Pauli Spin Research Articles

Valley–spin blockade and spin resonance in carbon nanotubes

The manipulation and readout of spin qubits in quantum dots have been successfully achieved using Pauli blockade, which forbids transitions between spin-triplet and spin-singlet states. Compared with spin qubits realized in III-V materials, group IV materials such as silicon and carbon are attractive for this application because of their low decoherence rates (nuclei with zero spins). However, valley degeneracies in the electronic band structure of these materials combined with Coulomb interactions reduce the energy difference between the blocked and unblocked states, significantly weakening the selection rules for Pauli blockade. Recent demonstrations of spin qubits in silicon devices have required strain and spatial confinement to lift the valley degeneracy. In carbon nanotubes, Pauli blockade can be observed by lifting valley degeneracy through disorder, but this makes the confinement potential difficult to control. To achieve Pauli blockade in low-disorder nanotubes, quantum dots have to be made ultrasmall, which is incompatible with conventional fabrication methods. Here, we exploit the bandgap of low-disorder nanotubes to demonstrate robust Pauli blockade based on both valley and spin selection rules. We use a novel stamping technique to create a bent nanotube, in which single-electron spin resonance is detected using the blockade. Our results indicate the feasibility of valley-spin qubits in carbon nanotubes.

Magnetic field dependence of Pauli spin blockade: A window into the sources of spin relaxation in silicon quantum dots

We investigate spin relaxation in a silicon double quantum dot via leakage current through Pauli blockade as a function of interdot detuning and magnetic field. A dip in leakage current as a function of magnetic field on an $\ensuremath{\sim}40$ mT field scale is attributed to spin-orbit mediated spin relaxation. On a larger ($\ensuremath{\sim}400$ mT) field scale, a peak in leakage current is seen in some, but not all, Pauli-blocked transitions, and is attributed to spin-flip cotunneling. Both dip and peak structure show good agreement between theory and experiment.

On the Majorana Equation: Relations between Its Complex Two-Component and Real Four-Component Eigenfunctions

We first derive without recourse to the Dirac equation the two-component Majorana equation with a mass term by a direct linearization of the relativistic dispersion relation of a massive particle. Thereby, we make only use of the complex conjugation operator and the Pauli spin matrices, corresponding to the irreducible representation of the Lorentz group. Then we derive the complex two-component eigenfunctions of the Majorana equation and the related quantum fields in a concise way, by exploiting the so-called chirality conjugation operator that involves the spin-flip operator. Subsequently, the four-component spinor solutions of the real Majorana equation are derived, and their intrinsic relations with the spinors of the complex two-component version of the Majorana equation are revealed and discussed extensively.

Compensation of rotation effect in a combination of retarders

In a cascaded system comprising a combination of oblique retarders, the effect of optical rotation is observed in addition to the overall retardation. This shows that the combined system does not behave as a pure oblique retarder. Analyzing such a general system using Pauli Spin matrices, it is shown that the effect of optical rotation may be completely annulled through the use of a suitably oriented retarder at the output of the cascaded system. The analysis assumes monochromaticity of the illuminating light beam.

Characteristics of Quantum Magnetosonic-Wave Dispersion

Using the quantum magnetohydrodynamics model, linear dispersion of magnetosonic waves are studied in a quasineutral quantum electron-ion plasmas in two distinct regimes of nonrelativistic and relativistic degeneracies taking into account the plasma composition effect. It is shown that the paramagnetic spin effects of the degenerated electrons plays a key role in dynamics of magnetosonic waves. The linear wave speed is found to have minimum value at some degeneracy parameter value in such plasmas. This is due to delicate interplay between relativistic degeneracy and the Pauli spin magnetization. It is also revealed that the plasma composition has significant effect on the linear dispersion of the relativistic degeneracy limit contrary to that of nonrelativistic case, and Zeeman energy has significant effect in nonrelativistic degeneracy regime unlike that of relativistic one in the linear perturbation limit. Current findings can have important applications in both inertial plasma confinement and astrophysical degenerate plasmas.

Readout of carbon nanotube vibrations based on spin-phonon coupling

We propose a scheme for spin-based detection of the bending motion in suspended carbon-nanotubes, using the curvature-induced spin-orbit interaction. We show that the resulting effective spin-phonon coupling can be used to down-convert the high-frequency vibration-modulated spin-orbit field to spin-flip processes at a much lower frequency. This vibration-induced spin-resonance can be controlled with an axial magnetic field. We propose a Pauli spin blockade readout scheme and predict that the leakage current shows pronounced peaks as a function of the external magnetic field. Whereas the resonant peaks allow for frequency readout, the slightly off-resonant current is sensitive to the vibration amplitude.

Entanglement, Kronecker Product, Pauli Spin Matrices and a Nonlinear Eigenvalue Problem

Entanglement for the eigenvectors of a nonlinear eigenvalue problem given by the Kronecker product of the Pauli spin matrices is investigated. Fully and partially entangled eigenvectors are found.

