Two-state Spin Research Articles

Dynamics of a Quantum System Interacting with White Non-Gaussian Baths: Poisson Noise Master Equation.

Quantum systems are unavoidably open to their surrounding degrees of freedom. The theory of open quantum systems is thus crucial to understanding the fluctuations, dissipation, and decoherence of a quantum system of interest. Typically, the bath is modeled as an ensemble of harmonic oscillators, which yields Gaussian statistics of the bath influence on the quantum systems. However, there are also phenomena in which the bath consists of two-state systems, spins, or anharmonic oscillators; therefore, the non-Gaussian properties of the bath become important. Nevertheless, a theoretical framework to describe quantum systems under the influence of such non-Gaussian baths is not well established. Here, we develop a theory to describe quantum dissipative systems affected by Poisson noise properties of the bath, because the Lévi-Itô decomposition theorem asserts that Poisson noise is fundamental in describing arbitrary white noise beyond Gaussian properties. We introduce a quantum bath model that allows for the consistent description of dissipative quantum systems. The obtained master equation reveals non-Gaussian bath effects in the white noise regime, and provides an essential step toward describing open quantum dynamics under the influence of generic baths.

Q-voter model with independence on signed random graphs: Homogeneous approximations.

The q-voter model with independence is generalized to signed random graphs and studied by means of Monte Carlo simulations and theoretically using the mean-field approximation and different forms of the pair approximation. In the signed network with quenched disorder, positive and negative signs associated randomly with the links correspond to reinforcing and antagonistic interactions, promoting, respectively, the same or opposite orientations of two-state spins representing agents' opinions; otherwise, the opinions are called mismatched. With probability 1-p, the agents change their opinions if the opinions of all members of a randomly selected q neighborhood are mismatched, and with probability p, they choose an opinion randomly. The model on networks with finite mean degree 〈k〉 and fixed fraction of the antagonistic interactions r exhibits ferromagnetic transition with varying the independence parameter p, which can be first or second order, depending on q and r, and disappears for large r. Besides, numerical evidence is provided for the occurrence of the spin-glass-like transition for large r. The order and critical lines for the ferromagnetic transition on the p vs r phase diagram obtained in Monte Carlo simulations are reproduced qualitatively by the mean-field approximation. Within the range of applicability of the pair approximation, for the model with 〈k〉 finite but 〈k〉≫q, predictions of the homogeneous pair approximation concerning the ferromagnetic transition show much better quantitative agreement with numerical results for small r but fail for larger r. A more advanced signed homogeneous pair approximation is formulated which distinguishes between classes of active links with a given sign connecting nodes occupied by agents with mismatched opinions; for the model with 〈k〉≫q its predictions agree quantitatively with numerical results in a whole range of r where the ferromagnetic transition occurs.

Dynamics of two-qubit quantum nonlocality in a Heisenberg chain model with the intrinsic decoherence

This paper investigates the dynamics of two-spin nonlocality generation in a Heisenberg XXX chain with Dzyaloshinskii-Moriya (DM) and Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) interactions. We analyze the two-spin nonlocality dynamics by using uncertainty-induced nonlocality, maximal Bell function, and log-negativity. We demonstrate that a separable two-spin Heisenberg XXX chain state, induced by two-spin antiferromagnetic interaction as well as x-component of DM and KSEA interactions, could evolve to maximal two-spin nonlocality state. The ability of preserving the maximal uncertainty-induced nonlocality can be enhanced by increasing the coupling strength of the spin-spin interaction coupling. The hierarchy principle is maintained for the two-spin Bell nonlocality and log-negativity entanglement. The two-spin log-negativity dynamics exhibits the phenomena of sudden death and birth. The sudden-death phenomenon is due to the intrinsic decoherence, which also causes a reduction in the two-spin nonlocality. While the sudden-birth phenomenon is due to two-spin antiferromagnetic interaction as well as x-component of DM and KSEA interactions. The two-spin uncertainty-induced nonlocality is more robust, against the intrinsic decoherence, than the other types of the nonlocality. The results indicate that by boosting the two-spin antiferromagnetic interaction, the produced nonlocality (resulting from the DM and KSEA x-component interactions) can be shielded from the intrinsic decoherence effect.

