Triplet–singlet spin relaxation via nuclei in a double quantum dot

Wigner-molecularization-enabled dynamic nuclear polarization

Multielectron semiconductor quantum dots (QDs) provide a novel platform to study the Coulomb interaction-driven, spatially localized electron states of Wigner molecules (WMs). Although Wigner-molecularization has been confirmed by real-space imaging and coherent spectroscopy, the open system dynamics of the strongly correlated states with the environment are not yet well understood. Here, we demonstrate efficient control of spin transfer between an artificial three-electron WM and the nuclear environment in a GaAs double QD. A Landau-Zener sweep-based polarization sequence and low-lying anticrossings of spin multiplet states enabled by Wigner-molecularization are utilized. Combined with coherent control of spin states, we achieve control of magnitude, polarity, and site dependence of the nuclear field. We demonstrate that the same level of control cannot be achieved in the non-interacting regime. Thus, we confirm the spin structure of a WM, paving the way for active control of correlated electron states for application in mesoscopic environment engineering.

Preparing Multipartite Entangled Spin Qubits via Pauli Spin Blockade

Preparing large-scale multi-partite entangled states of quantum bits in each physical form such as photons, atoms or electrons for each specific application area is a fundamental issue in quantum science and technologies. Here, we propose a setup based on Pauli spin blockade (PSB) for the preparation of large-scale W states of electrons in a double quantum dot (DQD). Within the proposed scheme, two W states of n and m electrons respectively can be fused by allowing each W state to transfer a single electron to each quantum dot. The presence or absence of PSB then determines whether the two states have fused or not, leading to the creation of a W state of n + m - 2 electrons in the successful case. Contrary to previous works based on quantum dots or nitrogen-vacancy centers in diamond, our proposal does not require any photon assistance. Therefore the 'complex' integration and tuning of an optical cavity is not a necessary prerequisite. We also show how to improve the success rate in our setup. Because requirements are based on currently available technology and well-known sensing techniques, our scheme can directly contribute to the advances in quantum technologies and, in particular in solid state systems.

Radio-Frequency-Detected Fast Charge Sensing in Undoped Silicon Quantum Dots

Spin qubits in silicon quantum dots offer a promising platform for a quantum computer as they have a long coherence time and scalability. The charge sensing technique plays an essential role in reading out the spin qubit as well as tuning the device parameters, and therefore, its performance in terms of measurement bandwidth and sensitivity is an important factor in spin qubit experiments. Here we demonstrate fast and sensitive charge sensing by radio frequency reflectometry of an undoped, accumulation-mode Si/SiGe double quantum dot. We show that the large parasitic capacitance in typical accumulation-mode gate geometries impedes reflectometry measurements. We present a gate geometry that significantly reduces the parasitic capacitance and enables fast single-shot readout. The technique allows us to distinguish between the singly- and doubly occupied two-electron states under the Pauli spin blockade condition in an integration time of 0.8 μs, the shortest value ever reported in silicon, by the signal-to-noise ratio of 6. These results provide a guideline for designing silicon spin qubit devices suitable for the fast and high-fidelity readout.

A silicon quantum-dot-coupled nuclear spin qubit

Single nuclear spins in the solid state are a potential future platform for quantum computing^1-3, because they possess long coherence times^4-6 and offer excellent controllability⁷. Measurements can be performed via localized electrons, such as those in single atom dopants^8,9 or crystal defects^10-12. However, establishing long-range interactions between multiple dopants or defects is challenging^13,14. Conversely, in lithographically defined quantum dots, tunable interdot electron tunnelling allows direct coupling of electron spin-based qubits in neighbouring dots^15-20. Moreover, the compatibility with semiconductor fabrication techniques²¹ may allow for scaling to large numbers of qubits in the future. Unfortunately, hyperfine interactions are typically too weak to address single nuclei. Here we show that for electrons in silicon metal-oxide-semiconductor quantum dots the hyperfine interaction is sufficient to initialize, read out and control single ²⁹Si nuclear spins. This approach combines the long coherence times of nuclear spins with the flexibility and scalability of quantum dot systems. We demonstrate high-fidelity projective readout and control of the nuclear spin qubit, as well as entanglement between the nuclear and electron spins. Crucially, we find that both the nuclear spin and electron spin retain their coherence while moving the electron between quantum dots. Hence we envision long-range nuclear-nuclear entanglement via electron shuttling³. Our results establish nuclear spins in quantum dots as a powerful new resource for quantum processing.

