Single Spin-1 Research Articles

Monitored nonadiabatic and coherent-controlled quantum unital Otto heat engines: First four cumulants.

Recently, measurement-based quantum thermal machines have drawn more attention in the field of quantum thermodynamics. However, the previous results on quantum Otto heat engines were either limited to special unital and nonunital channels in the bath stages, or a specific driving protocol at the work strokes and assuming the cycle being time-reversal symmetric, i.e., V^{†}=U (or V=U). In this paper, we consider a single spin-1/2 quantum Otto heat engine, by first replacing one of the heat baths by an arbitrary unital channel, and then we give the exact analytical expression of the characteristic function from which all the cumulants of heat and work emerge. We prove that under the effect of monitoring, ν_{2}>ν_{1} is a necessary condition for positive work, either for a symmetric or asymmetric-driven Otto cycle. Furthermore, going beyond the average we show that the ratio of the fluctuations of work and heat is lower and upper-bounded when the system is working as a heat engine. However, differently from the previous results in the literature, we consider the third and fourth cumulants as well. It is shown that the ratio of the third (fourth) cumulants of work and heat is not upper-bounded by unity nor lower-bounded by the third (fourth) power of the efficiency, as is the case for the ratio of fluctuations. Finally, we consider applying a specific unital map that plays the role of a heat bath in a coherently superposed manner, and we show the role of the initial coherence of the control qubit on efficiency, on the average work and its relative fluctuations.

Strong single-photon to two-photon bundles emission in spin-1 Jaynes–Cummings model

High-quality special nonclassical states beyond the strong single atom-cavity coupling regime are fundamental elements in quantum information science. Here, we study strong single-photon blockade to two-photon bundles emission in a single spin-1 atom coupled to an optical cavity by constructing a spin-1 Jaynes–Cummings model (JCM). By tuning the quadratic Zeeman shift, the energy-spectrum anharmonicity can be significantly enhanced, leading to a remarkable increase in the dressed-state splitting of the well-resolved n-photon resonance. The mechanism, which benefits from the internal degrees of freedom in high-spin systems, compensates for the strong coupling condition required by the multi-photon blockade, thereby facilitating the experimental feasibility of engineering special nonclassical states beyond the strong-coupling limit. It is shown that the photon emission from the spin-1 JCM demonstrates high-quality single photon and two-photon bundles with large steady-state photon numbers in the cavity-driven and atom-pump cases, respectively. In particular, compared to the two-level two-photon JCM, the antibunching amplitude of the three-order correlation function for two-photon bundles in the spin-1 JCM is enhanced by 3 orders of magnitude. More interestingly, a multimode transducer, enabling a transition from strong single-photon blockade to two-photon bundles and super-Poissonian photon emission, is achieved and highly controllable by the light-cavity detuning in the presence of both atom and cavity driven fields. This study based on the high-spin JCM broadens the scope of engineering special nonclassical quantum states beyond the standard two-level JCM. Our proposal not only opens up a new avenue for generating high-quality n-photon sources but also provides versatile applications in quantum networks and metrology.

Tailored magnetism of a molecule composed of two inverted tetrahedra with spin- ½ ions connected by a spin-1 ion at their common vertex

In this paper, we examine the magnetic properties of a molecule formed by two tetrahedra connected at their common vertex by a single spin-1 ion, while the corners of their two equilateral bases are occupied by spin-½ ions. The partition function was calculated and the relevant other variables were derived using the Heisenberg spin model. In the case of predominantly ferromagnetic exchange couplings, the spin structure is fully saturated and behaves like a large spin-4 unique magnet.Antiferromagnetic coupling can severely frustrate the spins of the nanodevice. This may lead to several exotic phenomena. Therefore, the magnetization can be quantified into plateaus separated by quantum phase transitions. A quantum spin liquid state is then encountered at low temperatures.The purpose of this contribution is to encourage experimentalists to develop molecular magnets as the basis for innovative nanoscale applications.