Geometrical and dynamical description of two interacting spins under the XXZ-type Heisenberg model

We consider a physical system consisting of two interacting spins governed by the [Formula: see text]-type Heisenberg Hamiltonian in an external magnetic field. We investigate the quantum evolution and the Riemannian geometry of the two-spin state space by means of the relevant Fubini–Study metric. The geometrical phase accumulated by the two-spin state is also examined under arbitrary and cyclic evolutions. By computing the evolution speed and the corresponding geodesic distance, we solve the quantum brachistochrone problem. The entanglement between the two spins is also studied via two approaches: the first one deals with the entanglement effect on the Fubini–Study metric and the geometrical phase, while the second one treats the entanglement effect on the evolution speed and the corresponding geodesic distance. Finally, we solve the quantum brachistochrone problem using the entanglement degree.

Are Quantum-Classical Hybrids Compatible with Ontological Cellular Automata?

Based on the concept of ontological states and their dynamical evolution by permutations, as assumed in the Cellular Automaton Interpretation (CAI) of quantum mechanics, we address the issue of whether quantum-classical hybrids can be described consistently in this framework. We consider chains of ‘classical’ two-state Ising spins and their discrete deterministic dynamics as an ontological model with an unitary evolution operator generated by pair-exchange interactions. A simple error mechanism is identified, which turns them into quantum mechanical objects: chains of qubits. Consequently, an interaction between a quantum mechanical and a ‘classical’ chain can be introduced and its consequences for this quantum-classical hybrid can be studied. We found that such hybrid character of composites, generally, does not persist under interactions and, therefore, cannot be upheld consistently, or even as a fundamental notion à la Kopenhagen interpretation, within CAI.

Adiabatic quantum state transfer in a semiconductor quantum-dot spin chain

Semiconductor quantum-dot spin qubits are a promising platform for quantum computation, because they are scalable and possess long coherence times. In order to realize this full potential, however, high-fidelity information transfer mechanisms are required for quantum error correction and efficient algorithms. Here, we present evidence of adiabatic quantum-state transfer in a chain of semiconductor quantum-dot electron spins. By adiabatically modifying exchange couplings, we transfer single- and two-spin states between distant electrons in less than 127 ns. We also show that this method can be cascaded for spin-state transfer in long spin chains. Based on simulations, we estimate that the probability to correctly transfer single-spin eigenstates and two-spin singlet states can exceed 0.95 for the experimental parameters studied here. In the future, state and process tomography will be required to verify the transfer of arbitrary single qubit states with a fidelity exceeding the classical bound. Adiabatic quantum-state transfer is robust to noise and pulse-timing errors. This method will be useful for initialization, state distribution, and readout in large spin-qubit arrays for gate-based quantum computing. It also opens up the possibility of universal adiabatic quantum computing in semiconductor quantum-dot spin qubits.

Ferromagnetic and spin-glass like transition in the q-neighbor Ising model on random graphs

The q-neighbor Ising model is investigated on homogeneous random graphs with a fraction of edges associated randomly with antiferromagnetic exchange integrals and the remaining edges with ferromagnetic ones. It is a nonequilibrium model for the opinion formation in which the agents, represented by two-state spins, change their opinions according to a Metropolis-like algorithm taking into account interactions with only a randomly chosen subset of their q neighbors. Depending on the model parameters in Monte Carlo simulations, phase diagrams are observed with first-order ferromagnetic transition, both first- and second-order ferromagnetic transitions and second-order ferromagnetic and spin-glass-like transitions as the temperature and fraction of antiferromagnetic exchange integrals are varied; in the latter case, the obtained phase diagrams qualitatively resemble those for the dilute spin-glass model. Homogeneous mean-field and pair approximations are extended to take into account the effect of the antiferromagnetic exchange interactions on the ferromagnetic phase transition in the model. For a broad range of parameters, critical temperatures for the first- or second-order ferromagnetic transition predicted by the homogeneous pair approximation show quantitative agreement with those obtained from Monte Carlo simulations; significant differences occur mainly in the vicinity of the tricritical point in which the critical lines for the second-order ferromagnetic and spin-glass-like transitions meet.Graphic abstract

Guest induced reversible on-off switching of elastic frustration in a 3D spin crossover coordination polymer with room temperature hysteretic behaviour.