Virtual-photon-mediated spin-qubit-transmon coupling

Spin qubits and superconducting qubits are among the promising candidates for realizing a solid state quantum computer. For the implementation of a hybrid architecture which can profit from the advantages of either approach, a coherent link is necessary that integrates and controllably couples both qubit types on the same chip over a distance that is several orders of magnitude longer than the physical size of the spin qubit. We realize such a link with a frequency-tunable high impedance SQUID array resonator. The spin qubit is a resonant exchange qubit hosted in a GaAs triple quantum dot. It can be operated at zero magnetic field, allowing it to coexist with superconducting qubits on the same chip. We spectroscopically observe coherent interaction between the resonant exchange qubit and a transmon qubit in both resonant and dispersive regimes, where the interaction is mediated either by real or virtual resonator photons.

Different qubit platforms each have their own advantages and disadvantages. By engineering couplings between them it may be possible to create a more capable hybrid device. Here the authors demonstrate coherent coupling between a semiconductor spin qubit and a superconducting transmon.

Quantifying the nonclassicality of pure dephasing

One of the central problems in quantum theory is to characterize, detect, and quantify quantumness in terms of classical strategies. Dephasing processes, caused by non-dissipative information exchange between quantum systems and environments, provides a natural platform for this purpose, as they control the quantum-to-classical transition. Recently, it has been shown that dephasing dynamics itself can exhibit (non)classical traits, depending on the nature of the system-environment correlations and the related (im)possibility to simulate these dynamics with Hamiltonian ensembles–the classical strategy. Here we establish the framework of detecting and quantifying the nonclassicality for pure dephasing dynamics. The uniqueness of the canonical representation of Hamiltonian ensembles is shown, and a constructive method to determine the latter is presented. We illustrate our method for qubit, qutrit, and qubit-pair pure dephasing and describe how to implement our approach with quantum process tomography experiments. Our work is readily applicable to present-day quantum experiments.

The presence of processes that cannot be simulated classically in open quantum system dynamics is acknowledged, but an exact quantifier for this non-classical character is still missing. Here, the authors provide a quantitative measure of non-classicality for purely dephasing evolutions.

Excited States in Bilayer Graphene Quantum Dots

We report ground- and excited-state transport through an electrostatically defined few-hole quantum dot in bilayer graphene in both parallel and perpendicular applied magnetic fields. A remarkably clear level scheme for the two-particle spectra is found by analyzing finite bias spectroscopy data within a two-particle model including spin and valley degrees of freedom. We identify the two-hole ground state to be a spin-triplet and valley-singlet state. This spin alignment can be seen as Hund's rule for a valley-degenerate system, which is fundamentally different from quantum dots in carbon nanotubes, where the two-particle ground state is a spin-singlet state. The spin-singlet excited states are found to be valley-triplet states by tilting the magnetic field with respect to the sample plane. We quantify the exchange energy to be 0.35 meV and measure a valley and spin g factor of 36 and 2, respectively.

Readout and control of the spin-orbit states of two coupled acceptor atoms in a silicon transistor

Coupling spin qubits to electric fields is attractive to simplify qubit manipulation and couple qubits over long distances. Electron spins in silicon offer long lifetimes, but their weak spin-orbit interaction makes electrical coupling challenging. Hole spins bound to acceptor dopants, spin-orbit-coupled J = 3/2 systems similar to Si vacancies in SiC and single Co dopants, are an electrically active spin system in silicon. However, J = 3/2 systems are much less studied than S = 1/2 electrons, and spin readout has not yet been demonstrated for acceptors in silicon. Here, we study acceptor hole spin dynamics by dispersive readout of single-hole tunneling between two coupled acceptors in a nanowire transistor. We identify m J = ±1/2 and m J = ±3/2 levels, and we use a magnetic field to overcome the initial heavy-light hole splitting and to tune the J = 3/2 energy spectrum. We find regimes of spin-like (+3/2 to -3/2) and charge-like (±1/2 to ±3/2) relaxations, separated by a regime of enhanced relaxation induced by mixing of light and heavy holes. The demonstrated control over the energy level ordering and hybridization are new tools in the J = 3/2 system that are crucial to optimize single-atom spin lifetime and electrical coupling.

