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A researcher in spintronics whose review with Daniel Lacour relates electrical resistance to the magnetic configuration of layered devices. A magnetic tunnel junction consists of two magnetic conductors separated by a thin insulating barrier; quantum tunnelling through the barrier depends on the electronic states available for each electron spin. This produces tunnelling magnetoresistance, illustrating how the magnetic state of a device can be read through an electrical measurement.^[ref]

An experimental physicist who coauthored the 2015 Delft electron-spin Bell test. The experiment entangled electron spins at sites separated by 1.3 kilometres. Efficient readout addressed the detection loophole, while fast random measurement choices and the separation addressed the locality loophole. The observed violation of a Bell inequality tested local realism without relying on fair sampling of undetected events.^[ref]

A researcher whose work with Alain Schuhl explains giant magnetoresistance through spin-dependent conduction in magnetic multilayers. In the Mott two-current model, the two electron spin channels can carry electric current with different resistances. Changing the relative magnetization directions of adjacent layers changes how strongly each channel is scattered. Their treatment connects microscopic scattering with a measurable resistance change and makes explicit the assumptions needed to treat the spin channels independently.^[ref]

The Bell test reported by Bas Hensen and collaborators used electron spins separated by $1.3\mathrm{km}$, efficient spin readout and rapid random measurement settings. Those features addressed detection and locality loopholes together. Its result tests Bell local causality with the stated experimental assumptions, rather than ruling out every possible hidden-variable theory.^[ref]

Let an isolated donor impurity admit an empty ionized state with statistical weight $g_0$ and a singly occupied neutral state with statistical weight $g_1$, with double occupation excluded. Its grand canonical ensemble weights are $g_0$ and $g_1{e}^{-\beta ({ϵ}_D-\mu )}$, so $r=g_1/g_0$ multiplies the occupied-to-empty ratio. A nondegenerate empty state and two allowed electron spin orientations give $r=2$; a simplified single-state occupation model uses $r=1$. With negligible electron holes and uncompensated donor impurities, charge neutrality and nondegenerate conduction occupation imply $n^2/(N_D-n)=(N_c/r)e^{-E_i/(k_{B}T)}$, where $E_i$ is the donor binding energy and $N_c$ the effective density of states.

A theoretical physicist whose research connects spin-orbit coupling with electrical control of electron spin. The coupling allows the electron's motion and local electric environment to affect its spin, providing routes to manipulation and transport in semiconductors. His review emphasizes how this link changes the meaning of spin currents and their relation to measurable spin accumulation.^[ref]

Fedor Jelezko works on solid-state quantum optics and spin control in diamond. His Ulm University CV identifies him in full and lists the exact 2004 nuclear-spin paper whose first-author byline is F. Jelezko, verifying the connection between the full name and the abbreviated record.^[ref]

That experiment addressed an electron spin coupled to a single Carbon-13 nuclear spin at a nitrogen-vacancy center. A laser initialized and read out the electron-spin-dependent signal, while microwave and radio frequency pulses manipulated the coupled levels. Nuclear-state changes were detected through the electron spin. The team observed nuclear Rabi oscillations and demonstrated a conditional two-qubit gate, providing a physical test of coherent control of an individually addressed spin system.^[ref]

For an original ideal pulse example, let a selected transition have resonant Rabi frequency $f_R=100\mathrm{kHz}$ and start entirely in one level. The two-level model gives transition probabilityA $2.5\mu \mathrm{s}$ pulse gives $P=1/2$, while a $5.0\mu \mathrm{s}$ pulse gives $P=1$. Scanning the pulse duration reveals an oscillation rather than a single population change. These are chosen ideal values; detuning, relaxation and readout noise limit a real measurement.

The isotropic magnetic interaction of a nuclear magnetic dipole moment with electron spin density at the atomic nucleus. A nonrelativistic penetrating $s$ orbital can have $|{\psi }_s(0){|}^2\ne 0$ and a substantial contact contribution to hyperfine structure. A filled paired shell cancels its net contact spin density in the independent-particle approximation; unpaired occupation and core polarization can restore it. Relativistic and finite nuclear-size effects modify the point-contact description.

