalized, the result is a set of molecule-adapted minimal basis functions that is built without any reference to atomic orbitals of the free atom. As examples, they are applied to the population analysis of halogenated methane derivatives, H-Be-Cl, and SF6, where they show some advantages relative to good alternative methods.

Electron correlations due to pair spin–orbit interaction in 2D electron systems

We show that the pair spin–orbit interaction (PSOI) created by the Coulomb fields of interacting electrons leads to the appearance of an unconventional correlated electronic state in two-dimensional materials with the large Rashba effect. The effect manifests itself at sufficiently strong PSOI as a sharp peak in the structure factor, indicating a tendency to form a striped structure with a spatial scale determined by the competition between the Coulomb repulsion and the PSOI-induced attraction of electrons. Above the critical value of PSOI, the system becomes unstable with respect to the charge density fluctuations on this scale.

Information scrambling and redistribution of quantum correlations through dynamical evolution in spin chains

We investigate the propagation of local bipartite quantum correlations, along with the tripartite mutual information to characterize the information scrambling through dynamical evolution of spin chains. Starting from an initial state with the first pair of spins in a Bell state, we study how quantum correlations spread to other parts of the system, using different representative spin Hamiltonians, viz. the Heisenberg Model, a spin-conserving model, the transverse-field XY model, a non-conserving but integrable model, and the kicked Harper model, a spin conserving but nonintegrable model. We show that the local correlations spread consistently in the case of spin-conserving dynamics in both integrable and nonintegrable cases, with a strictly nonnegative tripartite mutual information. In contrast, in the case of non-conserving dynamics, tripartite mutual information is negative and local pair correlations do not propagate.

Sign switching of superexchange mediated by a few electrons in a nonuniform magnetic field

Long-range interaction between distant spins is an important building block for the realization of a large quantum-dot network in which couplings between pairs of spins can be selectively addressed. Recent experiments on the coherent oscillation of logical states between remote spins facilitated by intermediate electron states were the first step for large-scale quantum information processing. Reaching this ultimate goal requires extensive studies on the superexchange interaction in different quantum-dot spatial arrangements and electron configurations. Here, we consider a linear triple quantum dot with two antiparallel spins in the outer dots forming the logical states while varying numbers of electrons in the middle dot form a mediator, which facilitates the superexchange interaction. We show that the superexchange is enhanced when the number of mediating electrons increases. In addition, we show that forming a four-electron triplet in the mediator dot further enhances the superexchange strength. Our work can be a guide to scale up the quantum-dot array with controllable and dense connectivity.

Quantum nonlocality and topological quantum phase transitions in the extended Ising chain

We use two-site quantum nonlocality to identify the topological quantum phase transitions (TQPTs) of the extended Ising model driven by varying system parameters. We investigate how the system parameters, including the anisotropies of the nearest-neighbor and the next-nearest-neighbor spin pairs, the transverse magnetic field, and the three-spin interaction, affect the quantum nonlocality. We show that the nonlocality cannot mark any TQPTs while its first derivative can perfectly characterize the TQPTs. By making the influences of the thermal fluctuations and the site distance of spin pairs on the critical behavior of the TQPTs analysis, we show that the sufficiently low temperature has a slight impact on the features of nonlocality and its first derivative while the site distance of spin pairs can significantly alter the properties of nonlocality and its first derivative. We further present the energy spectra and the trajectories of the winding vectors of the model to demonstrate that the quantum nonlocality can be employed to successfully signalize the TQPTs.

Collective effects on the performance and stability of quantum heat engines.

Recent predictions for quantum-mechanical enhancements in the operation of small heat engines have raised renewed interest in their study both from a fundamental perspective and in view of applications. One essential question is whether collective effects may help to carry enhancements over larger scales, when increasing the number of systems composing the working substance of the engine. Such enhancements may consider not only power and efficiency, that is, its performance, but, additionally, its constancy, that is, the stability of the engine with respect to unavoidable environmental fluctuations. We explore this issue by introducing a many-body quantum heat engine model composed by spin pairs working in continuous operation. We study how power, efficiency, and constancy scale with the number of spins composing the engine and introduce a well-defined macroscopic limit where analytical expressions are obtained. Our results predict power enhancements, in both finite-size and macroscopic cases, for a broad range of system parameters and temperatures, without compromising the engine efficiency, accompanied by coherence-enhanced constancy for finite sizes. We discuss these quantities in connection to thermodynamic uncertainty relations.

