Spin Projection Research Articles

Observation of Gravitational Waves from Two Neutron Star–Black Hole Coalescences

Abstract We report the observation of gravitational waves from two compact binary coalescences in LIGO’s and Virgo’s third observing run with properties consistent with neutron star–black hole (NSBH) binaries. The two events are named GW200105_162426 and GW200115_042309, abbreviated as GW200105 and GW200115; the first was observed by LIGO Livingston and Virgo and the second by all three LIGO–Virgo detectors. The source of GW200105 has component masses 8 . 9 − 1 . 5 + 1. 2 and 1. 9 − 0. 2 + 0. 3 M ⊙ , whereas the source of GW200115 has component masses 5. 7 − 2 . 1 + 1. 8 and 1. 5 − 0. 3 + 0. 7 M ⊙ (all measurements quoted at the 90% credible level). The probability that the secondary’s mass is below the maximal mass of a neutron star is 89%–96% and 87%–98%, respectively, for GW200105 and GW200115, with the ranges arising from different astrophysical assumptions. The source luminosity distances are 280 − 110 + 110 and 300 − 100 + 150 Mpc , respectively. The magnitude of the primary spin of GW200105 is less than 0.23 at the 90% credible level, and its orientation is unconstrained. For GW200115, the primary spin has a negative spin projection onto the orbital angular momentum at 88% probability. We are unable to constrain the spin or tidal deformation of the secondary component for either event. We infer an NSBH merger rate density of 45 − 33 + 75 Gpc − 3 yr − 1 when assuming that GW200105 and GW200115 are representative of the NSBH population or 130 − 69 + 112 Gpc − 3 yr − 1 under the assumption of a broader distribution of component masses.

Spin in a planar relativistic fermion problem

In this work we seek to clarify the role of spin in a quantum relativistic two-dimensional world. To this end, we solve the Dirac equation for two-dimensional motion with circular symmetry using both 3+1 and 2+1 Dirac equations for a fermion interacting with a uniform magnetic field perpendicular to the plane of motion. We find that, as remarked already by other authors, the spin projection s in the direction of the magnetic field can be emulated in the 2+1 Hamiltonian as a parameter preserving the anti-commutation relations between the several terms in the Hamiltonian, although it is not a quantum number in the two-dimensional world. We also find that there is an equivalence between a pure vector potential and a pure tensor potential under circular symmetry, if the former is multiplied by s. This holds for any dependence on the polar coordinate ρ. For the particular case of the uniform magnetic field, this means that this problem is equivalent to the two-dimensional Dirac oscillator.

Tunneling current and noise of entangled electrons in correlated double quantum dot

We developed general approach for the analysis of tunneling current and its zero frequency noise for a wide class of systems where electron transport occurs through the intermediate structure with localized electrons. Proposed approach opens the possibility to study electron transport through multi-electron correlated states and allows to reveal the influence of spatial and spin symmetry of the total system on the electron transport. This approach is based on Keldysh diagram technique in pseudo-particle representation taking into account the operator constraint on the number of pseudo-particles, which gives the possibility to exclude non-physical states. It was shown that spatial and spin symmetry of the total system can block some channels for electron transport through the correlated quantum dots. Moreover, it was demonstrated that the stationary tunneling current and zero frequency noise in correlated coupled quantum dots depend on initial state of the system. In the frame of the proposed approach it was also shown that for the parallel coupling of two correlated quantum dots to the reservoirs tunneling current and its zero frequency noise are suppressed if tunneling occurs through the entangled triplet state with zero total spin projection on the z axis or enhanced for the tunneling through the singlet state in comparison with electron transport through the uncorrelated localized single-electron state. Obtained results demonstrate that two-electron entangled states in correlated quantum dots give the possibility to tune the zero frequency noise amplitude by blocking some channels for electron transport that is very promising in the sense of two-electron entangled states application in quantum communication and logic devices. The obtained nonmonotonic behavior of Fano factor as a function of applied bias is the direct manifestation of the possibility to control the noise to signal ration in correlated quantum dots. We also provide detailed calculations of current and noise for both single type of carriers and two different types of carriers in the presence and in the absence of Coulomb interaction in Supplementary materials.

Optimizing Optical Tweezers Experiments for Magnetic Resonance Sensing with Nanodiamonds

In this Article we explore the requirements for enabling high quality optically detected magnetic resonance (ODMR) spectroscopy in a conventional gradient force optical tweezers using nanodiamonds containing nitrogen-vacancy (NV-) centers. We find that modulation of the infrared (1064 nm) trapping laser during spectroscopic measurements substantially improves the ODMR contrast compared with continuous wave trapping. The work is significant as it allows trapping and quantum sensing protocols to be performed in conditions where signal contrast is substantially reduced. We demonstrate the utility of the technique by resolving NV- spin projections within the ODMR spectrum. Manipulating the orientation of the nanodiamond via the trapping laser polarization, we observe changes in spectral features. Theoretical modeling then allows us to infer the crystallographic orientation of the NV-. This is an essential capability for future magnetic sensing applications of optically trapped nanodiamonds.

