Theory of phonon-induced spin relaxation in laterally coupled quantum dots

Anisotropic g-Factor and Spin-Orbit Field in a Germanium Hut Wire Double Quantum Dot

Holes in nanowires have drawn significant attention in recent years because of the strong spin-orbit interaction, which plays an important role in constructing Majorana zero modes and manipulating spin-orbit qubits. Here, from the strongly anisotropic leakage current in the spin blockade regime for a double dot, we extract the full g-tensor and find that the spin-orbit field is in plane with an azimuthal angle of 59° to the axis of the nanowire. The direction of the spin-orbit field indicates a strong spin-orbit interaction along the nanowire, which may have originated from the interface inversion asymmetry in Ge hut wires. We also demonstrate two different spin relaxation mechanisms for the holes in the Ge hut wire double dot: spin-flip co-tunneling to the leads, and spin-orbit interaction within the double dot. These results help establish feasibility of a Ge-based quantum processor.

All-optical generation and ultrafast tuning of non-linear spin Hall current

Spin Hall effect, one of the cornerstones in spintronics refers to the emergence of an imbalance in the spin density transverse to a charge flow in a sample under voltage bias. This study points to a novel way for an ultrafast generation and tuning of a unidirectional nonlinear spin Hall current by means of subpicosecond laser pulses of optical vortices. When interacting with matter, the optical orbital angular momentum (OAM) carried by the vortex and quantified by its topological charge is transferred to the charge carriers. The residual spin-orbital coupling in the sample together with confinement effects allow exploiting the absorbed optical OAM for spatio-temporally controlling the spin channels. Both the non-linear spin Hall current and the dynamical spin Hall angle increase for a higher optical topological charge. The reason is the transfer of a higher amount of OAM and the enhancement of the effective spin-orbit interaction strength. No bias voltage is needed. We demonstrate that the spin Hall current can be all-optically generated in an open circuit geometry for ring-structured samples. These results follow from a full-fledged propagation of the spin-dependent quantum dynamics on a time-space grid coupled to the phononic environment. The findings point to a versatile and controllable tool for the ultrafast generation of spin accumulations with a variety of applications such as a source for ultrafast spin transfer torque and charge and spin current pulse emitter.

Hyperfine-phonon spin relaxation in a single-electron GaAs quantum dot

Understanding and control of the spin relaxation time T1 is among the key challenges for spin-based qubits. A larger T1 is generally favored, setting the fundamental upper limit to the qubit coherence and spin readout fidelity. In GaAs quantum dots at low temperatures and high in-plane magnetic fields B, the spin relaxation relies on phonon emission and spin-orbit coupling. The characteristic dependence T1 ∝ B-5 and pronounced B-field anisotropy were already confirmed experimentally. However, it has also been predicted 15 years ago that at low enough fields, the spin-orbit interaction is replaced by the coupling to the nuclear spins, where the relaxation becomes isotropic, and the scaling changes to T1 ∝ B-3. Here, we establish these predictions experimentally, by measuring T1 over an unprecedented range of magnetic fields-made possible by lower temperature-and report a maximum T1 = 57 ± 15 s at the lowest fields, setting a record electron spin lifetime in a nanostructure.

Symmetric spin-orbit interaction in triple quantum dot and minimisation of spin-orbit leakage in CNOT gate

We analyse spin-orbit interaction in triple quantum dots and show that a symmetric spin-orbit Hamiltonian does not follow the standard form used in double quantum dots, as a consequence of the presence of the third dot in the setup. Furthermore, CNOT implementation schemes based on the exchange interaction were studied. It was shown that an antisymmetric Dzyaloshinsky-Moriya term is the dominant source of spin-orbit leakage from the computational space. We present a simple scheme for the minimisation of leakage that can be implemented in cases where interacting spins enclose parallelogram or equilateral triangle loops.