A binary reversible switch between low-temperature multi-step spin crossover (SCO), through the evolution of the population γHS(T) with high-spin (HS)-low-spin (LS) sequence: HS1LS0 (state 1) ↔ HS2/3LS1/3 (state 2) ↔ HS1/2LS1/2 (state 3) ↔ HS1/3LS2/3 (state 4) ↔ HS0LS1 (state 5), and complete one step hysteretic spin transition featuring 20 K wide thermal hysteresis centred at 290 K occurs in the three-dimensional (3D) Hofmann-type porous coordination polymer {FeII(3,8phen)[Au(CN)2]2}·xPhNO2 (3,8phen = 3,8-phenanthroline, PhNO2 = nitrobenzene), made up of two identical interpenetrated pcu-type frameworks. The included PhNO2 guest (x = 1, 1·PhNO2) acts as a molecular wedge between the interpenetrated 3D frameworks via PhNO2-3,8phen intermolecular recognition and is the source of the strong elastic frustration responsible for the multi-step regime. Detailed X-ray single crystal analysis reflects competition between spatial periodicities of structurally inequivalent HS and LS SCO centres featuring: (i) symmetry breaking (state 3) with ⋯HS–LS⋯ ordering with γHS = 1/2; and (ii) occurrence of spatial modulation of the structure providing evidence for stabilization of local or aperiodic ordered mixed spin states for states 2 and 4 (with γHS ≈ 2/3) and 4 (with γHS ≈ 1/3), respectively. Below c.a. 20 K, structural and magnetic analyses show the photogeneration of a metastable HS*, state 6. The room-temperature single-step hysteretic regime appears with release of the guest (x = 0, 1) and the elastic frustration, and reversibly switches back to the original four-step behaviour upon guest re-adsorption. Both uncommon relevant SCO events meeting in the same material represent a rare opportunity to compare them in the frame of antiferro- and ferro-elastic transitions.

Zeros of Holant Problems

We present fully polynomial-time (deterministic or randomised) approximation schemes for Holant problems, defined by a non-negative constraint function satisfying a generalised second-order recurrence modulo in a couple of exceptional cases. As a consequence, any non-negative Holant problem on cubic graphs has an efficient approximation algorithm unless the problem is equivalent to approximately counting perfect matchings, a central open problem in the area. This is in sharp contrast to the computational phase transition shown by two-state spin systems on cubic graphs. Our main technique is the recently established connection between zeros of graph polynomials and approximate counting.

Pair approximation for the q-voter model with independence on multiplex networks.

The q-voter model with independence is investigated on multiplex networks with full overlap of nodes in the layers. The layers are various complex networks corresponding to different levels of social influence. Detailed studies are performed for the model on multiplex networks with two layers with identical degree distributions, obeying the LOCAL&AND and GLOBAL&AND spin update rules differing by the way in which the q-lobbies of neighbors within different layers exert their joint influence on the opinion of a given agent. Homogeneous pair approximation is derived for a general case of a two-state spin model on a multiplex network and its predictions are compared with results of mean-field approximation and Monte Carlo simulations of the above-mentioned q-voter model with independence for a broad range of parameters. As the parameter controlling the level of agents' independence is changed ferromagnetic phase transition occurs which can be first- or second-order, depending on the size of the lobby q. Details of this transition, e.g., position of the critical points, critical exponents and the width of the possible hysteresis loop, depend on the topology and other features of the layers, in particular on the mean degree of nodes in the layers which is directly predicted by the homogeneous pair approximation. If the mean degree of nodes is substantially larger than the size of the q-lobby good agreement is obtained between numerical results and theoretical predictions based on the homogeneous pair approximation concerning the order and details of the ferromagnetic transition. In the case of the model on multiplex networks with layers in the form of homogeneous Erdős-Rényi and random regular graphs as well as weakly heterogeneous scale-free networks this agreement is quantitative, while in the case of layers in the form of strongly heterogeneous scale-free networks it is only qualitative. If the mean degree of nodes is small and comparable with q predictions of the homogeneous pair approximation are in general even qualitatively wrong.

Schottky anomaly of deSitter black holes

The interplay of black hole and cosmological horizons introduces distinctive thermodynamic behavior for deSitter black holes, including well-known upper bounds for the mass and entropy. We point to a new such feature, a Schottky peak in the heat capacity of Schwarzschild–deSitter (SdS) black holes. With this behavior in mind, we explore statistical models for the underlying quantum degrees of freedom of SdS holes. While a simple two-state spin model gives Schottky behavior, in order to capture the non-equilibrium nature of the SdS system we consider a system with a large number of non-interacting spins. We examine to what extent constrained states of this system reproduce the thermodynamic properties of the black hole. We also review results of a recent study of particle production in SdS spacetimes in light of the Schottky anomaly and our spin models.