Error-disturbance uncertainty relations in Faraday measurements

We examine error-disturbance relations in the quantum measurement of spin systems using an atom-light interface scheme. We model a single spin-1/2 system that interacts with a polarized light meter via a Faraday interaction. We formulate the error and disturbance of the model and examine the uncertainty relations. We find that, for the coherent light meter in pure polarization, both the error and disturbance behave like the cyclic oscillations due to the Faraday rotation in both the light and spin polarizations. We also examine a class of polarization-squeezed light meter, where we apply the phase-space approximation and characterize the role of squeezing. We derive the error-disturbance relations for these cases and find that the Heisenberg-Arthurs-Kelly uncertainty is violated while the tight Branciard-Ozawa uncertainty always holds. We note that, in the limit of weak interaction strength, the error and disturbance come to obey the unbiasedness condition and hence the Heisenberg-Arthurs-Kelly relation holds. The work contributes to our understanding of the quantum measurement of spin systems under the atom-light interface framework and may hold potential applications in quantum metrology, quantum state estimation, and control.

Properties of spin- 1/2 heavy baryons at nonzero temperature

The spectroscopic properties of single heavy spin-1/2 $\Lambda_{Q}$, $\Sigma_{Q}$, $\Xi^{(\prime)}_{Q}$ and $ \Omega_{Q}$ baryons are investigated at finite temperature in the framework of thermal QCD sum rule. We discuss the behavior of the mass and residue of these baryons with respect to temperature taking into account contributions of non-perturbative operators up to dimension eight. We include additional operators coming from the Wilson expansion due to breaking the Lorentz invariance at non-zero temperature. The obtained results show that the mass of these baryons remain stable up to roughly $T=108$ MeV while their residue are unchanged up to $T=93$ MeV. After these points, the mass and residue start to diminish by increasing the temperature. The shifts in the mass and residue for both the bottom and charm channels are considerably large and we observe the melting of these baryons near to the pseudo-critical temperature determined by recent lattice QCD calculations. We present our results for the mass of these baryons with both the positive and negative parity at $ T\rightarrow 0 $ limit, which are consistent with the existing theoretical predictions as well as experimental data.

Frustration-induced anomalous transport and strong photon decay in waveguide QED

We study the propagation of photons in a one-dimensional environment consisting of two non-interacting species of photons frustratingly coupled to a single spin-1/2. The ultrastrong frustrated coupling leads to an extreme mixing of the light and matter degrees of freedom, resulting in the disintegration of the spin and a breakdown of the "dressed-spin", or polaron, description. Using a combination of numerical and analytical methods, we show that the elastic response becomes increasingly weak at the effective spin frequency, showing instead an increasingly strong and broadband response at higher energies. We also show that the photons can decay into multiple photons of smaller energies. The total probability of these inelastic processes can be as large as the total elastic scattering rate, or half of the total scattering rate, which is as large as it can be. The frustrated spin induces strong anisotropic photon-photon interactions that are dominated by inter-species interactions. Our results are relevant to state-of-the-art circuit and cavity quantum electrodynamics experiments.

Magnetic hexamers interacting in layers in the (Na,K)2Cu3O(SO4)3 minerals

Magnetic properties and underlying magnetic models of the synthetic A$_2$Cu$_3$O(SO$_4)_3$ fedotovite (A = K) and puninite (A = Na) minerals, as well as the mixed euchlorine-type NaKCu$_3$O(SO$_4)_3$ are reported. We show that all these compounds contain magnetic Cu$_6$ hexamer units, which at temperatures below about 100 K act as single spin-1 entities. Weak interactions between these magnetic molecules lead to long-range order below $T_N$ = 3.4 K (A = Na), 4.7 K (A = NaK), and about 3.0 K (A = K). The formation of the magnetic order is elucidated by ab initio calculations that reveal two-dimensional inter-hexamer interactions within crystallographic $bc$ planes. This model indicates the presence of a weakly distorted square lattice of $S=1$ magnetic ions and challenges the earlier description of the A$_2$Cu$_3$O(SO$_4)_3$ minerals in terms of Haldane spin chains.