Integrated silicon qubit platform with single-spin addressability, exchange control and single-shot singlet-triplet readout

Silicon quantum dot spin qubits provide a promising platform for large-scale quantum computation because of their compatibility with conventional CMOS manufacturing and the long coherence times accessible using ²⁸Si enriched material. A scalable error-corrected quantum processor, however, will require control of many qubits in parallel, while performing error detection across the constituent qubits. Spin resonance techniques are a convenient path to parallel two-axis control, while Pauli spin blockade can be used to realize local parity measurements for error detection. Despite this, silicon qubit implementations have so far focused on either single-spin resonance control, or control and measurement via voltage-pulse detuning in the two-spin singlet–triplet basis, but not both simultaneously. Here, we demonstrate an integrated device platform incorporating a silicon metal-oxide-semiconductor double quantum dot that is capable of single-spin addressing and control via electron spin resonance, combined with high-fidelity spin readout in the singlet-triplet basis.

Significant progress has been made developing the different methods needed for a spin-based quantum computer but the challenge of integrating them remains. Fogarty et al. present a system with single-spin addressability, spin-spin interactions and high-fidelity readout that provides a scalable foundation for error-corrected devices.

Toward high-fidelity coherent electron spin transport in a GaAs double quantum dot

In this paper, we investigate how to achieve high-fidelity electron spin transport in a GaAs double quantum dot. Our study examines fidelity loss in spin transport from multiple perspectives. We first study incoherent fidelity loss due to hyperfine and spin-orbit interaction. We calculate fidelity loss due to the random Overhauser field from hyperfine interaction, and spin relaxation rate due to spin-orbit interaction in a wide range of experimental parameters with a focus on the occurrence of spin hot spots. A safe parameter regime is identified in order to avoid these spin hot spots. We then analyze systematic errors due to non-adiabatic transitions in the Landau-Zener process of sweeping the interdot detuning, and propose a scheme to take advantage of possible Landau-Zener-Stückelberg interference to achieve high-fidelity spin transport at a higher speed. At last, we study another systematic error caused by the correction to the electron g-factor from the double dot potential, which can lead to a notable phase error. In all, our results should provide a useful guidance for future experiments on coherent electron spin transport.

Parallel-Coupled Quantum Dots in InAs Nanowires

We use crystal-phase tuning during epitaxial growth of InAs nanowires to create quantum dots with very strong confinement. A set of gate electrodes are used to reproducibly split the quantum dots into even smaller pairs for which we can control the populations down to the last electron. The double quantum dots, which are parallel-coupled to source and drain, show clear and stable odd-even level pairing due to spin degeneracy and the strong confinement. The combination of hard-wall barriers to source and drain, shallow interdot tunnel barriers, and very high single-particle excitation energies allow an order of magnitude tuning of the strength for the first intramolecular bond. We show examples for nanowires with different facet orientations, and suggest possible mechanisms behind the reproducible double-dot formation.

Coherent coupling between a quantum dot and a donor in silicon

Individual donors in silicon chips are used as quantum bits with extremely low error rates. However, physical realizations have been limited to one donor because their atomic size causes fabrication challenges. Quantum dot qubits, in contrast, are highly adjustable using electrical gate voltages. This adjustability could be leveraged to deterministically couple donors to quantum dots in arrays of qubits. In this work, we demonstrate the coherent interaction of a ³¹P donor electron with the electron of a metal-oxide-semiconductor quantum dot. We form a logical qubit encoded in the spin singlet and triplet states of the two-electron system. We show that the donor nuclear spin drives coherent rotations between the electronic qubit states through the contact hyperfine interaction. This provides every key element for compact two-electron spin qubits requiring only a single dot and no additional magnetic field gradients, as well as a means to interact with the nuclear spin qubit.