Probing the singlet-triplet splitting in double quantum dots: Implications of the ac field amplitude

We consider a double quantum dot whose energy detuning is controlled by an ac electric field. We demonstrate an energy configuration for which the ac-induced current flowing through the double dot directly probes the spin-orbit anticrossing point for small ac field amplitudes. On the contrary, as the ac amplitude increases a current antiresonance is formed, and the direct information about the spin-orbit interaction is lost. This result indicates that a large ac amplitude is not necessarily advantageous for the spectroscopy of spin-orbit coupled two-spin states. Moreover, we investigate the ac-induced current peaks versus the ac amplitude and show a current suppression when the ac field forms spin blocked states. This effect gives rise to a characteristic pattern for the current which can be controlled at will by tuning the ac amplitude. Our results can be explored by performing electronic transport measurements in the spin blockade regime.

Entanglement estimation in non-optimal qubit states

In the last years, a relationship has been established between the quantum Fisher information (QFI) and quantum entanglement. In the case of two-qubit systems, all pure entangled states can be made useful for sub-shot-noise interferometry while their QFI meets a necessary and sufficient condition (Hyllus et al., 2010). In M-qubit systems, the QFI provides just a sufficient condition in the task of detecting the degree of entanglement of a generic state (Pezzé and Smerzi, 2009). In our work, we show analytically that, for a large class of one-parameter non-optimal two-qubit states, the maximally entangled states are associated with stationary points of the QFI, as a function of such parameter. We show, via numerical simulations, that this scenario is maintained for the generalisation of this class of states to a generic M-qubit system. Furthermore, we suggest a scheme for an interferometer able to detect the entanglement in a large class of two-spin states.

Nonlocality, quantum correlations, and violations of classical realism in the dynamics of two noninteracting quantum walkers

That quantum correlations can be generated over time between the spin and the position of a quantum walker is indisputable. The creation of bipartite entanglement has also been reported for two-walker systems. In this scenario, however, since the global state lies in a fourpartite Hilbert space, the question arises as to whether genuine multipartite entanglement may develop in time. Also, since the spatial degrees of freedom can be viewed as a noisy channel for the two-spin part, one may wonder how other nonclassical aspects, such as Bell nonlocality, Einstein-Podolsky-Rosen steering, quantum discord, and symmetrical quantum discord, evolve in time during the walk. The lack of analytical and numerical evidences which would allow one to address these questions is possibly due to the usual computational difficulties associated with the recursive nature of quantum walks. Here, we work around this issue by introducing a simplified Gaussian model which proves to be very accurate within a given domain and powerful for analytical studies. Then, for an instance involving two noninteracting quantum walkers, whose spins start in the singlet state, we quantify the aforementioned nonclassical features as a function of time, and evaluate violations of both realism and related aspects of locality. In addition, we analyze situations in which the initial two-spin state is affected by white noise. The typical scenario found is such that while genuine fourpartite entanglement increases over time, all the investigated nonclassical features vanish (suddenly or asymptotically) except realism-based nonlocality. Moreover, realism is prevented for all finite times. Our findings open perspectives for the understanding of the dynamics of quantum resources in quantum walks.

Absolute 1H polarization measurement with a spin-correlated component of magnetization by hyperpolarized MAS-DNP solid-state NMR

Sensitivity of magic-angle spinning (MAS) NMR spectroscopy has been dramatically improved by the advent of high-field dynamic nuclear polarization (DNP) technique and its rapid advances over the past decades. In this course, discussions on ways to improve the DNP enhancement factor or the overall sensitivity gain have been numerous, and led to a number of methodological and instrumental breakthroughs. Beyond the sensitivity gain, however, discussions on accurate quantification of the 1H polarization amplitude achievable in a sample with DNP have been relatively rare. Here, we propose a new method for quantifying the local 1H hyperpolarization amplitude, which is applicable to un-oriented/powdered solid samples under MAS NMR conditions. The method is based on the ability to observe the high-order spin-correlated term (2IzSz) intrinsic to a hyperpolarized IS two-spin state, separately from the lowest-order Zeeman term (Sz) in quasi-equilibrium magnetization. The quantification procedure does not require evaluation of signal amplitudes for a “microwave-off” condition and for an un-doped reference sample, and thus enables quick and accurate quantification unaffected by the effects of the paramagnetic quenching and the MAS-induced depolarization. The method is also shown to elucidate spatial polarization distribution through the 2IzSz term prepared domain-selectively. As a potential application, we also demonstrate 2D DQ-SQ spectroscopy utilizing the 2IzSz term that is generated in a spatially selective manner without using IS dipolar or J coupling. These salient features may be evolved into a way for characterizing mesoscopic molecular assemblies of medical/biological importance.