A macrorealistic test in hybrid quantum optomechanics

We discuss a scheme for macrorealistic theories of the Leggett–Garg form (Leggett and Garg 1985 Phys. Rev. Lett. 54 857). Our scheme is based on a hybrid optomechanical system. It seems reasonable to test these inequalities with an optomechanical system, since in an optomechanical cavity it is possible to create non-classical states of the mirror through a projective measurement on the cavity field. We will present the protocol to generate such non-classicality for a general optomechanical cavity and after we will carry out a theoretical test for one of the possible formulations of these inequalities using a hybrid optomechanical system. Specifically, the inequality will be investigated for an harmonic oscillator coupled to a two-level system, which replaces the light field of the cavity. The aim is to reproduce, with this system, the evolution of a single spin-1/2 for which the inequality is violated; this is achievable through the conditioning of the two-level system which will be used as an ancilla.

An algebraic classification of exceptional EFTs

We classify four-dimensional effective field theories (EFTs) with enhanced soft limits, which arise due to non-linearly realised symmetries on the Goldstone modes of such theories. We present an algorithm for deriving all possible algebras that can be non-linearly realised on a set of Goldstone modes with canonical propagators, linearly realised Poincaré symmetries and interactions at weak coupling. An important ingredient in our analysis is inverse Higgs trees which systematically incorporate the requirements for the existence of inverse Higgs constraints. These are the algebraic cousin of the on-shell soft data one provides for soft bootstrapping EFTs. We perform full classifications for single scalar and multiple spin-1/2 fermion EFTs and present a thorough analysis for multiple scalars. In each case there are only a small number of algebras consistent with field-dependent transformation rules, leading to the class of exceptional EFTs including the scalar sector of Dirac-Born-Infeld, Special Galileon and Volkov-Akulov theories. We also discuss the coupling of a U(1) gauge vector to the exceptional scalar theories, showing that there is a Special Galileon version of the full Dirac-Born-Infeld theory. This paper is part I in a series of two papers, with the second providing an algebraic classification of supersymmetric theories with non-linearly realised symmetries.

Drawing Single NMR Spins and Understanding Relaxation

How should we draw vectors to represent individual nuclear spins? Vectors in 3D space are merely a way of understanding the mathematics of quantum mechanics, which provides the “true” description of a single spin-½ nucleus. They are a useful aid to understanding, but there is no single “correct” vector representation, and the different vector models that are used have advantages and disadvantages. Here, we discuss the 2 standard vector models for a nuclear magnetic resonance spin: the up/down or alignment model and the 2-cone model, and we show how they relate to quantum mechanics. We show why both of these models are limited and discuss a third model, the uniform model, in which individual spins can be in any orientation. We demonstrate how the uniform model presents a clear and logically coherent description for spins: at equilibrium; following a 90° pulse; and during the subsequent relaxation back to equilibrium. The uniform model is fully consistent with quantum mechanics and leads to an understanding of coherence and relaxation that cannot be obtained from the other 2 models. We suggest that the uniform model is more helpful than the other 2 for most purposes.