In silicon, quantum information can be stored in donors or quantum dots, each with its advantages and limitations—particularly in terms of fabrication. Here the authors coherently couple a phosphorous donor’s electron spin to a quantum dot, encoding information in the hybrid two-electron system’s state.

Effective spin Hamiltonian of a gated triple quantum dot in the presence of spin-orbit interaction

We derive and study the effective spin Hamiltonian of a gated triple quantum dot that includes the effects of spin-orbit interaction and an external magnetic field. In the analysis of the resulting spin interaction in linear and in general triangular geometry of the dots, we show that the pairwise spin interaction does depend on the position of the third dot. The spin-orbit induced anisotropy, in addition to changing its strength, also changes its symmetry with the motion of the third quantum dot outside the linear arrangement. Our results present a simplified model that may be used in the design of quantum computers based on three-spin qubits.

Environmental noise spectroscopy with qubits subjected to dynamical decoupling

A qubit subjected to pure dephasing due to classical Gaussian noise can be turned into a spectrometer of this noise by utilizing its readout under properly chosen dynamical decoupling (DD) sequences to reconstruct the power spectral density of the noise. We review the theory behind this DD-based noise spectroscopy technique, paying special attention to issues that arise when the environmental noise is non-Gaussian and/or it has truly quantum properties. While we focus on the theoretical basis of the method, we connect the discussed concepts with specific experiments, and provide an overview of environmental noise models relevant for solid-state based qubits, including quantum-dot based spin qubits, superconducting qubits, and NV centers in diamond.

Monolithic OLED-Microwire Devices for Ultrastrong Magnetic Resonant Excitation

Organic light-emitting diodes (OLEDs) make highly sensitive probes to test magnetic resonance phenomena under unconventional conditions since spin precession controls singlet-triplet transitions of electron-hole pairs, which in turn give rise to distinct recombination currents in conductivity. Electron paramagnetic resonance can therefore be detected in the absence of spin polarization. We exploit this characteristic to explore the exotic regime of ultrastrong light-matter coupling, where the Rabi frequency of a charge carrier spin is of the order of the transition frequency of the two-level system. To reach this domain, we have to lower the Zeeman splitting of the spin states, defined by the static magnetic field B₀, and raise the strength of the oscillatory driving field of the resonance, B₁. This is achieved by shrinking the OLED and bringing the source of resonant radio frequency (RF) radiation as close as possible to the organic semiconductor in a monolithic device structure, which incorporates an OLED fabricated directly on top of an RF microwire within one monolithic thin-film device structure. With an RF driving power in the milliwatt range applied to the microwire, the regime of bleaching and inversion of the magnetic resonance signal is reached due to the onset of the spin-Dicke effect. In this example of ultrastrong light-matter coupling, the individual resonant spin transitions of electron-hole pairs become indistinguishable with respect to the driving field, and superradiance of the magnetic dipole transitions sets in.

High-Fidelity Single-Shot Singlet-Triplet Readout of Precision-Placed Donors in Silicon

In this work we perform direct single-shot readout of the singlet-triplet states in exchange coupled electrons confined to precision-placed donor atoms in silicon. Our method takes advantage of the large energy splitting given by the Pauli-spin blockaded (2,0) triplet states, from which we can achieve a single-shot readout fidelity of 98.4±0.2%. We measure the triplet-minus relaxation time to be of the order 3 s at 2.5 T and observe its predicted decrease as a function of magnetic field, reaching 0.5 s at 1 T.

Robust Single-Shot Spin Measurement with 99.5% Fidelity in a Quantum Dot Array

We demonstrate a new method for projective single-shot measurement of two electron spin states (singlet versus triplet) in an array of gate-defined lateral quantum dots in GaAs. The measurement has very high fidelity and is robust with respect to electric and magnetic fluctuations in the environment. It exploits a long-lived metastable charge state, which increases both the contrast and the duration of the charge signal distinguishing the two measurement outcomes. This method allows us to evaluate the charge measurement error and the spin-to-charge conversion error separately. We specify conditions under which this method can be used, and project its general applicability to scalable quantum dot arrays in GaAs or silicon.

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.

Quantum entanglement: facts and fiction - how wrong was Einstein after all?