Selective Excitation of Long-Lived Nuclear Spin States.

Nuclear magnetization storage, once limited by longitudinal and transverse relaxation lifetimes, T1 and T2, can be prolonged by symmetry-adapted nuclear spin order, i.e. long-lived states (LLS) and long-lived coherences (LLC), which have significantly extended relaxation time constants compared to T1 and T2, respectively. Excitation and/or detection of LLS currently involves pulses covering wide frequency ranges in high-magnetic-field spectrometers. This leads to excitation of unwanted signals that may overlap and interfere with the resonances of interest. Herein, we present a new pulse sequence that converts longitudinal magnetization to LLS and further to detectable magnetization using only frequency-selective pulses. We demonstrate the suitability of this sequence for different J-coupled spin pairs in dipeptide AlaGly and protein Ubiquitin. The newly developed method is adapted for investigations of LLS in complex systems such as proteins and mixtures of metabolites where selected molecular groups are to be investigated separately.

Revisiting dipolar relaxation of a homonuclear spin pair in the presence of a radio frequency field: A tutorial

NMR studies exploit spin relaxation in a multitude of different ways, providing information on molecular structure and dynamics. Calculating the relaxation rates of NMR active nuclei in multi-spin systems is often a prerequisite for the proper analysis of experimental data. For many researchers the calculations appear complex, often involving different basis sets or expressions describing relaxation in different frames. In this tutorial paper we derive expressions for dipolar relaxation of an I-S two spin spin-system in the presence of a B1 radio frequency field, where spins I and S can be either like or unlike. We consider two different approaches for the derivation of relaxation elements that have been used in the literature, including one where a series of transformations are carried out to the interaction representation of the effective field, comprising B1 and Zeeman components. A second procedure is based on the well-known Solomon equations. We show that both approaches lead to identical results, in the process presenting a pedagogical description of relaxation theory.

The discrete Chebyshev–Meckler–Mermin–Schwarz polynomials and spin algebra

The polynomials discovered by Chebyshev and subsequently related to spin transition probabilities by Meckler [Meckler, Phys. Rev. 111, 1447 (1958)] and Mermin and Schwarz [Found. Phys. 12, 101 (1982)] are studied, and their application to phase space representations of spin states and operators is examined. In particular, a formula relating the end-point value of the polynomials to scale factors relating different phase space representations of spherical harmonic operators is found. This formula is applied to illustrative calculations of Wigner functions for a single spin and the singlet state of a pair of spins.

Combining heteronuclear correlation NMR with spin-diffusion to detect relayed Cl–H–H and N–H–H proximities in molecular solids

Analysis of short-to-intermediate range intermolecular interactions offers a great way of characterizing the solid-state organization of small molecules and materials. This can be achieved by two-dimensional (2D) homo- and heteronuclear correlation NMR spectroscopy, for example, by carrying out experiments at high magnetic fields in conjunction with fast magic-angle spinning (MAS) techniques. But, detecting 2D peaks for heteronuclear dipolar coupled spin pairs separated by greater than 3 Å is not always straightforward, particularly when low-gamma quadrupolar nuclei are involved. Here, we present a 2D correlation NMR experiment that combines the advantages of heteronuclear-multiple quantum coherence (HMQC) and proton-based spin-diffusion (SD) pulse sequences using radio-frequency-driven-recouping (RFDR) to probe inter and intramolecular 1H-X (X = 14N, 35Cl) interactions. This experiment can be used to acquire 2D 1H{X}-HMQC filtered 1H–1H correlation as well as 2D 1H-X HMQC spectra. Powder forms of dopamine·HCl and l-histidine·HCl·H2O are characterized at high fields (21.1 T and 18.8 T) with fast MAS (60 kHz) using the 2D HMQC-SD-RFDR approach. Solid-state NMR results are complemented with NMR crystallography analyses using the gauge-including projector augmented wave (GIPAW) approach. For histidine·HCl·H2O, 2D peaks associated with 14N–1H–1H and 35Cl–1H–1H distances of up to 4.4 and 3.9 Å have been detected. This is further corroborated by the observation of 2D peaks corresponding to 14N–1H–1H and 35Cl–1H–1H distances of up to 4.2 and 3.7 Å in dopamine·HCl, indicating the suitability of the HMQC-SD-RFDR experiments for detecting medium-range proximities in molecular solids.

