The exchange coupling between quantum dot spin qubits is isotropic, which restricts the types of quantum gates that can be formed. Here, we propose a method for controlling anisotropic interactions between spins arranged in a bus geometry. The symmetry is broken by an external magnetic field, resulting in XXZ-type interactions that can efficiently generate Greenberger-Horne-Zeilinger (GHZ) states or universal gate sets for exchange-only quantum computing. Analysis of the bus ground state provides a link between quantum critical phenomena and the communication capacity.
Quantum scars are enhancements of quantum probability density along classical periodic orbits. We study the recently discovered phenomenon of strong, perturbation-induced quantum scarring in the two-dimensional harmonic oscillator exposed to a homogeneous magnetic field. We demonstrate that both the geometry and the orientation of the scars are fully controllable with a magnetic field and a focused perturbative potential, respectively. These properties may open a path into an experimental scheme to manipulate electric currents in nanostructures fabricated in a two-dimensional electron gas.
We present measurements on gate-defined double quantum dots in Ge-Si core-shell nanowires, which we tune to a regime with visible shell filling in both dots. We observe a Pauli spin blockade and can assign the measured leakage current at low magnetic fields to spin-flip cotunneling, for which we measure a strong anisotropy related to an anisotropic g-factor. At higher magnetic fields we see signatures for leakage current caused by spin-orbit coupling between (1,1)-singlet and (2,0)-triplet states. Taking into account these anisotropic spin-flip mechanisms, we can choose the magnetic field dire…
Coulomb interaction among electrons is found to have profound effects on the electronic properties of anisotropic quantum dots in a perpendicular external magnetic field, and in the presence of the Rashba spin-orbit interaction. This is more evident in optical transitions, which we find in this system to be highly anisotropic and super-intense, in particular, for large values of the anisotropy parameter.
We propose a controllable way of tuning Fano resonances in open quantum dots in the absence of magnetic field. A quantum dot can be modified by changing the gate voltages that define the dot itself. An extra degree of freedom can be introduced by means of a controllable repulsive perturbation, such as the one induced by scanning a Atomic Force Microscope tip on a real sample. We numerically investigate the coupling between localized states in the dot and the continuum in the leads. The advantage of such position controllable perturbation is the selective manipulation of the quantum dot states.…
We predict a spin pure dephasing channel in electron relaxation between states with unequal Zeeman splittings, exemplified by a spin-preserving electron tunneling between quantum dots in a magnetic field. The dephasing is caused by a mismatch in electron $g$-factors in the dots leading to distinguishability of phonons emitted during tunneling with opposite spins. Combining multiband $\boldsymbol{k}{\cdot}\boldsymbol{p}$ modeling and dynamical simulations via a Master equation we show that this fundamental effect of spin measurement effected by the phonon bath may be widely controlled by the si…
We have developed a theory of the one-phonon intraband resonance Raman scattering (IRRS) in anisotropic quantum dots subjected to an arbitrarily directed magnetic field. The differential Raman cross section is obtained. The resonance structure of the Raman cross section is studied. It is shown that the quantum dot subjected in a magnetic field can be used as the detector of phonon modes. The interesting multiplet structure of the resonance peaks is studied.
We have studied the absorption of electromagnetic radiation of an anisotropic quantum dot taking into account the spin-flip processes that is associated with the interaction of the electrons with optical phonons. It is shown that these processes lead to the resonance absorption. Explicit formula is derived for the absorption coefficient. The positions of the resonances peaks are found.
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.