An experimental physicist who studied electrical injection of electron spin and spin accumulation in lateral metallic devices. A separate detector measured the spin signal away from the main charge-current path, suppressing ordinary magnetoresistance backgrounds. Comparing electrode materials and measuring at low and room temperature made the apparatus a test of how far spin information survives in a metal.^[ref]

An experimental condensed matter physicist who coauthored controlled rotations of a single electron spin in a double quantum dot. An on-chip alternating magnetic field drove electron paramagnetic resonance; short bursts produced Rabi oscillations observed through spin-dependent transport. The experiment supplied a way to manipulate a spin qubit in a gated quantum dot, rather than only prepare or measure it.^[ref]

Friedrich Hund organized complicated atomic spectral lines through relationships between the angular momenta and energy levels of many-electron configurations. In modern notation, a term symbol ${}^{2S+1}{L}_J$ records total electron spin $S$, total orbital angular momentum $L$ and coupled total angular momentum $J$. For example, $S=1$ permits three spin projections, whereas $S=0$ permits one. The classification reduces a large pattern of lines to relationships between fewer quantum states. This modern spin notation should be distinguished from the historical language of his original spectral analysis.^[ref]

An effective local exchange coupling can favor parallel electron spins in different orbitals on the same atom. The displayed sign convention represents that preference. It underlies the high-spin tendency in Hund's rules and the alignment of itinerant and core spins used in double exchange. The coupling is an effective description of intra-atomic Coulomb and exchange energies, rather than a separate classical magnetic force.

For electron spin $s=1/2$, first add orbital and spin angular momenta to obtain $j=L\pm 1/2$. For nuclear spin $I=1$, add again to obtain $F=|j-1|,|j-1|+1,\dots ,j+1$. The projection has $2F+1$ possible values. A hydrogenic bound state still requires $L\le n-1$.

An interaction between a nucleus's magnetic or electric multipole moments and its electronic surroundings. Magnetic contact and dipolar terms can couple nuclear spin to electron spin or orbital magnetic moments. The resulting small energy shifts contribute to hyperfine structure; the contact term can also mediate conduction-electron-mediated exchange between nuclear moments in a metal.

An experimental condensed matter physicist who coauthored single-shot electrical measurement of an individual electron spin. The quantum dot converted the spin state into a charge change, detected by a nearby quantum point contact. This made the outcome of one trapped electron's spin measurement accessible electrically, a necessary operation for proposed semiconductor qubits.^[ref]

Landau diamagnetism is the orbital response of mobile electrons to an applied magnetic field, arising from quantization of their transverse motion. For a noninteracting three-dimensional isotropic electron gas with quadratic dispersion, electron spin with $g=2$ and magnetic fields weak enough for the smooth-response limit, its susceptibility is ${\chi }_L=-{\chi }_P/3$, where ${\chi }_P$ is the Pauli paramagnetism susceptibility. Band effective masses, interactions, dimensionality and resolved magnetic quantum oscillations can change this simple relation.

For a left-handed incoming neutrino, unpolarized electrons, and electron vector/axial couplings $c_V,c_A$, the four-fermion interaction gives $\overline{|\mathcal{M}{|}^2}=4G_F^2[(c_V+c_A{)}^2{s}^2+(c_V-c_A{)}^2{u}^2]$. Integrating massless two-body Lorentz-invariant phase space yields $\sigma =G_F^{2}s(c_V^2+c_V{c}_A+c_A^2)/(3\pi )$. The electron spin average is included, while no sterile neutrino helicity is averaged in.

A nitrogen-vacancy center is a point defect in diamond consisting of a nitrogen atom occupying a carbon lattice site next to a vacancy defect. The surrounding diamond remains the host crystal; the adjacent impurity and missing atom create a localized electronic system. Its electron spin and optical response make individual defects accessible to quantum control.^[ref]

A2004 experiment coupled the defect's electron spin to one nearby carbon-13 nuclear spin. Laser pulses provided optical preparation/readout, while microwave and radio frequency pulses manipulated the spin system. The researchers observed coherent nuclear-spin oscillations and implemented a conditional two-qubit operation.^[ref] Detecting fluorescence thus provided access to a spin experiment inside a solid, rather than requiring electrical contact to the individual defect.