Absence of spin susceptibility decrease in a bulk organic superconductor with triangular lattice

The study of non-$s$-wave unconventional superconductivities in strongly correlated electron systems has been a central issue in condensed matter physics for more than 30 years. In such unconventional superconductivities, $d$-wave Cooper pairing with antiparallel spins has been often observed in various quasi-two-dimensional (quasi-2D) bulk systems. Interestingly, many theories predicted that the triangular lattice causes the $d$-wave pairing to be unstable and may lead to more exotic pairing such as parallel spin (spin-triplet) pairing. Here we focus on a bulk organic triangular-lattice system in which superconductivity emerges near a nonmagnetic Mott insulating phase. We demonstrate, by using low-power nuclear magnetic resonance (NMR) measurements, that the spin susceptibility of the superconducting state retains the normal state value even deep in the superconducting state. This result indicates the possibility that the material exhibits spin-triplet superconductivity. Our finding will bring insights also into understanding the 2D materials with triangular moir\'e superlattices that are considered also to show unconventional superconductivities near Mott-like insulating states.

Robust quantum entanglement and teleportation in the tetrapartite spin-1/2 square clusters: Theoretical study on the effect of a cyclic four-spin exchange

The whole entanglement measure so-called geometric Π4 average of tangles and bipartite entanglement of the antiferromagnetic spin-1/2 XXX Heisenberg model on a tetranuclear square cluster with cyclic four-spin interaction are rigorously examined by the help of thermal negativities. The model comprises two nearest-neighbor exchange couplings J1 and J2 such that J1≫J2. When the cyclic four-spin exchange is zero, the maximum value of whole entanglement Π4 is achieved at low enough temperatures and relatively high magnetic fields (B≈J1). Also, maximum bipartite entanglement between pair spins with exchange coupling J1 is achievable at high temperature and high magnetic field. This quantity remains alive for sufficiently high temperature and high magnetic field values comparable with the relevant exchange coupling J1. A nonzero value of the cyclic four-spin exchange notably enhances the degree of the whole entanglement, while it weakens the bipartite entanglement degree. We demonstrate that the whole entanglement reaches an unconventional minimum at a special parameter region of cyclic four-spin exchange almost ten order of magnitude smaller than J1, where the system is in a quantum antiferromagnetic state. The real complex [Cu4L4(H2O)4](ClO4)4 as a strong antiferromagnetic tetranuclear square compound provides us an experimental representative to estimate the strength of the whole and bipartite entanglements at high enough temperature. It is demonstrated that the entanglement negativities of this complex are yet depend on the considered cyclic four-spin interaction even though its magnitude is significantly smaller than J1. We realize that the possibility of quantum teleportation through a couple of discrete Cu4II complexes would solely happen for the magnetic fields lower than a critical value. It is also demonstrated that enhancing the cyclic four-spin exchange results in diminishing the average fidelity. Moreover, we conclude that the quantum Fisher information investigated for the pair of spins with exchange interaction J1 reaches its minimum close to the critical magnetic field at which a ground-state phase transition occurs from highly entangled state to separable one.

Prediction of 1H Singlet Relaxation via Intermolecular Dipolar Couplings Using the Molecular Dynamics Method.

Dissolution dynamic nuclear polarization has been applied in various fields, including chemistry, biology, and medical science. To expand the scope of these applications, the nuclear singlet state, which is decoherence-free against dipolar relaxation between spin pairs, has been studied experimentally, theoretically, and numerically. The singlet state composed of proton spins is used in several applications, such as enhanced polarization preservation, molecular tagging to probe slow dynamic processes, and detection of ligand-protein complexes. In this study, we predict the lifetimes of the nuclear spin states composed of proton spin pairs using the molecular dynamics method and quantum chemistry simulations. We consider intramolecular dipolar, intermolecular dipolar between solvent and solute, chemical shift anisotropy, and spin-rotation interactions. In particular, the relaxation rate of intermolecular dipolar interactions is calculated using the molecular dynamics method for various solvents. The calculated values and the experimental values are of the same order of magnitude. Our program would provide insight into the molecular design of several NMR applications and would be helpful in predicting the nuclear spin relaxation time of synthetic molecules in advance.

