Spin Entanglement Research Articles

Spin–orbit coupling in the presence of strong atomic correlations

We explore the influence of contact interactions on a synthetically spin–orbit coupled system of two ultracold trapped atoms. Even though the system we consider is bosonic, we show that a regime exists in which the competition between the contact and spin–orbit interactions results in the emergence of a ground state that contains a significant contribution from the anti-symmetric spin state. This ground state is unique to few-particle systems and does not exist in the mean-field regime. The transition to this state is signalled by an inversion in the average momentum from being dominated by centre-of-mass momentum to relative momentum and also affects the global entanglement shared between the real- and pseudo-spin spaces. Indeed, competition between the interactions can also result in avoided crossings in the ground state which further enhances these correlations. However, we find that correlations shared between the pseudo-spin states are strongly depressed due to the spin–orbit coupling and therefore the system does not contain spin–spin entanglement.

Robust scalable architecture for a hybrid spin-mechanical quantum entanglement system

Practical quantum information technique requires a large scalable quantum network. We proposed a hybrid system for deterministic scalable spin entanglement network based on nitrogen-vacancy (NV) centers in diamond coupling with carbon nanotube. The fault-tolerant entangled gate between two remote NV centers can be realized with vibrating nanotube assisted spin-spin interaction with current experimental technology. This interaction can be directly generalized to multi-NV-center entanglement architecture. Moreover, the effects of the single spin dephasing (SSD) and spin cross relaxation (SCR) on this state generation process were analyzed in detail. We found that the decay rate scales as ${N}^{2}$, corresponding to the number of independent decoherence channels. However, by employing dressed state protection and independent tunable interaction method, SSD and SCR can be mitigated efficiently and the decay rate of the generated multi-NV-center entanglement scales as $N$, which boosts the size of the entanglement network up to hundreds of qubits. Such a hybrid quantum system compatible with current topological protection provides a useful platform for the investigation of quantum computation.

Visualizing spin degrees of freedom in atoms and molecules

In this work we show how constructing Wigner functions of heterogeneous quantum systems leads to new capability in the visualization of quantum states of atoms and molecules. This method allows us to display quantum correlations (entanglement) between spin and spatial degrees of freedom (spin-orbit coupling) and between spin degrees of freedom, as well as more complex combinations of spin and spatial entanglement. This is important as there is growing recognition that such properties affect the physical characteristics, and chemistry, of atoms and molecules. Our visualizations are sufficiently accessible that, with some preparation, those with a nontechnical background can gain an appreciation of subtle quantum properties of atomic and other systems. By providing insights and modeling capability, our phase-space representation will be of great utility in understanding aspects of atomic physics and chemistry not available with current techniques.

Correlation-coupling entropy as a measure of strong electron correlation and fragment-conditional density spin polarization as a measure of electron entanglement

Quantum entanglement has been one of the hottest topics in current day physics, since it is the driving force behind quantum cryptography, quantum teleportation, and quantum computing. Several measures of quantification of entanglement have been proposed, each of which can often only be applied to a few specific systems. In this paper we derive a kinematic measure of entanglement that is capable of giving a full description of Einstein-Podolsky-Rosen entanglement in molecular systems. The associated ``coupled entropy'' energy contribution generates the correct amount of strong correlation energy for the ${\mathrm{H}}_{2}$ and ${\mathrm{N}}_{2}$ prototype systems, and is shown to be able to perform the same feat if it is explicitly used as the correlation component in the density-matrix functional context. And, finally, we propose a nonkinematic way to measure the entanglement of spins by using the conditional density of the system.

Quantum computing with classical bits

A bit-quantum map relates probabilistic information for Ising spins or classical bits to quantum spins or qubits. Quantum systems are subsystems of classical statistical systems. The Ising spins can represent macroscopic two-level observables, and the quantum subsystem employs suitable expectation values and correlations. We discuss static memory materials based on Ising spins for which boundary information can be transported through the bulk in a generalized equilibrium state. They can realize quantum operations as the Hadamard or CNOT-gate for the quantum subsystem. Classical probabilistic systems can account for the entanglement of quantum spins. An arbitrary unitary evolution for an arbitrary number of quantum spins can be described by static memory materials for an infinite number of Ising spins which may, in turn, correspond to continuous variables or fields. We discuss discrete subsets of unitary operations realized by a finite number of Ising spins. They may be useful for new computational structures. We suggest that features of quantum computation or more general probabilistic computation may be realized by neural networks, neuromorphic computing or perhaps even the brain. This does neither require small isolated entities nor very low temperature. In these systems the processing of probabilistic information can be more general than for static memory materials. We propose a general formalism for probabilistic computing for which deterministic computing and quantum computing are special limiting cases.