We experimentally determine isotropic and anisotropic g-factor corrections in lateral GaAs single-electron quantum dots. We extract the Zeeman splitting by measuring the tunnel rates into the individual spin states of an empty quantum dot for an in-plane magnetic field with various strengths and directions. We quantify the Zeeman energy and find a linear dependence on the magnetic field strength which allows us to extract the g-factor. The measured g-factor is understood in terms of spin-orbit interaction induced isotropic and anisotropic corrections to the GaAs bulk g-factor. Because this imp…
Spin qubits hosted in silicon (Si) quantum dots (QD) are attractive due to their exceptionally long coherence times and compatibility with the silicon transistor platform. To achieve electrical control of spins for qubit scalability, recent experiments have utilized gradient magnetic fields from integrated micro-magnets to produce an extrinsic coupling between spin and charge, thereby electrically driving electron spin resonance (ESR). However, spins in silicon QDs experience a complex interplay between spin, charge, and valley degrees of freedom, influenced by the atomic scale details of the …
Nanoantenna enhanced ultrafast emission from colloidal quantum dots as quantum emitters is required for fast quantum communications. On chip integration of such devices require a scalable and high throughput technology. We report self-assembly lithography technique of preparing hybrid of gold-nanorods antenna over a com- pact CdSe quantum dot monolayer. We demonstrate resonant and off resonant gold nanorod antenna enhanced radiative and anisotropic decay. Extensive simulations explain the mechanism of the decay rates and the role of antenna in both random and a compact monolayer of quantum dot…
The absorption of electromagnetic radiation of an anisotropic quantum dot is theoretically investigated taking into account the processes associated with simultaneous scattering from ionized impurities. It is shown that the scattering of electrons by impurities leads to the resonance absorption even if we have only one impurity in the quantum dot. Explicit formula is derived for the absorption coefficient. The positions of the resonances peaks are found. The effects of external magnetic field on the resonance absorption are studied.
The influence of the spin-orbit interactions on the energy spectrum of two-electron laterally coupled quantum dots is investigated. The effective Hamiltonian for a spin qubit pair proposed in F. Baruffa et al., Phys. Rev. Lett. 104, 126401 (2010) is confronted with exact numerical results in single and double quantum dots in zero and finite magnetic field. The anisotropic exchange Hamiltonian is found quantitatively reliable in double dots in general. There are two findings of particular practical importance: i) The model stays valid even for maximal possible interdot coupling (a single dot), …
We study the anisotropic orbital effect in the electric field tunability of the phonon induced spin-flip rate in quantum dots (QDs). Our study shows that anisotropic gate potential enhances the spin-flip rate and reduces the level crossing point to a lower quantum dot radius due to the suppression of the Land$\acute{e}$ g-factor towards bulk crystal. In the range of $10^4-10^6$ V/cm, the electric field tunability of the phonon induced spin-flip rate can be manipulated through strong Dresselhaus spin-orbit coupling. These results might assist the development of a spin based solid state quantum …
We report integrated charge sensing measurements on a Si/SiGe double quantum dot. The quantum dot is shown to be tunable from a single, large dot to a well-isolated double dot. Charge sensing measurements enable the extraction of the tunnel coupling, t, between the quantum dots as a function of the voltage on the top gates defining the device. Control of the voltage on a single such gate tunes the barrier separating the two dots. The measured tunnel coupling is an exponential function of the gate voltage. The ability to control t is an important step towards controlling spin qubits in silicon …
We reexamine the tunneling density of states in quantum dots and nanoparticles within the model which is extension of the universal Hamiltonian to the case of uniaxial anisotropic exchange. We derive the exact analytical result for the tunneling density of states in the case of arbitrary single-particle energy spectrum. We find that, similar to the case of the isotropic exchange, the tunneling density of states as a function of energy has the maximum due to a finite value of the total spin of the ground state near the Stoner instability. We demonstrate that there are no additional extrema whic…
We study the effect of elastic anisotropic biaxial strain on the light emitted by neutral excitons confined in different kinds of semiconductor quantum dots (QDs). We find that the light polarization rotates by up to 80 degree and the excitonic fine structure splitting varies by several tens of $μ$eVs as the strain is varied. By means of a continuum model we mainly ascribe the observed effects to substantial changes of the hole wave function. These results show that strain-fields of a few permill magnitude are suffcient to dramatically modify the electronic structure of QDs.
In this paper, a detailed analysis of anisotropic effects on the phonon induced spin relaxation rate in III-V semiconductor quantum dots (QDs) is carried out. We show that the accidental degeneracy due to level crossing between the first and second excited states of opposite electron spin states in both isotropic and anisotropic QDs can be manipulated with the application of externally applied gate potentials. In particular, anisotropic gate potentials enhance the phonon mediated spin-flip rate and reduce the cusp-like structure to lower magnetic fields, in addition to the lower QDs radii in I…
g-factor tuning of electrons in quantum dots is studied as function of in-plane and perpendicular magnetic fields for different confinements. Rashba and Dresselhaus effects are considered, and comparison is made between wide- and narrow-gap materials. The interplay between magnetic fields and intrinsic spin-orbit coupling is analyzed, with two distinct phases found in the spectrum for GaAs in perpendicular field. The anisotropy of the g-factor is reported, and good agreement with available experimental findings is obtained.