Flipping spins in mass transferring binaries and origin of spin-orbit misalignment in binary black holes

Close stellar binaries are prone to undergo a phase of stable mass transfer in which a star loses mass to its companion. Assuming that the donor star loses mass along the instantaneous interstellar axis, we derive the orbit-averaged equations of motion describing the evolution of the donor rotational angular momentum vector (spin) which accompanies the transfer of mass. We consider: (i) a model in which the mass transfer rate is constant within each orbit and (ii) a phase-dependent rate in which all mass per orbit is lost at periapsis. In both cases, we find that the ejection of $\gtrsim 30$ per cent of the donor's initial mass causes its spin to nearly flip onto the orbital plane of the binary, independently of the initial spin-orbit alignment. Moreover, we show that the spin flip due to mass transfer can easily dominate over tidal synchronisation in any giant stars and main-sequence stars with masses $\sim1.5$ to $5\,\rm M_\odot$. Finally, the general equations of motion, including tides, are used to evolve a realistic population of massive binary stars leading to the formation of binary black holes. Assuming that the stellar core and envelope are fully coupled, the resulting tilt of the first-born black hole reduces its spin projection onto the orbit normal by a factor $\sim\mathcal{O}(0.1)$. This result supports previous studies in favour of an insignificant contribution to the effective spin projection, $\chi_{\rm eff}$, in binary black holes formed from the evolution of field binaries.

Spin transport in polarization induced two-dimensional electron gas channel in c-GaN nano-wedges

A two-dimensional electron gas (2DEG), which has recently been shown to develop in the central vertical plane of a wedge-shaped c-oriented GaN nanowall due to spontaneous polarization effect, offers a unique scenario, where the symmetry between the conduction and valence band is preserved over the entire confining potential. This results in the suppression of Rashba coupling even when the shape of the wedge is not symmetric. Here, for such a 2DEG channel, relaxation time for different spin projections is calculated as a function of donor concentration and gate bias. Our study reveals a strong dependence of the relaxation rate on the spin-orientation and density of carriers in the channel. Most interestingly, relaxation of spin oriented along the direction of confinement has been found to be completely switched off. Upon applying a suitable bias at the gate, the process can be switched on again. Exploiting this fascinating effect, an electrically driven spin-transistor has been proposed.

Transformation of spin and orbital angular momentum in second-harmonic generation process at oblique incidence of light from the surface of an isotropic medium with spatial dispersion of quadratic nonlinearity.

We discuss key features of the conversion of spin and orbital angular momentum of electromagnetic waves in the process of second-harmonic generation from the surface of the isotropic medium at oblique incidence. Conservation of the projections of spin and orbital parts of angular momentum of interacting waves onto the normal to the surface is shown for an arbitrary case of polarization and mode structure of the incident light beam.

Spin-projected QM/MM Free Energy Simulations for Oxidation Reaction of Guanine in B-DNA by Singlet Oxygen.

Guanine is the most susceptible base to oxidation damage induced by reactive oxygen species including singlet oxygen (1O2, 1Δg). We clarify whether the first step of guanine oxidation in B−DNA proceeds via either a zwitterionic or a diradical intermediate. The free energy profiles are calculated by means of a combined quantum mechanical and molecular mechanical (QM/MM) method coupled with the adaptive biasing force (ABF) method. To describe the open‐shell electronic structure of 1O2 correctly, the broken‐symmetry spin‐unrestricted density functional theory (BS−UDFT) with an approximate spin projection (AP) correction is applied to the QM region. We find that the effect of spin contamination on the activation and reaction free energies is up to ∼8 kcal mol−1, which is too large to be neglected. The QM(AP−ULC−BLYP)/MM‐based free energy calculations also reveal that the reaction proceeds through a diradical transition state, followed by a conversion to a zwitterionic intermediate. Our computed activation energy of 5.2 kcal mol−1 matches experimentally observed range (0∼6 kcal mol−1).

Simplicity Out of Complexity: Band Structure for W20O58 Superconductor.

The band structure, density of states, and the Fermi surface of a recently discovered superconductor, oxygen-deficient tungsten oxide WO that is equivalent to WO, is studied within the density functional theory (DFT) in the generalized gradient approximation (GGA). Here we show that despite the extremely complicated structure containing 78 atoms in the unit cell, the low-energy band structure is quite feasible. Fermi level is crossed by no more than 10 bands per one spin projection (and even 9 bands per pseudospin projection when the spin-orbit coupling is considered) originating from the t 5d-orbitals of tungsten atoms forming zigzag chains. These bands become occupied because of the specific zigzag octahedra distortions. To demonstrate the role of distortions, we compare band structures of WO with the real crystal structure and with the idealized one. We also propose a basis for a minimal low-energy tight-binding model for WO.