Probing the Lee–Yang zeros of a spin bath by correlation functions and entanglement of two spins

We study the Lee–Yang zeros of the quantum ferromagnetic Ising bath via the interaction with the two probe spins. Similarly, as in an earlier paper (Wei and Liu 2012 Phys. Rev. Lett. 109, 185701), the problem of detecting the zeros is reduced to the exploration of the time evolution of the probe spins. As a result, the relation between the Lee–Yang zeros of the bath and correlation functions of the probe system is obtained. Also, we obtain the relation between the Lee–Yang zeros and values of the entanglement of the probe spins. We apply these results to the 1D Ising spin model with nearest-neighbor interaction, which can be prepared on trapped atoms.

Entanglement balance of quantum (e,2e) scattering processes

The theory of quantum information constitutes the functional value of the quantum entanglement, i.e., quantum entanglement is essential for high fidelity of quantum protocols, while fundamental physical processes behind the formation of quantum entanglement are less relevant for practical purposes. In the present work, we explore physical mechanisms leading to the emergence of quantum entanglement in the initially disentangled system. In particular, we analyze spin entanglement of outgoing electrons in a nonrelativistic quantum $(e,2e)$ collision on a target with one active electron. Our description exploits the time-dependent scattering formalism for typical conditions of scattering experiments, and contrary to the customary stationary formalism operates with realistic scattering states. We quantify the spin entanglement in the final scattering channel through the pair concurrence and express it in terms of the experimentally measurable spin-resolved $(e,2e)$ triple differential cross sections. Besides, we consider Bell's inequality and inspect the regimes of its violation in the final channel. We address both the pure and the mixed initial spin state cases and uncover kinematical conditions of the maximal entanglement of the outgoing electron pair. The numerical results for the pair concurrence, entanglement of formation, and violation of Bell's inequality obtained for the $(e,2e)$ ionization process of atomic hydrogen show that the entangled electron pairs indeed can be formed in the $(e,2e)$ collisions even with spin-unpolarized projectile and target electrons in the initial channel. The positive entanglement balance---the difference between entanglements of the initial and final electron pairs---can be measured in the experiment.

Spin-Correlated Radical Pairs as Quantum Sensors of Bidirectional ET Mechanisms in Photosystem I.

Following light-generated electron transfer reactions in photosynthetic reaction center proteins, an entangled spin qubit (radical) pair is created. The exceptional sensitivity of entangled quantum spin states to weak magnetic interactions, structure, and local environments was used to monitor the directionality of electron transfer in Photosystem I (PSI). Electron paramagnetic resonance (EPR) spectra of radical pairs formed via each symmetric branch of cofactors, A or B, exhibit distinctive line shapes. By photochemical reduction and biochemical modification of PSI we created samples where the radical pair(s) from (1) only A branch, (2) only B branch, or (3) both A and B branches are detectable. These PSI samples were used to analyze the asymmetry of electron transfer as a function of temperature, freezing condition, and temperature cycling. The temperature dependency agrees with a dynamic model in which the conformational states of the protein regulate the directionality of electron transfer. High spectral resolution afforded by high-frequency (130 GHz) EPR, combined with extra resolution afforded by deuterated proteins, provides new mechanistic insight via structural and environmental sensitivity of the entangled electron spins of photogenerated radical pairs.

The cosmological constant effect on the quantum entanglement

In Schwarzschild-de Sitter space-time, the effect of a gravitational field near a massive body black hole on the spin entanglement has been studied for two-qubits in the case of triplet and singlet states of a two particles system in a circular geodesic motion. It is found that the effect of the cosmological constant on the robustness of the Wooters concurrence is more important in the triplet state than in the singlet one even in the extended region around the black hole

The Einstein-Podolsky-Rosen paradox and SU(2) relativity

The EPR paradox dates back to 1935 when Einstein et al., through the use of non commuting operators, proposed that quantum mechanics was not complete[1] in that it suggested a “spooky action at a distance.” Later in 1964 John Bell was able to express the dilemma in a simple inequality[2] involving spin singlet states. If the inequality were satisfied then Einstein was correct and if it were violated then it favored the quantum mechanics point of view. In what follows, we present two approaches to Bell’s inequality, and then offer an interpretation from the viewpoint of quantum mechanics based on the principle that the whole is more than the sum of its parts. This is then combined with the properties of the SU(2) group to give a more intuitive understanding of non-locality and spin entanglement from the perspective of the relativistic characteristics of rotations.