Einstein was wrong with his 1927 Solvay Conference claim that quantum mechanics is incomplete and incapable of describing diffraction of single particles. However, the Einstein-Podolsky-Rosen paradox of entangled pairs of particles remains lurking with its 'spooky action at a distance'. In molecules quantum entanglement can be viewed as basis of both chemical bonding and excitonic states. The latter are important in many biophysical contexts and involve coupling between subsystems in which virtual excitations lead to eigenstates of the total Hamiltonian, but not for the separate subsystems. The author questions whether atomic or photonic systems may be probed to prove that particles or photons may stay entangled over large distances and display the immediate communication with each other that so concerned Einstein. A dissociating hydrogen molecule is taken as a model of a zero-spin entangled system whose angular momenta are in principle possible to probe for this purpose. In practice, however, spins randomize as a result of interactions with surrounding fields and matter. Similarly, no experiment seems yet to provide unambiguous evidence of remaining entanglement between single photons at large separations in absence of mutual interaction, or about immediate (superluminal) communication. This forces us to reflect again on what Einstein really had in mind with the paradox, viz. a probabilistic interpretation of a wave function for an ensemble of identically prepared states, rather than as a statement about single particles. Such a prepared state of many particles would lack properties of quantum entanglement that make it so special, including the uncertainty upon which safe quantum communication is assumed to rest. An example is Zewail's experiment showing visible resonance in the dissociation of a coherently vibrating ensemble of NaI molecules apparently violating the uncertainty principle. Einstein was wrong about diffracting single photons where space-like anti-bunching observations have proven recently their non-local character and how observation in one point can remotely affect the outcome in other points. By contrast, long range photon entanglement with immediate, superluminal response is still an elusive, possibly partly misunderstood issue. The author proposes that photons may entangle over large distances only if some interaction exists via fields that cannot propagate faster than the speed of light. An experiment to settle this 'interaction hypothesis' is suggested.

A new regime of Pauli-spin blockade

Pauli-spin blockade (PSB) is a transport phenomenon in double quantum dots that allows for a type of spin to charge conversion often used to probe fundamental physics such as spin relaxation and singlet-triplet coupling. In this paper, we theoretically explore Pauli-spin blockade as a function of magnetic field B applied parallel to the substrate. In the well-studied low magnetic field regime, where PSB occurs in the forward (1, 1) → (0, 2) tunneling direction, we highlight some aspects of PSB that are not discussed in detail in existing literature, including the change in size of both bias triangles measured in the forward and reverse biasing directions as a function of B. At higher fields, we predict a crossover to "reverse PSB" in which current is blockaded in the reverse direction due to the occupation of a spin singlet as opposed to the traditional triplet blockade that occurs at low fields. The onset of reverse PSB coincides with the development of a tail like feature in the measured bias triangles and occurs when the Zeeman energy of the polarized triplet equals the exchange energy in the (0, 2) charge configuration. In Si quantum dots, these fields are experimentally accessible; thus, this work suggests a way to observe a crossover in magnetic field to qualitatively different behavior.

Spin-Orbit Coupling at the Level of a Single Electron

We utilize electron counting techniques to distinguish a spin-conserving fast tunneling process and a slower process involving spin flips in AlGaAs/GaAs-based double quantum dots. By studying the dependence of the rates on the interdot tunnel coupling of the two dots, we find that as many as 4% of the tunneling events occur with a spin flip related to spin-orbit coupling in GaAs. Our measurement has a fidelity of 99% in terms of resolving whether a tunneling event occurred with a spin flip or not.

Single donor electronics and quantum functionalities with advanced CMOS technology

Recent progresses in quantum dots technology allow fundamental studies of single donors in various semiconductor nanostructures. For the prospect of applications figures of merits such as scalability, tunability, and operation at relatively large temperature are of prime importance. Beyond the case of actual dopant atoms in a host crystal, similar arguments hold for small enough quantum dots which behave as artificial atoms, for instance for single spin control and manipulation. In this context, this experimental review focuses on the silicon-on-insulator devices produced within microelectronics facilities with only very minor modifications to the current industrial CMOS process and tools. This is required for scalability and enabled by shallow trench or mesa isolation. It also paves the way for real integration with conventional circuits, as illustrated by a nanoscale device coupled to a CMOS circuit producing a radio-frequency drive on-chip. At the device level we emphasize the central role of electrostatics in etched silicon nanowire transistors, which allows to understand the characteristics in the full range from zero to room temperature.