Spin-orbit coupling and electric-dipole spin resonance in a nanowire double quantum dot

We study the electric-dipole transitions for a single electron in a double quantum dot located in a semiconductor nanowire. Enabled by spin-orbit coupling (SOC), electric-dipole spin resonance (EDSR) for such an electron can be generated via two mechanisms: the SOC-induced intradot pseudospin states mixing and the interdot spin-flipped tunneling. The EDSR frequency and strength are determined by these mechanisms together. For both mechanisms the electric-dipole transition rates are strongly dependent on the external magnetic field. Their competition can be revealed by increasing the magnetic field and/or the interdot distance for the double dot. To clarify whether the strong SOC significantly impact the electron state coherence, we also calculate relaxations from excited levels via phonon emission. We show that spin-flip relaxations can be effectively suppressed by the phonon bottleneck effect even at relatively low magnetic fields because of the very large g-factor of strong SOC materials such as InSb.

Coupling a single electron spin to a microwave resonator: controlling transverse and longitudinal couplings

Microwave-frequency superconducting resonators are ideally suited to perform dispersive qubit readout, to mediate two-qubit gates, and to shuttle states between distant quantum systems. A prerequisite for these applications is a strong qubit-resonator coupling. Strong coupling between an electron-spin qubit and a microwave resonator can be achieved by correlating spin- and orbital degrees of freedom. This correlation can be achieved through the Zeeman coupling of a single electron in a double quantum dot to a spatially inhomogeneous magnetic field generated by a nearby nanomagnet. In this paper, we consider such a device and estimate spin-resonator couplings of order ∼1 MHz with realistic parameters. Further, through realistic simulations, we show that precise placement of the double-dot relative to the nanomagnet allows to select between a purely longitudinal coupling (commuting with the bare spin Hamiltonian) and a purely transverse (spin non-conserving) coupling. Additionally, we suggest methods to mitigate dephasing and relaxation channels that are introduced in this coupling scheme. This analysis gives a clear route toward the realization of coherent state transfer between a microwave resonator and a single electron spin in a GaAs double quantum dot with a fidelity above 90%. Improved dynamical decoupling sequences, low-noise environments, and longer-lived microwave cavity modes may lead to substantially higher fidelities in the near future.

Signatures of Hyperfine, Spin-Orbit, and Decoherence Effects in a Pauli Spin Blockade

We detect in real time interdot tunneling events in a weakly coupled two-electron double quantum dot in GaAs. At finite magnetic fields, we observe two characteristic tunneling times T_{d} and T_{b}, belonging to, respectively, a direct and a blocked (spin-flip-assisted) tunneling. The latter corresponds to the lifting of a Pauli spin blockade, and the tunneling times ratio η=T_{b}/T_{d} characterizes the blockade efficiency. We find pronounced changes in the behavior of η upon increasing the magnetic field, with η increasing, saturating, and increasing again. We explain this behavior as due to the crossover of the dominant blockade-lifting mechanism from the hyperfine to spin-orbit interactions and due to a change in the contribution of the charge decoherence.

Hole spin relaxation in InAs/GaAs quantum dot molecules

We calculate the spin-orbit induced hole spin relaxation between Zeeman sublevels of vertically stacked InAs quantum dots. The widely used Luttinger-Kohn Hamiltonian, which considers coupling of heavy- and light-holes, reveals that hole spin lifetimes (T1) of molecular states significantly exceed those of single quantum dot states. However, this effect can be overcome when cubic Dresselhaus spin-orbit interaction is strong. Misalignment of the dots along the stacking direction is also found to be an important source of spin relaxation.