In the present paper, the collective near-field effects in a two-graphene sheets plasmonic waveguide loaded with an array of Ag$_2$Se quantum dots excited by external radiation are theoretically studied. This research aims to develop a theoretical approach to realizing controllable excitation and the propagation of surface plasmon polaritons (SPPs) in planar graphene waveguides. The proposed model is based on the semiclassical description that implies the dispersion equation's solution for SPPs excited in two coupled graphene sheets and the embedded quantum dots' energy spectra analysis. Using…
The interaction between electrons in arrays of electrostatically defined quantum dots is naturally described by a Fermi-Hubbard Hamiltonian. Moreover, the high degree of tunability of these systems make them a powerful platform to simulate different regimes of the Hubbard model. However, most quantum dot array implementations have been limited to one-dimensional linear arrays. In this letter, we present a square lattice unit cell of 2$\times$2 quantum dots defined electrostatically in a AlGaAs/GaAs heterostructure using a double-layer gate technique. We probe the properties of the array using …
The spin-orbit coupling influences the total spin of semiconductor quantum dots. We analyze the theoretical prediction for the combined effects of spin-orbit coupling, weak vertical magnetic fields and deformation of the dot. Our results allow the characterization of the quantum dots as spin switches, controllable with electric gates.
We study the variation in the Land$\acute{\text{e}}$ g-factor of electron spins induced by both anisotropic gate potentials and magnetic fields in InAs quantum dots for possible implementation towards solid state quantum computing. In this paper, we present analytical expressions and numerical simulations of the variation in the Land$\acute{\text{e}}$ g-factor for both isotropic and anisotropic quantum dots. Using both analytical techniques and numerical simulations, we show that the Rashba spin-orbit coupling has a major contribution in the variation of the g-factor with electric fields befor…
We study the exchange interaction between two hole-spin qubits in a double quantum dot setup in a silicon nanowire in the presence of magnetic and electric fields. Based on symmetry arguments we show that there exists an effective spin that is conserved even in highly anisotropic semiconductors, provided that the system has a twofold symmetry with respect to the direction of the applied magnetic field. This finding facilitates the definition of qubit basis states and simplifies the form of exchange interaction for two-qubit gates in coupled quantum dots. If the magnetic field is applied along …
Intense terahertz laser field is shown to have a profound effect on the electronic and optical properties of quantum rings, where the isotropic and anisotropic quantum rings can now be treated on equal footing. We have demonstrated that in isotropic quantum rings the laser field creates irregular AB oscillations that are usually expected in anisotropic rings. Further, we have shown for the first time that intense laser fields can restore the {\it isotropic} physical properties in anisotropic quantum rings. In principle, all types of anisotropies (structural, effective masses, defects, etc.) ca…
We have measured the Zeeman splitting of quantum levels in few-electron quantum dots (QDs) formed in narrow bandgap InSb nanowires via the Schottky barriers at the contacts under application of different spatially orientated magnetic fields. The effective g-factor tensor extracted from the measurements is strongly anisotropic and level-dependent, which can be attributed to the presence of strong spin-orbit interaction (SOI) and asymmetric quantum confinement potentials in the QDs. We have demonstrated a successful determination of the principal values and the principal axis orientations of the…
Spin valves form a key building block in a wide range of spintronic concepts and devices from magnetoresistive read heads to spin-transfer-torque oscillators. We elucidate the dependence of the magnetic damping in the free layer on the angle its equilibrium magnetization makes with that in the fixed layer. The spin pumping-mediated damping is anisotropic and tensorial, with Gilbert- and Bloch-like terms. Our investigation reveals a mechanism for tuning the free layer damping in-situ from negligible to a large value via the orientation of fixed layer magnetization, especially when the magnets a…
We study theoretically phonon-assisted spin relaxation of an electron confined in an elliptical quantum dot (QD) subjected to a tilted magnetic field. In the presence of both Rashba and Dresselhaus spin-orbit terms, the relaxation rate is anisotropic with respect to the in-plane field orientation. This anisotropy originates from the interference, at nonzero tilt angle, between the two spin-orbit terms. We show that, in a narrow range of magnetic field orientations, the relaxation rate exhibits anomalous sensitivity to variations of the QD parameters. In this range, the relative change in the r…