Signatures of magnetic-field-driven quantum phase transitions in the entanglement entropy and spin dynamics of the Kitaev honeycomb model

The main question we address is how to probe the fractionalized excitations of a quantum spin liquid (QSL), for example, in the Kitaev honeycomb model. By analyzing the energy spectrum and entanglement entropy, for antiferromagnetic couplings and a field along either [111] or [001], we find a gapless QSL phase sandwiched between the non-Abelian Kitaev QSL and polarized phases. Increasing the field strength towards the polarized limit destroys this intermediate QSL phase, resulting in a considerable reduction in the number of frequency modes and the emergence of a beating pattern in the local dynamical correlations, possibly observable in pump-probe experiments.

Exploring the entanglement of free spin- , spin-1 and spin-2 fields * * Supported by the NSFC (11875111)

In this study, we explore the entanglement of free spin- , spin-1, and spin-2 fields. We start with an example involving Majorana fields in 1+1 and 2+1 dimensions. Subsequently, we perform the Bogoliubov transformation and express the vacuum state with a particle pair state in the configuration space, which is used to calculate the entropy. This clearly demonstrates that the entanglement entropy originates from the particles across the boundary. Finally, we generalize this method to free spin-1 and spin-2 fields. These higher free massless spin fields have well-known complications owing to gauge redundancy. We deal with the redundancy by gauge-fixing in the light-cone gauge. We show that this gauge provides a natural tensor product structure in the Hilbert space, while surrendering explicit Lorentz invariance. We also use the Bogoliubov transformation to calculate the entropy. The area law emerges naturally by this method.

Quantum dissonance in chiral graphene nanoribbons

Based on the effective spin-ladder model, we study the properties of quantum dissonance (Q) between two edge spins in chiral graphene nanoribbons (CGNRs) thermalized with a reservoir at temperature T, and discuss the influences of relative location between two edge spins, ribbon width, temperature, and on-site Coulomb repulsion (U) on Q. The results show that Q is widely present in Wannier edge states. For intra-edge coupled spin pairs, quantum entanglement (E) is zero, but there still exists considerable value of Q. Interestingly, Q always keeps a constant for entangled edge spin pairs. Considering the thermal effect, it shows that Q always decays with the increasing temperature T, and the decay rate is very sensitive to the intensity of U. Compared Q with E and total quantum correlation (quantum discord, denoted by D), we conjecture that the quantum correlations for a bipartite Wannier edge state in CGNRs satisfy the relation Q ⩽ D–E.

Pauli-based fermionic teleportation with free massive particles by electron-exchange collisions

Fundamental non-locality in quantum mechanical scattering processes is investigated by means of Fermionic teleportation. Our scenario employs free massive particles, electrons and atoms, within a twofold electron-exchange collision approach whereby, in the first collision, also generating the necessary spin–spin entanglement between initially unpolarized electrons and atoms. It is shown that in a second collision an arbitrary spin polarization state of a free electron can be teleported onto the other electron which has never been in contact with the first one. The underlying scheme relies on and is a direct consequence of the Pauli-principle and makes use of a high symmetry in spin space thereby avoiding restoration of the teleported states. The scattering process (teleportation) is highly symmetric allowing for interchanging the electronic and atomic constituents without loss of generality. Re-interpretation of Li and Na data reveals the feasibility and capability of Fermionic teleportation demonstrated by numerical and experimental data for the teleportation fidelity.

Evolution of entanglement in electron–electron collisions

The collision between two electrons is treated in a time-dependent three-dimensional approach involving a two-electron wave packet, which is composed of stationary solutions of the two-electron Schroedinger equation with Coulomb interaction. As a quantitative measure of the entanglement between the two electrons we employ a renormalized linear entropy, which is readily obtainable from the one-electron reduced density matrix in real space. Starting with a non-entangled initial state consisting of two separate one-electron packets, the scattering process is visualized on a femtosecond time scale by a sequence of snap shots of the one-electron density. The corresponding evolution of the linear entropy is shown for several energy values up to 200 eV (per electron in the center-of-mass system). The maximal entanglement, which is characterized by the asymptotic value of the linear entropy, is found to decrease strongly with increasing energy. The entropy for anti-parallel spins turns out to be almost the same as for parallel spins, which means that spin entanglement is vastly dominated by spatial entanglement.

Photogenerated Spin-Entangled Qubit (Radical) Pairs in DNA Hairpins: Observation of Spin Delocalization and Coherence.