Bell inequalities for entangled qubits: quantitative tests of quantum character and nonlocality on quantum computers.

This work provides quantitative tests of the extent of violation of two inequalities applicable to qubits coupled into Bell states, using IBM's publicly accessible quantum computers. Violations of the inequalities are well established. Our purpose is not to test the inequalities, but rather to determine how well quantum mechanical predictions can be reproduced on quantum computers, given their current fault rates. We present results for the spin projections of two entangled qubits, along three axes A, B, and C, with a fixed angle θ between A and B and a range of angles θ' between B and C. For any classical object that can be characterized by three observables with two possible values, inequalities govern relationships among the probabilities of outcomes for the observables, taken pairwise. From set theory, these inequalities must be satisfied by all such classical objects; but quantum systems may violate the inequalities. We have detected clear-cut violations of one inequality in runs on IBM's publicly accessible quantum computers. The Clauser-Horne-Shimony-Holt (CHSH) inequality governs a linear combination S of expectation values of products of spin projections, taken pairwise. Finding S > 2 rules out local, hidden variable theories for entangled quantum systems. We obtained values of S greater than 2 in our runs prior to error mitigation. To reduce the quantitative errors, we used a modification of the error-mitigation procedure in the IBM documentation. We prepared a pair of qubits in the state |00〉, found the probabilities to observe the states |00〉, |01〉, |10〉, and |11〉 in multiple runs, and used that information to construct the first column of an error matrix M. We repeated this procedure for states prepared as |01〉, |10〉, and |11〉 to construct the full matrix M, whose inverse is the filtering matrix. After applying filtering matrices to our averaged outcomes, we have found good quantitative agreement between the quantum computer output and the quantum mechanical predictions for the extent of violation of both inequalities as functions of θ'.

Estimation of spin contamination errors in DFT/plane-wave calculations of solid materials using approximate spin projection scheme

Estimation and the importance of spin contamination errors (SCEs) in theoretical calculations related to open-shell molecular systems are well known. However, there is no estimation scheme available for density functional theory (DFT)/plane-wave, a standard first-principles method for solid materials. Therefore, in this study, we established the estimation scheme of SCE in DFT/plane-wave using approximate spin projection, and the new scheme was applied to typical models with stable antiferromagnetic states to illustrate the importance of SCE correction in solid systems.

Source properties of the lowest signal-to-noise-ratio binary black hole detections

We perform a detailed parameter estimation study of binary black hole merger events reported in Zackay et al. and Venumadhav et al.. These are some of the faintest signals reported so far, and hence, relative to the loud events in the GWTC-1 catalog, the data should have lesser constraining power on their intrinsic parameters. Hence we examine the robustness of parameter inference to choices made in the analysis, as well as any potential systematics. We check the impact of different methods of estimating the noise power spectral density, different waveform models, and different priors for the compact object spins. For most of the events, the resulting differences in the inferred values of the parameters are much smaller than their statistical uncertainties. The estimation of the effective spin parameter $\chi_{\mathrm{eff}}$, i.e. the projection of the mass-weighted total spin along the angular momentum, can be sensitive to analysis choices for two of the sources with the largest effective spin magnitudes, GW151216 and GW170403. The primary differences arise from using a 3D isotropic spin prior: the tails of the posterior distributions should be interpreted with care and due consideration of the other data analysis choices.

Quasiparticle Mass Enhancement as a Measure of Entanglement in the Kondo Problem.

We analyze the quantum entanglement between opposite spin projection electrons in the ground state of the Anderson impurity model. In this model, a single level impurity with intralevel repulsion U is tunnel coupled to a free electron gas. The Anderson model presents a strongly correlated many body ground state with mass enhanced quasiparticle excitations. We find, using both analytical and numerical tools, that the quantum entanglement between opposite spin projection electrons is a monotonic universal function of the quasiparticle mass enhancement Z in the Kondo regime. This indicates that the interaction induced mass enhancement, which is generally used to quantify correlations in quantum many body systems, could be used as a measure of entanglement in the Kondo problem.