The spin structure and spin dynamics of excitons in an ensemble of (In,Al)As/AlAs quantum dots (QDs) with type-I band alignment, containing both direct and indirect band gap dots, are studied. Time-resolved and spectral selective techniques are used to distinguish between the direct and indirect QDs. The exciton fine structure is studied by means of optical alignment and optical orientation techniques in magnetic fields applied in the Faraday or Voigt geometries. A drastic difference in emission polarization is found for the excitons in the direct QDs involving a $Γ$-valley electron and the ex…
Exact-diagonalization calculations for N=3 electrons in anisotropic quantum dots, covering a broad range of confinement anisotropies and strength of inter-electron repulsion, are presented for zero and low magnetic fields. The excitation spectra are analyzed as a function of the strength of the magnetic field and for increasing quantum-dot anisotropy. Analysis of the intrinsic structure of the many-body wave functions through spin-resolved two-point correlations reveals that the electrons tend to localize forming Wigner molecules. For certain ranges of dot parameters (mainly at strong anisotro…
Controllable interaction between photons and distant spins via vacuum Rabi oscillations
QuTech and Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学量子纳米科学卡弗里研究所）；Netherlands Organization for Applied Scientific Research (TNO)（荷兰应用科学研究组织）
We investigate the wave functions, spectrum, and g-factor anisotropy of low-energy electrons confined to self-assembled, pyramidal InAs quantum dots (QDs) subject to external magnetic and electric fields. We present the construction of trial wave functions for a pyramidal geometry with hard-wall confinement. We explicitly find the ground and first excited states and show the associated probability distributions and energies. Subsequently, we use these wave functions and 8-band $k\cdot p$ theory to derive a Hamiltonian describing the QD states close to the valence band edge. Using a perturbativ…
We propose a scheme to prepare arbitrary superpositions of quantum states in double quantum--dots irradiated by coherent microwave pulses. Solving the equations of motion for the dot density matrix, we find that dephasing rates for such superpositions can be quantitatively infered from additional electron current pulses that appear due to a controllable breakdown of coherent population trapping in the dots.
Charge-neutral excitons in semiconductor quantum dots have a small finite energy separation caused by the anisotropic exchange splitting. Coherent excitation of neutral excitons will generally excite both exciton components, unless the excitation is parallel to one of the dipole axes. We present a polaron master equation model to describe two-exciton pumping using a coherent continuous wave pump field in the presence of a realistic anisotropic exchange splitting. We predict a five-peak incoherent spectrum, thus generalizing the Mollow triplet to become a Mollow quintuplet. We experimentally co…
A gate electric field has a small but non-negligible effect on the phase of the valley-orbit coupling in Si quantum dots. Finite interdot tunneling between valley eigenstates in a double quantum dot is enabled by a small difference in the phase of the valley-orbit coupling between the two dots, and it in turn allows controllable rotations of two-dot valley eigenstates at a level anticrossing. We present a comprehensive analytical discussion of this process, with estimates for realistic structures.
We carried out a nested Schrieffer-Wolff transformation of an Anderson two-impurity Hamiltonian to study the spin-spin coupling between two dynamical quantum dots under the influence of rotating transverse magnetic field. As a result of the rotating field, we predict a novel Ising type spin-spin coupling mechanism between quantum dots, whose strength is tunable via the magnitude of the rotating field. The strength of the new coupling could be comparable to the strength of the RKKY coupling. The dynamical coupling with the intristic RKKY coupling enables to construct a four level system of maxi…
The knowledge of electron and hole g-factors, their control and engineering are key for the usage of the spin degree of freedom for information processing in solid state systems. The electronic g-factor will be materials dependent, the effect being larger for materials with large spin-orbit coupling. Since electrons can be individually trapped into quantum dots in a controllable manner, they may represent a good platform for the implementation of quantum information processing devices. Here we use self-assembled quantum dots of InAs embedded in GaAs for the g-factor control and engineering.