Robust double Weyl semimetal phase in a nonmagnetic hexagonal lattice system

We propose a simple strategy to find possible linear double Weyl semimetals (WSMs) among nonmagnetic materials. This strategy can reproduce several known robust WSM candidates, covering orthorhombic, tetragonal, and cubic lattice systems. This kind of WSM hosts Weyl points (WPs) carrying double chiral charges when spin degeneracy is considered while spin-orbit coupling (SOC) is switched off, and dispersions along all three directions are linear, distinct from the parabolic double WPs proposed in $\mathrm{HgC}{\mathrm{r}}_{2}\mathrm{S}{\mathrm{e}}_{4}$. When SOC is included, these double-charge WPs split into two single spin-1/2 WPs with equal chirality. Following this strategy and combining with ab initio structural prediction techniques, we propose a candidate for such kind of WSMs, rooted in a high-pressure phase of $\mathrm{Ti}{\mathrm{S}}_{2}$ with space group $P\text{\ensuremath{-}}62m$. In this system, all the WPs are pinned at the same energy due to crystal symmetry. In addition, the minimum spacing between opposite-chirality WPs is $\ensuremath{\sim}0.23\phantom{\rule{0.16em}{0ex}}\AA{}{}^{\ensuremath{-}1}$, which makes it a promising robust WSM candidate.

Creation of a Dirac monopole-antimonopole pair in a spin-1 Bose-Einstein condensate

We theoretically demonstrate that a pair of Dirac monopoles with opposite synthetic charges can be created within a single spin-1 Bose-Einstein condensate by steering the spin degrees of freedom by external magnetic fields. Although the net synthetic magnetic charge of this configuration vanishes, both the monopole and the antimonopole are accompanied by vortex filaments carrying opposite angular momenta. Such a Dirac dipole can be realized experimentally by imprinting a spin texture with a nonlinear magnetic field generated by a pair of coils in a modified Helmholtz configuration. We also investigate the case where the initial state for the dipole-creation procedure is pierced by a quantized vortex line with a winding number k. It is shown that if k = -1, the resulting monopole and antimonopole lie along the core of a singly quantized vortex whose sign is reversed at the locations of the monopoles. For k = -2, the monopole and antimonopole are connected by a vortex line segment carrying two quanta of angular momentum, and hence the dipole as a whole is an isolated configuration. In addition, we simulate the long-time evolution of the dipoles in the magnetic field used to create them. For k = 0, each of the semi-infinite doubly quantized vortices splits into two singly quantized vortices, as in the case of a single Dirac monopole. For k = -1 and k = -2, the initial vortices deform into a vortex with a kink and a vortex ring, respectively.