Mueller matrix roots depolarization parameters

The Mueller matrix roots decomposition recently proposed by Chipman in [1] and its three associated families of depolarization (amplitude depolarization, phase depolarization, and diagonal depolarization) are explored. Degree of polarization maps are used to differentiate among the three families and demonstrate the unity between phase and diagonal depolarization, while amplitude depolarization remains a distinct class. Three families of depolarization are generated via the averaging of different forms of two nondepolarizing Mueller matrices. The orientation of the resulting depolarization follows the cyclic permutations of the Pauli spin matrices. The depolarization forms of Mueller matrices from two scattering measurements are analyzed with the matrix roots decomposition-a sample of ground glass and a graphite and wood pencil tip.

Single-Shot Measurement of Triplet-Singlet Relaxation in aSi/SiGeDouble Quantum Dot

We investigate the lifetime of two-electron spin states in a few-electron Si/SiGe double dot. At the transition between the (1,1) and (0,2) charge occupations, Pauli spin blockade provides a readout mechanism for the spin state. We use the statistics of repeated single-shot measurements to extract the lifetimes of multiple states simultaneously. When the magnetic field is zero, we find that all three triplet states have equal lifetimes, as expected, and this time is ~10 ms. When the field is nonzero, the T(0) lifetime is unchanged, whereas the T- lifetime increases monotonically with the field, reaching 3 sec at 1 T.

Leakage-current line shapes from inelastic cotunneling in the Pauli spin blockade regime

We find the leakage current through a double quantum dot in the Pauli spin blockade regime accounting for inelastic (spin-flip) cotunneling processes. Taking the energy-dependence of this spin-flip mechanism into account allows for an accurate description of the current as a function of applied magnetic fields, gate voltages, and an inter-dot tunnel coupling. In the presence of an additional local dephasing process or nonuniform magnetic field, we obtain a simple closed-form analytical expression for the leakage current giving the full dependence on an applied magnetic field and energy detuning. This work is important for understanding the nature of leakage, especially in systems where other spin-flip mechanisms (due, e.g., to hyperfine coupling to nuclear spins or spin-orbit coupling) are weak, including silicon and carbon-nanotube or graphene quantum dots.

Pauli Spin Blockade in a Highly Tunable Silicon Double Quantum Dot

Double quantum dots are convenient solid-state platforms to encode quantum information. Two-electron spin states can be detected and manipulated using quantum selection rules based on the Pauli exclusion principle, leading to Pauli spin blockade of electron transport for triplet states. Coherent spin states would be optimally preserved in an environment free of nuclear spins, which is achievable in silicon by isotopic purification. Here we report on a deliberately engineered, gate-defined silicon metal-oxide-semiconductor double quantum dot system. The electron occupancy of each dot and the inter-dot tunnel coupling are independently tunable by electrostatic gates. At weak inter-dot coupling we clearly observe Pauli spin blockade and measure a large intra-dot singlet-triplet splitting > 1 meV. The leakage current in spin blockade has a peculiar magnetic field dependence, unrelated to electron-nuclear effects and consistent with the effect of spin-flip cotunneling processes. The results obtained here provide excellent prospects for realising singlet-triplet qubits.

Valley Blockade Quantum Switching in Silicon Nanostructures

In analogy to the Coulomb and the Pauli spin blockade, based on the electrostatic repulsion and the Pauli exclusion principle respectively, the concept of valley blockade in Silicon nanostructures is explored. The valley parity operator is defined. Valley blockade is determined by the parity conservation of valley composition eigenvectors in quantum transport. A Silicon quantum changeover switch based on a triple of donor quantum dots capable to separate electrons having opposite valley parity by virtue of the valley parity conservation is proposed. The quantum changeover switch represents a novel kind of hybrid quantum based classical logic device.

Pauli spin blockade in undoped Si/SiGe two-electron double quantum dots

We demonstrate double quantum dots fabricated in undoped Si/SiGe heterostructures relying on a double top-gated design. Charge sensing shows that we can reliably deplete these devices to zero charge occupancy. Measurements and simulations confirm that the energetics are determined by the gate-induced electrostatic potentials. Pauli spin blockade has been observed via transport through the double dot in the two electron configuration, a critical step in performing coherent spin manipulations in Si.

Upper critical magnetic field in Ba0.68K0.32Fe2As2 and Ba(Fe0.93Co0.07)2As2

We report measurements of the temperature dependence of the radio-frequency magnetic penetration depth in Ba_0.68K_0.32Fe_2As_2 and Ba(Fe_0.93Co_0.07)_2As_2 single crystals in pulsed magnetic fields up to 60 T. From our data, we construct an H-T phase diagram for the inter-plane (H || c) and in-plane (H || ab) directions for both compounds. For both field orientations in Ba_0.68K_0.32Fe_2As_2, we find a concave curvature of the Hc2(T) lines with decreasing anisotropy and saturation towards lower temperature. Taking into account Pauli spin paramagnetism we can describe Hc2(T) and its anisotropy. In contrast, we find that Pauli paramagnetic pair breaking is not essential for Ba(Fe_0.93Co_0.07)_2As_2. For this electron-doped compound, the data support a Hc2(T) dependence that can be described by the Werthamer Helfand Hohenberg model for H || ab and a two-gap behavior for H || c.