The ability to prepare physical qubits in specific initial quantum states is a critical requirement for their use in quantum information science (QIS). Subnanosecond photoinduced electron transfer in a structurally well-defined donor-acceptor system can be used to produce an entangled spin qubit (radical) pair in a pure initial singlet state fulfilling this criterion. Synthetic DNA is a promising platform on which to build spin qubit arrays with fixed spatial relationships; therefore, we have prepared a series of DNA hairpins in which naphthalenediimide (NDI) is the chromophore/acceptor hairpin linker, variable-length diblock A- and G-tracts are intermediate donors, and a stilbenediether (Sd) is the terminal donor. Photoexcitation of NDI in these DNA hairpins generates high-yield, long-lived, entangled spin qubit pairs at 85 K, and time-resolved and pulse electron paramagnetic resonance (EPR) spectroscopies are used to probe their spin dynamics. Specifically, measurements of the distance-dependent dipolar coupling between the two spins are used to obtain the average spin qubit pair distance in the absence of the terminal Sd donor and reveal that one of the spins is fully delocalized across up to five adjacent guanines in a G-tract on the EPR time scale. We have recently shown that extensive spin hopping between degenerate sites accessible to one spin of the pair may result in spin decoherence. However, we observe a strong out-of-phase electron spin echo envelope modulation (OOP-ESEEM) signal from the NDI•--Sd•+ spin qubit pair in DNA hairpins showing that spin coherence is maintained across a 2 adenine A-tract followed by a 2-4 guanine G-tract as a result of rapid spin transport to Sd. These results demonstrate that pulse-EPR can manipulate coherent spin states in DNA hairpins, which is essential for quantum gate operations relevant to QIS applications.

Cooling by Cooper pair splitting

The electrons forming a Cooper pair in a superconductor can be spatially separated preserving their spin entanglement by means of quantum dots coupled to both the superconductor and independent normal leads. We investigate the thermoelectric properties of such a Cooper pair splitter and demonstrate that cooling of a reservoir is an indication of non-local correlations induced by the entangled electron pairs. Moreover, we show that the device can be operated as a non-local thermoelectric heat engine. Both as a refrigerator and as a heat engine, the Cooper pair splitter reaches efficiencies close to the thermodynamic bounds. As such, our work introduces an experimentally accessible heat engine and a refrigerator driven by entangled electron pairs in which the role of quantum correlations can be tested.

Group-theoretical classification of multipole order: Emergent responses and candidate materials

The multipole moment is an established concept of electrons in solids. Entanglement of spin, orbital, and sublattice degrees of freedom is described by the multipole moment, and spontaneous multipole order is a ubiquitous phenomenon in strongly correlated electron systems. In this paper, we present group-theoretical classification theory of multipole order in solids. Intriguing duality between the real space and momentum space properties is revealed for odd-parity multipole order which spontaneously breaks inversion symmetry. Electromagnetic responses in odd-parity multipole states are clarified on the basis of the classification theory. A direct relation between the multipole moment and the magnetoelectric effect, Edelstein effect, magnetopiezoelectric effect, and dichromatic electron transport is demonstrated. More than 110 odd-parity magnetic multipole materials are identified by the group-theoretical analysis. Combining the list of materials with the classification tables of multipole order, we predict emergent responses of the candidate materials.

Entanglement and entropy in electron–electron scattering

Treating Coulomb scattering of two free electrons in a stationary approach, we explore the momentum and spin entanglement created by the interaction. We show that a particular discretisation provides an estimate of the von Neumann entropy of the one-electron reduced density matrix from the experimentally accessible Shannon entropy.For spinless distinguishable electrons the entropy is sizeable at low energies, indicating strong momentum entanglement, and drops to almost zero at energies of the order of 10 keV when the azimuthal degree of freedom is integrated out, i.e. practically no entanglement and almost pure one-electron states. If spin is taken into account, the entropy for electrons with antiparallel spins should be larger than in the parallel-spin case, since it embodies both momentum and spin entanglement. Surprisingly, this difference, as well as the deviation from the spin-less case, is extremely small for the complete scattering state. Strong spin entanglement can however be obtained by post-selecting states at scattering angle π/2.

Magnetic resonance with number states versus coherent states

In this paper, we study the interaction of quantized radio-frequency (rf)/microwave-field with nuclear spin in Nuclear Magnetic Resonance (NMR) or electron spin in Electron Paramagnetic Resonance (EPR). In magnetic resonance experiments, interaction of quantized rf-field leads to entanglement of spin with the electromagnetic field. In an entangled state, the spins are depolarized with no net transverse magnetization, which cannot give a detectable signal in inductive detection (or Q detection) that detects transverse magnetization. We show that when the electromagnetic field is in coherent state, inductive detection becomes possible. We use the mathematics of quantum optics to study the evolution of a coherent rf-field with a sample of all polarized spins. We show that evolution can be solved in closed form as a separable state of rf-field and spin ensemble, where spin ensemble evolves according to Bloch equations in an rf-field. We extend the analysis and results to a spin ensemble with Boltzmann polarization. The rabi frequency and coupling strength of spins to rf-field depends on number state of the rf-field. We show that in interaction with a coherent rf-field, this variation in coupling strength introduces negligible error.