Electrical Control of g-Factor in a Few-Hole Silicon Nanowire MOSFET

Hole spins in silicon represent a promising yet barely explored direction for solid-state quantum computation, possibly combining long spin coherence, resulting from a reduced hyperfine interaction, and fast electrically driven qubit manipulation. Here we show that a silicon-nanowire field-effect transistor based on state-of-the-art silicon-on-insulator technology can be operated as a few-hole quantum dot. A detailed magnetotransport study of the first accessible hole reveals a g-factor with unexpectedly strong anisotropy and gate dependence. We infer that these two characteristics could enable an electrically driven g-tensor-modulation spin resonance with Rabi frequencies exceeding several hundred mega-Hertz.

Self-Assembled Wigner Crystals as Mediators of Spin Currents and Quantum Information

Technological applications of many-body structures that emerge in gated devices under minimal control are largely unexplored. Here we show how emergent Wigner crystals in a semiconductor quantum wire can facilitate a pivotal requirement for a scalable quantum computer, namely, transmitting quantum information encoded in spins faithfully over a distance of micrometers. The fidelity of the transmission is remarkably high, faster than the relevant decohering effects, independent of the details of the spatial charge configuration in the wire, and realizable in dilution refrigerator temperatures. The transfer can evidence near unitary many-body nonequilibrium dynamics hitherto unseen in a solid-state device. It could also be useful in spintronics as a method for pure spin current over a distance without charge movement.

Radio frequency measurements of tunnel couplings and singlet-triplet spin states in Si:P quantum dots

Spin states of the electrons and nuclei of phosphorus donors in silicon are strong candidates for quantum information processing applications given their excellent coherence times. Designing a scalable donor-based quantum computer will require both knowledge of the relationship between device geometry and electron tunnel couplings, and a spin readout strategy that uses minimal physical space in the device. Here we use radio frequency reflectometry to measure singlet–triplet states of a few-donor Si:P double quantum dot and demonstrate that the exchange energy can be tuned by at least two orders of magnitude, from 20 μeV to 8 meV. We measure dot–lead tunnel rates by analysis of the reflected signal and show that they change from 100 MHz to 22 GHz as the number of electrons on a quantum dot is increased from 1 to 4. These techniques present an approach for characterizing, operating and engineering scalable qubit devices based on donors in silicon.

Donor spin states in silicon are good quantum bit candidates due to their long coherence times. Here, the authors use radio frequency reflectometry to measure singlet and triplet states, and to determine the tunnel coupling between few-donor silicon double quantum dots and the electrical leads.

Exchange-Induced Spin Blockade in a Two-Electron Double Quantum Dot

We have experimentally identified the exchange-induced spin blockade in a GaAs double quantum dot. The transport is suppressed only when the eigenstates are well-defined singlet and triplet states, and thus sensitive to dynamic nuclear-spin polarization that causes singlet-triplet mixing. This gives rise to unusual current spectra, such as a sharp current dip and an asymmetric current profile near the triplet resonance of a double quantum dot. Numerical simulations suggest that the current dip is a signature of identical nuclear-spin polarization in the two dots, which is attractive for coherent spin manipulations in a material with nuclear spins.

Quantum Manipulation of Two-Electron Spin States in Isolated Double Quantum Dots

We studied experimentally the dynamics of the exchange interaction between two antiparallel electron spins in an isolated double quantum dot where coupling to the electron reservoirs can be ignored. We demonstrate that the level of control of such a double dot is higher than in conventional double dots. In particular, it allows us to couple coherently two electron spins in an efficient manner following a scheme initially proposed by Loss and DiVincenzo [Phys. Rev. A 57, 120 (1998)]. The present study demonstrates that isolated quantum dots are a possible route to increase the number of coherently coupled quantum dots.