Voltage-Selective Bidirectional Polarization and Coherent Rotation of Nuclear Spins in Quantum Dots

We propose and demonstrate that the nuclear spins of the host lattice in GaAs double quantum dots can be polarized in either of two opposite directions, parallel or antiparallel to an external magnetic field. The direction is selected by adjusting the dc voltage. This nuclear polarization manifests itself by repeated controlled electron-nuclear spin scattering in the Pauli spin-blockade state. Polarized nuclei are also controlled by means of nuclear magnetic resonance. This Letter confirms that the nuclear spins in quantum dots are long-lived quantum states with a coherence time of up to 1 ms, and may be a promising resource for quantum-information processing such as quantum memories for electron spin qubits.

Pauli Spin Paramagnetism and Electronic Specific Heat in Generalised d-Dimensions

The variations of pauli spin paramagnetic susceptibility and the electronic specific heat of solids, are calculated as functions of temperature following the free electron approximation, in generalised d-dimensions. The results are compared and become consistent with that obtained in three dimensions. Interestingly, the Pauli spin paramagnetic susceptibility becomes independent of temperature only in two dimensions.

Magnetic-field-induced reduction of the low-temperature superfluid density in cuprate superconductors

The weak magnetic field induced reduction of the low-temperature superfluid density in cuprate superconductors is studied based on the kinetic energy driven superconducting mechanism. The electromagnetic response kernel is evaluated by considering both couplings of the electron charge and electron magnetic momentum with a weak magnetic field and employed to calculate the superfluid density, then the main features of the weak magnetic field induced reduction of the low-temperature superfluid density are well reproduced. The theory also shows that the striking behavior of the weak magnetic field induced reduction of the low-temperature superfluid density is intriguingly related to both depairing due to the Pauli spin polarization and nonlocal response in the vicinity of the d-wave gap nodes on the Fermi surface to a weak magnetic field.

Mesoscopic admittance of a double quantum dot

We calculate the mesoscopic admittance $G(\omega)$ of a double quantum dot (DQD),which can be measured directly using microwave techniques. This quantity reveals spectroscopic information on the DQD and is also directly sensitive to a Pauli spin blockade effect. We then discuss the problem of a DQD coupled to a high quality photonic resonator. When the photon correlation functions can be developed along a random-phase-approximation-like scheme, the response of the resonator gives an access to $G(\omega)$.

Reduction of coating induced polarization aberrations by controlling the polarization statevariation

The mechanism of coating induced polarization state variation is analysed by theJones matrix. Pauli spin matrices are used to establish the relationship betweencoating induced polarization state variation and polarization aberrations.To reduce coating induced polarization aberrations, we propose thatδ = 0 andTs = Tp at arbitrary incident angle should be appended as two additional optimization goals ofoptical coating design when the requirements of transmittance are met. Two typicalanti-reflection (AR) coatings are designed and the polarization state variation induced bythem is simulated. The MTF (modulation transfer function) calculated by polarization raytracing is applied to evaluate the polarization aberrations of the practical lithographyobjective system with the two AR coatings. All the obtained results show that thecoating induced polarization aberrations can be reduced by optimizing the angledependent properties of the optical coating without additional optical elements.

Electron transport and anisotropy of the upper critical magnetic field in Ba0.68K0.32Fe2As2 single crystals

Early work on the iron-arsenide compounds supported the view, that a reduced dimensionality might be a necessary prerequisite for high-Tc superconductivity. Later, however, it was found that the zero-temperature upper critical magnetic field, Hc2(0), for the 122 iron pnictides is in fact rather isotropic. Here, we report measurements of the temperature dependence of the electrical resistivity, \Gamma(T), in Ba0.5K0.5Fe2As2 and Ba0.68K0.32Fe2As2 single crystals in zero magnetic field and for Ba0.68K0.32Fe2As2 as well in static and pulsed magnetic fields up to 60 T. We find that the resistivity of both compounds in zero field is well described by an exponential term due to inter-sheet umklapp electron-phonon scattering between light electrons around the M point to heavy hole sheets at the \Gamma point in reciprocal space. From our data, we construct an H-T phase diagram for the inter-plane (H || c) and in-plane (H || ab) directions for Ba0.68K0.32Fe2As2. Contrary to published data for underdoped 122 FeAs compounds, we find that Hc2(T) is in fact anisotropic in optimally doped samples down to low temperatures. The anisotropy parameter, {\gamma} = Habc2/Hcc2, is about 2.2 at Tc. For both field orientations we find a concave curvature of the Hc2 lines with decreasing anisotropy and saturation towards lower temperature. Taking into account Pauli spin paramagnetism we perfectly can describe Hc2(T) and its anisotropy.