We prepare a gate-defined quadruple quantum dot to study the gate-tunability of single to quadruple quantum dots with finite inter-dot tunnel couplings. The measured charging energies of various double dots suggest that the dot size is governed by gate geometry. For the triple and quadruple dots we study gate-tunable inter-dot tunnel couplings. Particularly for the triple dot we find that the effective tunnel coupling between side dots significantly depends on the alignment of the center dot potential. These results imply that the present quadruple dot device has gate performance relevant for …
Optical studies of a bright exciton provide only limited information about the hole anisotropy in a quantum dot. In this work we present a universal method to study heavy hole anisotropy using a dark exciton in a moderate in-plane magnetic field. By analysis of the linear polarization of the dark exciton photoluminescence we identify both isotropic and anisotropic contributions to the hole g-factor. We employ this method for a number of individual self-assembled CdTe/ZnTe quantum dots, demonstrating a variety of behaviors of in-plane hole g-factor: from almost fully anisotropic to almost isotr…
The metallic tip of a scanning force microscope operated at 300 mK is used to locally induce a potential in a fully controllable double quantum dot defined via local anodic oxidation in a GaAs/AlGaAs heterostructure. Using scanning gate techniques we record spatial images of the current through the sample for different numbers of electrons on the quantum dots (i.e., for different quantum states). Owing to the spatial resolution of current maps, we are able to determine the spatial position of the individual quantum dots, and investigate their apparent relative shifts due to the voltage applied…
We present an all-electron calculation of the hyperfine parameters for conduction electrons in Si, showing that: (i) all parameters scale linearly with the spin density at a $^{29}$Si site; (ii) the isotropic term is over 30 times larger than the anisotropic part; (iii) conduction electron charge density at a Si nucleus is consistent with experimental estimates; (iv) Overhauser fields in natural Si quantum dots (QDs) are two orders of magnitude smaller than in GaAs QDs. This reinforces the outstanding performance of Si in keeping spin coherence and opens access to reliable quantitative informa…
We present a highly controllable double quantum dot device based on bilayer graphene. Using a device architecture of interdigitated gate fingers, we can control the interdot tunnel coupling between 1 to 4 GHz and the mutual capacitive coupling between 0.2 and 0.6 meV, independently of the charge occupation of the quantum dots. The charging energy and hence the dot size remains nearly unchanged. The tuning range of the tunnel coupling covers the operating regime of typical silicon and GaAs spin qubit devices.
We derive the quantum rate equations for an Aharonov-Bohm interferometer with two vertically coupled quantum dots embedded in each of two arms by means of the nonequilibrium Green's function in the sequential tunneling regime. Basing on these equations, we investigate time-dependent resonant tunneling under a small amplitude irradiation and find that the resonant photon-assisted tunneling peaks in photocurrent demonstrate a combination behavior of Fano and Lorentzian resonances due to the interference effect between the two pathways in this parallel configuration, which is controllable by thre…
The full time-dependent four-wave mixing polarization in quantum dots is microscopically calculated, taking into account acoustic phonon-assisted transitions between different exciton states of the dot. It is shown that quite different dephasing times of higher exciton states in pancake anisotropic InGaAs quantum dots are responsible for the experimentally observed [1] double-exponential decay in the photon echo signal.
Phonon-induced spin relaxation in coupled lateral quantum dots in the presence of spin-orbit coupling is calculated. The calculation for single dots is consistent with experiment. Spin relaxation in double dots at useful interdot couplings is dominated by spin hot spots that are strongly anisotropic. Spin hot spots are ineffective for a diagonal crystallographic orientation of the dots with a transverse in-plane field. This geometry is proposed for spin-based quantum information processing.