Reconfigurable Quantum-Dot Molecules Created by Atom Manipulation

Quantum-dot molecules were constructed on a semiconductor surface using atom manipulation by scanning tunneling microscopy (STM) at 5 K. The molecules consist of several coupled quantum dots, each of which comprises a chain of charged adatoms that electrostatically confines intrinsic surface-state electrons. The coupling takes place across tunnel barriers created reversibly using the STM tip. These barriers have an invariant, reproducible atomic structure and can be positioned-and repeatedly repositioned-to create a series of reconfigurable quantum-dot molecules with atomic precision.

Dispersively Detected Pauli Spin-Blockade in a Silicon Nanowire Field-Effect Transistor

We report the dispersive readout of the spin state of a double quantum dot formed at the corner states of a silicon nanowire field-effect transistor. Two face-to-face top-gate electrodes allow us to independently tune the charge occupation of the quantum dot system down to the few-electron limit. We measure the charge stability of the double quantum dot in DC transport as well as dispersively via in situ gate-based radio frequency reflectometry, where one top-gate electrode is connected to a resonator. The latter removes the need for external charge sensors in quantum computing architectures and provides a compact way to readout the dispersive shift caused by changes in the quantum capacitance during inter-dot charge transitions. Here, we observe Pauli spin-blockade in the high-frequency response of the circuit at finite magnetic fields between singlet and triplet states. The blockade is lifted at higher magnetic fields when intra-dot triplet states become the ground state configuration. A line shape analysis of the dispersive phase shift reveals furthermore an intra-dot valley-orbit splitting Δvo of 145 μeV. Our results open up the possibility to operate compact complementary metal-oxide semiconductor (CMOS) technology as a singlet-triplet qubit and make split-gate silicon nanowire architectures an ideal candidate for the study of spin dynamics.

Identifying single electron charge sensor events using wavelet edge detection

The operation of solid-state qubits often relies on single-shot readout using a nanoelectronic charge sensor, and the detection of events in a noisy sensor signal is crucial for high fidelity readout of such qubits. The most common detection scheme, comparing the signal to a threshold value, is accurate at low noise levels but is not robust to low-frequency noise and signal drift. We describe an alternative method for identifying charge sensor events using wavelet edge detection. The technique is convenient to use and we show that, with realistic signals and a single tunable parameter, wavelet detection can outperform thresholding and is significantly more tolerant to 1/f and low-frequency noise.

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.

Retrodictive derivation of the radical-ion-pair master equation and Monte Carlo simulation with single-molecule quantum trajectories

Radical-ion-pair reactions, central in photosynthesis and the avian magnetic compass mechanism, have been recently shown to be a paradigm system for applying quantum information science in a biochemical setting. The fundamental quantum master equation describing radical-ion-pair reactions is still under debate. Here we use quantum retrodiction to formally refine the theory put forward in the paper by Kominis [I. K. Kominis, Phys. Rev. E 83, 056118 (2011)]. We also provide a rigorous analysis of the measure of singlet-triplet coherence required for deriving the radical-pair master equation. A Monte Carlo simulation with single-molecule quantum trajectories supports the self-consistency of our approach.

Quantum dynamics of the avian compass

The ability of migratory birds to orient relative to the Earth's magnetic field is believed to involve a coherent superposition of two spin states of a radical electron pair. However, the mechanism by which this coherence can be maintained in the face of strong interactions with the cellular environment has remained unclear. This paper addresses the problem of decoherence between two electron spins due to hyperfine interaction with a bath of spin-1/2 nuclei. Dynamics of the radical pair density matrix are derived and shown to yield a simple mechanism for sensing magnetic field orientation. Rates of dephasing and decoherence are calculated ab initio and found to yield millisecond coherence times, consistent with behavioral experiments.

Hole spin coherence in a Ge/Si heterostructure nanowire

Relaxation and dephasing of hole spins are measured in a gate-defined Ge/Si nanowire double quantum dot using a fast pulsed-gate method and dispersive readout. An inhomogeneous dephasing time T2* 0.18 μs exceeds corresponding measurements in III–V semiconductors by more than an order of magnitude, as expected for predominately nuclear-spin-free materials. Dephasing is observed to be exponential in time, indicating the presence of a broadband noise source, rather than Gaussian, previously seen in systems with nuclear-spin-dominated dephasing.