Spin Resonance in a Quantum Dot at the Edge of a Topological Insulator with the Inclusion of Continuum States

The dynamics of electronic states under the action of a periodic electric field applied to a quantum dot created by magnetic barriers at the one-dimensional edge of a two-dimensional topological insulator based on a HgTe/CdTe quantum well has been studied. A configuration with two discrete levels is considered and transitions to continuum states above barriers are taken into account. The frequency of oscillations of the discrete level populations has been calculated for various field amplitudes. It has been shown numerically and analytically that the inclusion of the continuous spectrum leads to a decrease in the total population of discrete levels in time. The characteristic times of this decrease corresponding to transitions to continuum have been determined. The dynamics of average values of the energy, spin projections, coordinates, local probability density, and local spin density has been calculated. Time-averaged local probability density current that describes the quantum dot escape at transitions to the continuous spectrum has been calculated. The results of this work can be useful for the design of new generations of nanoelectronics and spintronics devices based on topological insulators.

PT -Symmetric Qubit-System States in the Probability Representation of Quantum Mechanics

PT-symmetric qubit-system states are considered in the probability representation of quantum mechanics. The new energy eigenvalue equation for probability distributions identified with qubit and qutrit states is presented in an explicit form. A possibility to test PT-symmetry and its violation by measuring the probabilities of spin projections for qubits in three perpendicular directions is discussed.

Filtering spins by scattering from a lattice of point magnets

Nature creates electrons with two values of the spin projection quantum number. In certain applications, it is important to filter electrons with one spin projection from the rest. Such filtering is not trivial, since spin-dependent interactions are often weak, and cannot lead to any substantial effect. Here we propose an efficient spin filter based upon scattering from a two-dimensional crystal, which is made of aligned point magnets. The polarization of the outgoing electron flux is controlled by the crystal, and reaches maximum at specific values of the parameters. In our scheme, polarization increase is accompanied by higher reflectivity of the crystal. High transmission is feasible in scattering from a quantum cavity made of two crystals. Our findings can be used for studies of low-energy spin-dependent scattering from two-dimensional ordered structures made of magnetic atoms or aligned chiral molecules.

238U FISSION NEAR THE THRESHOLD

Using the data on angular distribution of fission fragments, a threshold has been determined in a dipole fission channel with J = 1 spin projection to the nucleus symmetry axis. It has been shown that the peak observed in the 238U fission cross section is determined by the contribution from the quadrupole excitation.

Electronic and magnetic properties of graphene quantum dots with two charged vacancies

Electronic and magnetic properties of a system of two charged vacancies in hexagonal shaped graphene quantum dots are investigated using a mean-field Hubbard model as a function of the Coulomb potential strength β of the charge impurities and the distance R between them. For β=0, the magnetic properties of the vacancies are dictated by Lieb’s rules where the opposite (same) sublattice vacancies are coupled antiferromagnetically (ferromagnetically) and exhibit Fermi oscillations. Here, we demonstrate the emergence of a non-magnetic regime within the subcritical region: as the Coulomb potential strength is increased to β∼0.1, before reaching the frustrated atomic collapse regime, the magnetization is strongly suppressed and the ground state total spin projection is given by Sz=0 both for opposite and same sublattice vacancy configurations. When long-range electron–electron interactions are included within extended mean-field Hubbard model, the critical value for the frustrated collapse increases from βcf∼0.28 to βcf∼0.36 for R<27Å.

Frequency of Spin-Injection Radiation in the Magnetic Junction as a Function of the Spin Mobility of Electrons

Taking into account the difference in the mobilities of electrons with different spin projections, the frequencies of spin-injection radiation in the current-carrying magnetic contact formed by two ferromagnets are calculated. It is shown that these frequencies are in the terahertz range at a certain current density exceeding the threshold value, and the current density required to generate terahertz radiation can be, even at small values of the electron mobility difference, two orders of magnitude less than that in the absence of the electron mobility difference. The effect of the spin polarization ratio of ferromagnets that form a magnetic junction on the radiation frequency is analyzed.

Associative memory on qutrits by means of quantum annealing

When associative memory is implemented on the well-studied Hopfield network, patterns are recorded in the interaction constants between binary neurons. These constants are chosen so that each pattern should have its own minimum energy of the system described by the Ising model. In the quantum version of the Hopfield network, it was proposed to recall such states by the adiabatic change of the Hamiltonian in time. Qubits, quantum elements with two states, for example, spins with S = 1/2 were considered as neurons. In this paper, for the first time, we study the function of associative memory using three-level quantum elements—qutrits, represented by spins with S = 1. We record patterns with the help of projection operators. This choice is due to the need to operate with a state with a zero spin projection, whose interaction with the magnetic field vanishes. We recall the state corresponding to one of the patterns recorded in the memory, or superposition of such states by means of quantum annealing. To equalize the probabilities of finding the system in different states of superposition, an auxiliary Hamiltonian is proposed, which is turned off at the end of evolution. Simulations were performed on two and three qutrits and an increase in the memory capacity after replacing qubits with qutrits was shown.