Spectroscopy of double quantum dot two-spin states by tuning the interdot barrier

Transport spectroscopy of two-spin states in a double quantum dot can be performed by an AC electric field which tunes the energy detuning. However, a problem arises when the transition rate between the states is small and, consequently, the AC-induced current is suppressed. Here, we show that if the AC field tunes the inter-dot tunnel barrier then for large detuning the transition rate increases drastically resulting in high current. Multi-photon resonances are enhanced by orders of magnitude. Our study demonstrates an efficient way for fast two-spin transitions.

Exchange interactions in two-state systems: rare earth pyrochlores

The general form of the nearest neighbour exchange interaction for rare earth pyrochlores is derived based on symmetry. Generally, the rare earth angular momentum degeneracy is lifted by the crystal electric field (CEF) into singlets and doublets. When the CEF ground state is a doublet that is well-separated from the first excited state the CEF ground state doublet can be treated as a pseudo-spin of some kind. The general form of the nearest neighbour exchange interaction for pseudo-spins on the pyrochlore lattice is derived for three different types of pseudo-spins. The methodology presented in this paper can be applied to other two-state spin systems with a high space group symmetry.

Rational design of stealthy hyperuniform two-phase media with tunable order.

Disordered stealthy hyperuniform materials are exotic amorphous states of matter that have attracted recent attention because of their novel structural characteristics (hidden order at large length scales) and physical properties, including desirable photonic and transport properties. It is therefore useful to devise algorithms that enable one to design a wide class of such amorphous configurations at will. In this paper, we present several algorithms enabling the systematic identification and generation of discrete (digitized) stealthy hyperuniform patterns with a tunable degree of order, paving the way towards the rational design of disordered materials endowed with novel thermodynamic and physical properties. To quantify the degree of order or disorder of the stealthy systems, we utilize the discrete version of the τ order metric, which accounts for the underlying spatial correlations that exist across all relevant length scales in a given digitized two-phase (or, equivalently, a two-spin state) system of interest. Our results impinge on a myriad of fields, ranging from physics, materials science and engineering, visual perception, and information theory to modern data science.

Hole Spin Resonance and Spin-Orbit Coupling in a Silicon Metal-Oxide-Semiconductor Field-Effect Transistor.

We study hole spin resonance in a p-channel silicon metal-oxide-semiconductor field-effect transistor. In the subthreshold region, the measured source-drain current reveals a double dot in the channel. The observed spin resonance spectra agree with a model of strongly coupled two-spin states in the presence of a spin-orbit-induced anticrossing. Detailed spectroscopy at the anticrossing shows a suppressed spin resonance signal due to spin-orbit-induced quantum state mixing. This suppression is also observed for multiphoton spin resonances. Our experimental observations agree with theoretical calculations.

Entanglement dynamics for two spins in an optical cavity - field interaction induced decoherence and coherence revival.

We in this paper study quantum correlations for two neutral spin-particles coupled with a single-mode optical cavity through the usual magnetic interaction. Two-spin entangled states for both antiparallel and parallel spin-polarizations are generated under the photon coherent-state assumption. Based on the quantum master equation we derive the time-dependent quantum correlation of Clauser-Horne-Shimony-Holt (CHSH) type explicitly in comparison with the well known entanglement-measure concurrence. In the two-spin singlet state, which is recognized as one eigenstate of the system, the CHSH correlation and concurrence remain in their maximum values invariant with time and independent of the average photon-numbers either. The correlation varies periodically with time in the general entangled-states for the low average photon-numbers. When the photon number increases to a certain value the oscillation becomes random and the correlations are suppressed below the Bell bound indicating the decoherence of the entangled states. In the high photon-number limit the coherence revivals periodically such that the CHSH correlation approaches the upper bound value at particular time points associated with the cavity-field period.