Driven dissipative dynamics and topology of quantum impurity systems

In this review, we provide an introduction to and an overview of some more recent advances in real-time dynamics of quantum impurity models and their realizations in quantum devices. We focus on the Ohmic spin–boson and related models, which describe a single spin-1/2 coupled with an infinite collection of harmonic oscillators. The topics are largely drawn from our efforts over the past years, but we also present a few novel results. In the first part of this review, we begin with a pedagogical introduction to the real-time dynamics of a dissipative spin at both high and low temperatures. We then focus on the driven dynamics in the quantum regime beyond the limit of weak spin–bath coupling. In these situations, the non-perturbative stochastic Schrödinger equation method is ideally suited to numerically obtain the spin dynamics as it can incorporate bias fields hz(t) of arbitrary time-dependence in the Hamiltonian. We present different recent applications of this method: (i) how topological properties of the spin such as the Berry curvature and the Chern number can be measured dynamically, and how dissipation affects the topology and the measurement protocol, (ii) how quantum spin chains can experience synchronization dynamics via coupling with a common bath. In the second part of this review, we discuss quantum engineering of spin–boson and related models in circuit quantum electrodynamics (cQED), quantum electrical circuits, and cold-atoms architectures. In different realizations, the Ohmic environment can be represented by a long (microwave) transmission line, a Luttinger liquid, a one-dimensional Bose–Einstein condensate or a chain of superconducting Josephson junctions. We show that the quantum impurity can be used as a quantum sensor to detect properties of a bath at minimal coupling, and how dissipative spin dynamics can lead to new insight in the Mott–superfluid transition. Dans cette revue, nous proposons une introduction et une vue d'ensemble de quelques progrès parmi les plus récents dans le domaine de la dynamique en temps réel des modèles d'impuretés quantiques et de leurs réalisations dans les dispositifs quantiques. Nous nous intéressons au modèle spin–boson avec dissipation ohmique et aux modèles associés, qui décrivent un seul spin 1/2 couplé à une collection infinie d'oscillateurs harmoniques. Les sujets abordés s'inspirent en grande partie de nos travaux de ces dernières années, mais nous présentons également quelques résultats nouveaux. Nous commençons la première partie de cette revue par une introduction pédagogique à la dynamique en temps réel d'un spin dissipatif à hautes et basses températures. Nous nous intéressons ensuite à la dynamique dirigée en régime quantique au-delà de la limite de faible couplage spin–bain. Dans ces situations, la méthode faisant appel à l'équation de Schroedinger stochastique non perturbative est idéale pour obtenir numériquement la dynamique de spin, car elle permet d'incorporer des champs de polarisation hz(t) de dépendance temporelle arbitraire dans le hamiltonien. Nous présentons différentes applications récentes de cette méthode : (i) comment les propriétés topologiques du spin telles que la courbure de Berry et le nombre de Chern peuvent être mesurées dynamiquement, et comment la dissipation affecte la topologie et le protocole de mesure ; (ii) comment les chaînes de spin quantiques suivent la dynamique de synchronisation par couplage avec un bain commun. Dans la deuxième partie de cette revue, nous discutons l'ingénierie quantique du modèle spin-boson et des modèles associés en électrodynamique quantique des circuits (cQED), des circuits électriques quantiques et des architectures d'atomes froids. Dans différentes réalisations, l'environnement ohmique peut être représenté par une longue ligne de transmission (micro-ondes), un liquide de Luttinger, un condensat de Bose–Einstein unidimensionnel, une chaîne de jonctions Josephson supraconductrices. Nous montrons que l'impureté quantique peut être utilisée comme un capteur quantique pour détecter les propriétés d'un bain au couplage minimal, et comment la dynamique de spin dissipative peut conduire à de nouvelles perspectives dans la transition Mott–superfluide.

Enhancing sensitivity in quantum metrology by Hamiltonian extensions

A well-studied scenario in quantum parameter estimation theory arises when the parameter to be estimated is imprinted on the initial state by a Hamiltonian of the form $\theta G$. For such "phase shift Hamiltonians" it has been shown that one cannot improve the channel quantum Fisher information by adding ancillas and letting the system interact with them. Here we investigate the general case, where the Hamiltonian is not necessarily a phase shift, and show that in this case in general it \emph{is} possible to increase the quantum channel information and to reach an upper bound. This can be done by adding a term proportional to the derivative of the Hamiltonian, or by subtracting a term to the original Hamiltonian. Both methods do not make use of any ancillas and show therefore that for quantum channel estimation with arbitrary parameter-dependent Hamiltonian, entanglement with an ancillary system is not necessary to reach the best possible sensitivity. By adding an operator to the Hamiltonian we can also modify the time scaling of the channel quantum Fisher information. We illustrate our techniques with NV-center magnetometry and the estimation of the direction of a magnetic field in a given plane using a single spin-1 as probe.

Optimal control of single spin‐1/2 quantum systems

The purpose of this study is to explore the optimal control problems for a class of single spin-1/2 quantum ensembles. The system in question evolves on a manifold in ℛ3 and is modelled as a bilinear control form whose states are represented as coherence vectors. An associated matrix Lie group system with state space SO(3) is introduced in order to facilitate solving the given problem. The controllability as well as the reachable set of the system is first analysed in detail. Then, the maximum principle is applied to the optimal control for system evolving on the Lie group of special orthogonal matrices of dimension 3, with cost that is quadratic in the control input. As an illustrative example, the authors apply their result to perform a reversible logic quantum operation NOT on single spin-1/2 system. Explicit expressions for the optimal control are given which are linked to the initial state of the system.