For an ideal resonantly driven two-state model, a Rabi oscillation gives transition probability $P(t)={\sin }^2(\Omega t/2)$, where $\Omega$ is the angular Rabi frequency. A pulse lasting $\pi /\Omega$ ideally transfers the population, while $2\pi /\Omega$ returns it. This illustrates controlled coherent evolution; actual fluorescence counts and gate accuracy also depend on preparation, readout and loss of coherence.

A localized orbital with two electron spin states has energies $E_0=0$, $E_1=ϵ$ and $E_2=2ϵ+U$. Its zero-temperature equilibrium occupation minimizes ${\mathcal{E}}_N=E_N-\mu N$, where $\mu$ is the chemical potential. For repulsion $U>0$, the occupation is successively $0,1,2$ as $\mu$ crosses $ϵ$ and $ϵ+U$. For attraction $U<0$, the singly occupied state is never the minimum: the occupation jumps from $0$ to $2$ at $\mu =ϵ+U/2$. Exactly at a crossing the ground-state occupation is not unique.

At positive temperature, its grand canonical partition function is $\Xi =1+2e^{-\beta (ϵ-\mu )}+e^{-\beta (2ϵ+U-2\mu )}$, where $\beta =1/(k_{B}T)$. The expected value of the occupation follows by differentiating: $⟨N⟩=k_{B}T{\partial }_{\mu }\ln \Xi$. The factor two counts the two singly occupied microstates, not an additional pair state.

Write $k=e^2/(4\pi {ϵ}_0)$ and retain the nuclear Coulomb potential. In spherical coordinates, the total potential energy iswhen $\beta =-\alpha /2$; $P_2(u)=(3u^2-1)/2$ is a Legendre polynomial. Treat the added term using quadratic anisotropic perturbation of hydrogen and degenerate perturbation theory in the $n=2$ hydrogen energy eigenbasis. It preserves parity and $m$, so it cannot mix $2s$ with $2p$, or distinct $2p$ magnetic sublevels.

For a hydrogen atom, the hydrogen radial second moment givesThe angular expectation values of ${\cos }^2\theta$ are $1/3$ for an $s$ orbital, $3/5$ for $p_0$, and $1/5$ for $p_{\pm 1}$, obtained by integrating the squared spherical harmonics. Therefore the five lowest spatial quantum states, counting statistical weight, have first-order energy levelsEach spatial quantum state has two electron spin states when spin-orbit coupling and the magnetic field are omitted. Thus these are five spatial states but only three distinct first-order energies; five distinct energies would be an incorrect reading. The accidental $2s,2p_{\pm 1}$ equality can be lifted at higher order. Quantitatively the added shifts must also be small compared with neighboring principal-shell gaps; $\alpha \ll k/a_0^3$ is an asymptotic condition, not a guarantee for arbitrary large $n$.

For general $\beta$, the $1s$ expectation value isIt does not cancel every order. At $\beta =-2\alpha$, $V_{\mathrm{ext}}=-2\alpha r^2{P}_2(\cos \theta )$ couples $1s$ to $d$ orbitals. For example its angular matrix element with $Y_{20}$ is $1/\sqrt{5}$, and the $3d$ radial matrix element is nonzero. The second-order nondegenerate perturbation theory sum has negative denominators, so this is a concrete nonzero higher-order contribution.

There is also a global limitation: for either negative $\beta$ above, $V(0,0,z)=-k/|z|+\beta z^2\to -\infty$. A localized wavepacket translated far along $z$ has fixed kinetic energy but arbitrarily negative potential energy, proving there is no true lowest energy level. The results describe local perturbative resonance poles, or a potential completed to a confining form far from the atomic nucleus. No globally exact ground-state cancellation exists for the potential as printed.