Spin-relaxation anisotropy in a GaAs quantum dot

We report that the electron spin-relaxation time T_{1} in a GaAs quantum dot with a spin-1/2 ground state has a 180° periodicity in the orientation of the in-plane magnetic field. This periodicity has been predicted for circular dots as being due to the interplay of Rashba and Dresselhaus spin orbit contributions. Different from this prediction, we find that the extrema in the T_{1} do not occur when the magnetic field is along the [110] and [11[over ¯]0] crystallographic directions. This deviation is attributed to an elliptical dot confining potential. The T_{1} varies by more than 1 order of magnitude when rotating a 3 T field, reaching about 80 ms for the optimal angle. We infer from the data that in our device the signs of the Rashba and Dresselhaus constants are opposite.

Electrically protected resonant exchange qubits in triple quantum dots

We present a modulated microwave approach for quantum computing with qubits comprising three spins in a triple quantum dot. This approach includes single- and two-qubit gates that are protected against low-frequency electrical noise, due to an operating point with a narrowband response to high frequency electric fields. Furthermore, existing double quantum dot advances, including robust preparation and measurement via spin-to-charge conversion, are immediately applicable to the new qubit. Finally, the electric dipole terms implicit in the high frequency coupling enable strong coupling with superconducting microwave resonators, leading to more robust two-qubit gates.

Simultaneous spin-charge relaxation in double quantum dots

We investigate phonon-induced spin and charge relaxation mediated by spin-orbit and hyperfine interactions for a single electron confined within a double quantum dot. A simple toy model incorporating both direct decay to the ground state of the double dot and indirect decay via an intermediate excited state yields an electron spin relaxation rate that varies nonmonotonically with the detuning between the dots. We confirm this model with experiments performed on a GaAs double dot, demonstrating that the relaxation rate exhibits the expected detuning dependence and can be electrically tuned over several orders of magnitude. Our analysis suggests that spin-orbit mediated relaxation via phonons serves as the dominant mechanism through which the double-dot electron spin-flip rate varies with detuning.

Fast and robust spin manipulation in a quantum dot by electric fields

We apply an invariant-based inverse engineering method to control, by time-dependent electric fields, the spin dynamics in a quantum dot with spin-orbit coupling in a weak magnetic field. The designed electric fields provide a shortcut to adiabatic processes that flip the spin rapidly, thus avoiding decoherence effects. This approach, being robust with respect to the device-dependent noise, can open new possibilities for spin-based quantum information processing.

Theory of spin relaxation in two-electron lateral coupled quantum dots

A global quantitative picture of the phonon-induced two-electron spin relaxation in GaAs double quantum dots is presented using highly accurate numerics. Wide regimes of interdot coupling, magnetic field magnitude and orientation, and detuning are explored in the presence of a nuclear bath. Most important, the giant magnetic anisotropy of the singlet-triplet relaxation can be controlled by detuning switching the principal anisotropy axes: a protected state becomes unprotected upon detuning and vice versa. It is also established that nuclear spins can dominate spin relaxation for unpolarized triplets even at high magnetic fields, contrary to common belief.

Pumped double quantum dot with spin-orbit coupling

We study driven by an external electric field quantum orbital and spin dynamics of electron in a one-dimensional double quantum dot with spin-orbit coupling. Two types of external perturbation are considered: a periodic field at the Zeeman frequency and a single half-period pulse. Spin-orbit coupling leads to a nontrivial evolution in the spin and orbital channels and to a strongly spin- dependent probability density distribution. Both the interdot tunneling and the driven motion contribute into the spin evolution. These results can be important for the design of the spin manipulation schemes in semiconductor nanostructures.PACS numbers: 73.63.Kv,72.25.Dc,72.25.Pn.

Spin edge helices in a perpendicular magnetic field

We present an exact solution to the problem of the spin edge states in the presence of equal Bychkov-Rashba and Dresselhaus spin-orbit fields in a two-dimensional electron system, restricted by a hard-wall confining potential and exposed to a perpendicular magnetic field. We find that the spectrum of the spin edge states depends critically on the orientation of the sample edges with respect to the crystallographic axes. Such a strikingly different spectral behavior generates new modes of the persistent spin helix-spin edge helices with novel properties, which can be tuned by the applied electric and magnetic fields.