Spin-based effects and transport properties of a spin-orbit-coupled hexagonal optical lattice

We investigate an ultracold Fermi gas in a hexagonal lattice subjected to a strong Rashba spin-orbit coupling (SOC). We focus on the marginal Abelian limit with the strength of SOC $\ensuremath{\kappa}=\ensuremath{\pi}/2$, where the derived Dirac fermions are spin-1/2 spinors in contrast to the pure hexagonal lattice. We find a double-degeneracy at the center of the Brillouin zone, which is a spin-3/2 Dirac-Weyl fermion that can be represented as two spin-1/2 fermions. While at the corner of the Brillouin zone, there occur another two spin-1/2 fermions. These Dirac spinors display a verity of spin textures beyond the usual topological properties. Furthermore, we investigate the energy spectrum of one-dimensional (1D) zigzag and armchair ribbons, and show that the appearance of a new cone at the center of the Brillouin zone can induce two flat bands in a 1D zigzag ribbon. These unique properties allow us to transport a single spin-1/2 Dirac spinor through the 1D zigzag ribbon with two quasi-two-dimensional leads, where only the spin-up or spin-down freedom of the Dirac spinors can transit through the ribbon.

Quantum contextuality for a relativistic spin-1/2 particle

The quantum predictions for a single nonrelativistic spin-1/2 particle can be reproduced by noncontextual hidden variables. Here we show that quantum contextuality for a relativistic electron moving in a Coulomb potential naturally emerges if relativistic effects are taken into account. The contextuality can be identified through the violation of noncontextuality inequalities. We also discuss quantum contextuality for the free Dirac electron as well as the relativistic Dirac oscillator.

An Efficient Algorithm for Simulating the Real-Time Quantum Dynamics of a Single Spin-1/2 Coupled to Specific Spin-1/2 Baths

An efficient algorithm for the computation of the real-time dependence of a single quantum spin-1/2 coupled to a specific set of quantum spin-1/2 baths is presented. The specific spin baths have couplings only with the spin operators Sx between bath spins and the central spin. We calculate spin expectation values, the quantum purity, the von Neumann entropy, and the off-diagonal components of the reduced density matrix for the central spin once the bath spins have been traced out. The algorithm does not require the storage of any vector larger than of size 2, even though the size of the Hilbert space is 2N+1, where N is the number of bath spins. Results are presented for the central spin connected to different sizes and types of spin baths, and for different initial states for the central spin and for the bath spins. Results are also compared to those for more general baths.

Generation of maximally entangled states with subluminal Lorentz boosts

Recent work has studied entanglement between the spin and momentum components of a single spin-1/2 particle and showed that maximal entanglement is obtained only when boosts approach the speed of light. Here we extend the boost scenario to general geometries and show that, intriguingly, maximal entanglement can be achieved with boosts less than the speed of light. Boosts approaching the speed of light may even decrease entanglement. We also provide a geometric explanation for this behavior.

Dynamics of a Single Spin-1/2 Coupled to x- and y-Spin Baths: Algorithm and Results

The real-time dynamics of a single spin-1/2 particle, called the central spin, coupled to the x ( y )-components of the spins of one or more baths is simulated. The bath Hamiltonians contain interactions of x ( y )-components of the bath spins only but are general otherwise. An efficient algorithm is described which allows solving the time-dependent Schr’odinger equation for the central spin, even if the x ( y ) baths contain hundreds of spins. The algorithm requires storage for 2 × 2 matrices only, no matter how many spins are in the baths. We calculate the expectation value of the central spin, as well as its von Neumann entropy S( t ), the quantum purity P( t ), and the off-diagonal elements of the quantum density matrix. In the case of coupling the central spin to both x - and y - baths the relaxation of S( t ) and P( t ) with time is a power law, compared to an exponential if the central spin is only coupled to an x -bath. The effect of different initial states for the central spin and bath is studied. Comparison with more general spin baths is also presented.