Freezing of the Lattice in the Kagome Lattice Heisenberg Antiferromagnet Zn-Barlowite ZnCu_{3}(OD)_{6}FBr.

We use ^{79}Br nuclear quadrupole resonance (NQR) to demonstrate that ultraslow lattice dynamics set in below the temperature scale set by the Cu-Cu superexchange interaction J (≃160 K) in the kagome lattice Heisenberg antiferromagnet Zn-barlowite. The lattice completely freezes below 50K, and ^{79}Br NQR line shapes become twice broader due to increased lattice distortions. Moreover, the frozen lattice exhibits an oscillatory component in the transverse spin echo decay, a typical signature of pairing of nuclear spins by indirect nuclear spin-spin interaction. This indicates that some Br sites form structural dimers via a pair of kagome Cu sites prior to the gradual emergence of spin singlets below ∼30 K. Our findings underscore the significant roles played by subtle structural distortions in determining the nature of the disordered magnetic ground state of the kagome lattice.

Frustrated spin-[formula omitted] Heisenberg magnet on an [formula omitted]-stacked honeycomb bilayer: High-order study of the collinear magnetic phases of the [formula omitted]–[formula omitted]–[formula omitted] model

The zero-temperature phase diagram of the frustrated spin-12J1–J2–J1⊥ Heisenberg magnet on an AA-stacked honeycomb bilayer lattice is studied using the coupled cluster method implemented to very high orders. On each monolayer the spins interact via nearest-neighbor (NN) and frustrating next-nearest-neighbor isotropic antiferromagnetic Heisenberg interactions with respective strength parameters J1>0 and J2≡κJ1>0. The two layers are coupled such that NN interlayer pairs of spins also interact via a similar isotropic Heisenberg interaction of strength J1⊥≡δJ1, which may be of either sign. In particular, we locate with high accuracy the complete phase boundaries in the κ–δ half-plane with κ>0 of the two quasiclassical collinear antiferromagnetic phases with Néel or Néel-II magnetic order in each monolayer, and the interlayer NN pairs of spins either aligned (for δ<0) or anti-aligned (for δ>0) to one another. Compared to the two-sublattice Néel order, in which all NN intralayer pairs of spins are antiparallel to one another, the four-sublattice Néel-II order is characterized by NN intralayer pairs of spins on the honeycomb lattice being antiparallel to one another along zigzag (or sawtooth) chains in a specified direction from among the three equivalent honeycomb-lattice directions, and parallel to one another for the corresponding interchain pairs.

Two-Photon Absorption in Electron Donor–Acceptor Dyads and Triads Using Classical and Entangled Photons: Potential Systems for Photon-to-Spin Quantum Transduction

Photon-to-spin quantum transduction, i.e., the exchange of coherence between photons and spins, is important for establishing links between localized molecular qubit systems performing logic and/or sensing operations and similar systems at different physical locations. We are developing molecular systems to explore how transduction can be implemented by using entangled photons to produce entangled spin pairs by ultrafast electron transfer leading to spin-correlated radical pairs (SCRPs). We have prepared and systematically evaluated electron transfer dyads and triads based on a 9-(N-piperidinyl)perylene-3,4-dicarboximide (6PMI) donor, a naphthalene-1,8:4,5-bis(dicarboximide) (NDI) acceptor, and a tetrathiofulvalene (TTF) secondary donor, which are prepared with and without a phenyl spacer between the 6PMI and NDI to give 6PMI-NDI, 6PMI-Ph-NDI, TTF-6PMI-NDI, and TTF-6PMI-Ph-NDI. We used transient absorption, fluorescence-detected classical two-photon-absorption, and entangled two-photon-absorption (ETPA) spectroscopies to characterize the optical properties of these systems, while time-resolved EPR spectroscopy was used to characterize their photogenerated SCRPs. The results show that the ETPA cross section depends entirely on the presence of 6PMI and NDI in the 6PMI-NDI and 6PMI-Ph-NDI dyads, but in the triads TTF-6PMI-NDI and TTF-6PMI-Ph-NDI, the presence of the Ph spacer significantly affects the ETPA cross section. These results provide important information for designing molecular systems to implement photon-to-spin quantum transduction using entangled photons.