Theory of anisotropic exchange in laterally coupled quantum dots

The effects of spin-orbit coupling on the two-electron spectra in lateral coupled quantum dots are investigated analytically and numerically. It is demonstrated that in the absence of magnetic field, the exchange interaction is practically unaffected by spin-orbit coupling, for any interdot coupling, boosting prospects for spin-based quantum computing. The anisotropic exchange appears at finite magnetic fields. A numerically accurate effective spin Hamiltonian for modeling spin-orbit-induced two-electron spin dynamics in the presence of magnetic field is proposed.

Electrical control of spin relaxation in a quantum dot

We demonstrate electrical control of the spin relaxation time T1 between Zeeman-split spin states of a single electron in a lateral quantum dot. We find that relaxation is mediated by the spin-orbit interaction, and by manipulating the orbital states of the dot using gate voltages we vary the relaxation rate W identical withT1(-1) by over an order of magnitude. The dependence of W on orbital confinement agrees with theoretical predictions, and from these data we extract the spin-orbit length. We also measure the dependence of W on the magnetic field and demonstrate that spin-orbit mediated coupling to phonons is the dominant relaxation mechanism down to 1 T, where T1 exceeds 1 s.

Semiconductor spintronics

Spintronics refers commonly to phenomena in which the spin of electrons in a solid state environment plays the determining role. In a more narrow sense spintronics is an emerging research field of electronics: spintronics devices are based on a spin control of electronics, or on an electrical and optical control of spin or magnetism. While metal spintronics has already found its niche in the computer industry—giant magnetoresistance systems are used as hard disk read heads—semiconductor spintronics is yet to demonstrate its full potential. This review presents selected themes of semiconductor spintronics, introducing important concepts in spin transport, spin injection, Silsbee-Johnson spin-charge coupling, and spin-dependent tunneling, as well as spin relaxation and spin dynamics. The most fundamental spin-dependent interaction in nonmagnetic semiconductors is spin-orbit coupling. Depending on the crystal symmetries of the material, as well as on the structural properties of semiconductor based heterostructures, the spin-orbit coupling takes on different functional forms, giving a nice playground of effective spin-orbit Hamiltonians. The effective Hamiltonians for the most relevant classes of materials and heterostructures are derived here from realistic electronic band structure descriptions. Most semiconductor device systems are still theoretical concepts, waiting for experimental demonstrations. A review of selected proposed, and a few demonstrated devices is presented, with detailed description of two important classes: magnetic resonant tunnel structures and bipolar magnetic diodes and transistors. In view of the importance of ferromagnetic semiconductor materials, a brief discussion of diluted magnetic semiconductors is included. In most cases the presentation is of tutorial style, introducing the essential theoretical formalism at an accessible level, with case-study-like illustrations of actual experimental results, as well as with brief reviews of relevant recent achievements in the field.

Suppression of spin relaxation in an InAs nanowire double quantum dot

We investigate the triplet-singlet relaxation in a double quantum dot defined by top gates in an InAs nanowire. In the Pauli spin blockade regime, the leakage current can be mainly attributed to spin relaxation. While at weak and strong interdot coupling relaxation is dominated by two individual mechanisms, the relaxation is strongly reduced at intermediate coupling and finite magnetic field. In addition we observe a characteristic bistability of the spin-nonconserving current as a function of magnetic field. We propose a model where these features are explained by the polarization of nuclear spins enabled by the interplay between hyperfine and spin-orbit mediated relaxation.

Geometrical spin dephasing in quantum dots

We study spin-orbit mediated relaxation and dephasing of electron spins in quantum dots. We show that higher order contributions provide a relaxation mechanism that dominates for low magnetic fields and is of geometrical origin. In the low-field limit relaxation is dominated by coupling to electron-hole excitations and possibly 1/f noise rather than phonons.