We demonstrate delicate control over the Kondo effect and its interplay with quantum interference in an Aharonov-Bohm interferometer containing one Kondo dot and one noninteracting dot. It is shown that the Kondo resonance undergoes a dramatic evolution as the interdot tunnel coupling progressively increases. A novel triple Kondo splitting occurs from the interference between constant and Lorentzian conduction bands that cooperate in forming the Kondo singlet. The device also manifests a highly controllable Fano-Kondo effect in coherent electronic transport, and can be tuned to a regime where …
We report the realization of nanotube-based quantum dot structures that use local electrostatic gating to produce individually controllable dots in series along a nanotube. Electrostatic top-gates produce depletion regions in the underlying tube; a pair of such depletion regions defines a quantum dot. Transparencies of tunnel barriers as well as the electrostatic energies, within single and multiple dots, can be tuned by gate voltages. The approach allows accurate control over multiple devices on a single tube, and serves as a design paradigm for nanotube-based electronics and quantum systems.
We devise a platform for noise-resistant quantum computing using the valley degree of freedom of Si quantum dots. The qubit is encoded in two polarized (1,1) spin-triplet states with different valley compositions in a double quantum dot, with a Zeeman field enabling unambiguous initialization. A top gate gives a difference in the valley splitting between the dots, allowing controllable interdot tunneling between opposite valley eigenstates, which enables one-qubit rotations. Two-qubit operations rely on a stripline resonator, and readout on charge sensing. Sensitivity to charge and spin fluctu…
Semiconductor quantum dots have emerged as promising candidates for implementation of quantum information processing since they allow for a quantum interface between stationary spin qubits and propagating single photons. In the meanwhile, transition metal dichalcogenide (TMD) monolayers have moved to the forefront of solid-state research due to their unique band structure featuring a large band gap with degenerate valleys and non-zero Berry curvature. Here we report the observation of quantum dots in monolayer tungsten-diselenide with an energy that is 20 to 100 meV lower than that of two dime…
Highly accurate numerical results of phonon-induced two-electron spin relaxation in silicon double quantum dots are presented. The relaxation, enabled by spin-orbit coupling and the nuclei of $^{29}$Si (natural or purified abundance), are investigated for experimentally relevant parameters, the interdot coupling, the magnetic field magnitude and orientation, and the detuning. We calculate relaxation rates for zero and finite temperatures (100 mK), concluding that our findings for zero temperature remain qualitatively valid also for 100 mK. We confirm the same anisotropic switch of the axis of …
We theoretically investigate the angular and spin dependent transport in normal-metal/helical-multiferroic/ferromagnetic heterojunctions. We find a tunneling anisotropic magnetoresistance (TAMR) effect due to the spiral magnetic order in the tunnel junction and to an effective spin-orbit coupling induced by the topology of the localized magnetic moments in the multiferroic spacer. The predicted TAMR effect is efficiently controllable by an external electric field due to the magnetoelectric coupling.
Phonon-induced orbital and spin relaxation rates of single electron states in lateral single and double quantum dots are obtained numerically for realistic materials parameters. The rates are calculated as a function of magnetic field and interdot coupling, at various field and quantum dot orientations. It is found that orbital relaxation is due to deformation potential phonons at low magnetic fields, while piezoelectric phonons dominate the relaxation at high fields. Spin relaxation, which is dominated by piezoelectric phonons, in single quantum dots is highly anisotropic due to the interplay…
We have demonstrated few-electron quantum dots in Si/SiGe and InGaAs, with occupation number controllable from N = 0. These display a high degree of spatial symmetry and identifiable shell structure. Magnetospectroscopy measurements show that two Si-based devices possess a singlet N =2 ground state at low magnetic field and therefore the two-fold valley degeneracy is lifted. The valley splittings in these two devices were 120 and 270 μeV, suggesting the presence of atomically sharp interfaces in our heterostructures.
Polar optical-phonon modes are derived analytically for spheroidal quantum dots with wurtzite crystal structure. The developed theory is applied to a freestanding spheroidal ZnO quantum dot and to a spheroidal ZnO quantum dot embedded into a MgZnO crystal. The wurtzite (anisotropic) quantum dots are shown to have strongly different polar optical-phonon modes in comparison with zincblende (isotropic) quantum dots. The obtained results allow one to explain and accurately predict phonon peaks in the Raman spectra of wurtzite nanocrystals, nanorods (prolate spheroids), and epitaxial quantum dots (…