Spin-current Seebeck effect in quantum dot systems

We first bring up the concept of the spin-current Seebeck effect based on a recent experiment (Vera-Marun et al 2012 Nature Phys. 8 313), and investigate the spin-current Seebeck effect in quantum dot (QD) systems. Our results show that the spin-current Seebeck coefficient S is sensitive to different polarization states of the QD, and therefore can be used to detect the polarization state of the QD and monitor the transitions between different polarization states of the QD. The intradot Coulomb interaction can greatly enhance S due to the stronger polarization of the QD. By using the parameters for a typical QD whose intradot Coulomb interaction U is one order of magnitude larger than the linewidth Γ, we demonstrate that the maximum value of S can be enhanced by a factor of 80. On the other hand, for a QD whose Coulomb interaction is negligible, we show that one can still obtain a large S by applying an external magnetic field.

Steady-state entanglement in the nuclear spin dynamics of a double quantum dot

We propose a scheme for the deterministic generation of steady-state entanglement between the two nuclear spin ensembles in an electrically defined double quantum dot. Because of quantum interference in the collective coupling to the electronic degrees of freedom, the nuclear system is actively driven into a two-mode squeezedlike target state. The entanglement buildup is accompanied by a self-polarization of the nuclear spins towards large Overhauser field gradients. Moreover, the feedback between the electronic and nuclear dynamics leads to multistability and criticality in the steady-state solutions.

Charge sensed Pauli blockade in a metal-oxide-semiconductor lateral double quantum dot

We report Pauli blockade in a multielectron silicon metal-oxide-semiconductor double quantum dot with an integrated charge sensor. The current is rectified up to a blockade energy of 0.18 ± 0.03 meV. The blockade energy is analogous to singlet-triplet splitting in a two electron double quantum dot. Built-in imbalances of tunnel rates in the MOS DQD obfuscate some edges of the bias triangles. A method to extract the bias triangles is described, and a numeric rate-equation simulation is used to understand the effect of tunneling imbalances and finite temperature on charge stability (honeycomb) diagram, in particular the identification of missing and shifting edges. A bound on relaxation time of the triplet-like state is also obtained from this measurement.

Proposal for a phonon laser utilizing quantum-dot spin states

We propose a nanoscale realization of a phonon laser utilizing phonon-assisted spin flips in quantum dots to amplify sound. Owing to a long spin relaxation time, the device can be operated in a strong pumping regime, in which the population inversion is close to its maximal value allowed under Fermi statistics. In this regime, the threshold for stimulated emission is unaffected by spontaneous spin flips. Considering a nanowire with quantum dots defined along its length, we show that a further improvement arises from confining the phonons to one dimension, and thus reducing the number of phonon modes available for spontaneous emission. Our work calls for the development of nanowire-based, high-finesse phonon resonators.

Ultrafast optical control of individual quantum dot spin qubits

Single spins in semiconductor quantum dots form a promising platform for solid-state quantum information processing. The spin-up and spin-down states of a single electron or hole, trapped inside a quantum dot, can represent a single qubit with a reasonably long decoherence time. The spin qubit can be optically coupled to excited (charged exciton) states that are also trapped in the quantum dot, which provides a mechanism to quickly initialize, manipulate and measure the spin state with optical pulses, and to interface between a stationary matter qubit and a 'flying' photonic qubit for quantum communication and distributed quantum information processing. The interaction of the spin qubit with light may be enhanced by placing the quantum dot inside a monolithic microcavity. An entire system, consisting of a two-dimensional array of quantum dots and a planar microcavity, may plausibly be constructed by modern semiconductor nano-fabrication technology and could offer a path toward chip-sized scalable quantum repeaters and quantum computers. This article reviews the recent experimental developments in optical control of single quantum dot spins for quantum information processing. We highlight demonstrations of a complete set of all-optical single-qubit operations on a single quantum dot spin: initialization, an arbitrary SU(2) gate, and measurement. We review the decoherence and dephasing mechanisms due to hyperfine interaction with the nuclear-spin bath, and show how the single-qubit operations can be combined to perform spin echo sequences that extend the qubit decoherence from a few nanoseconds to several microseconds, more than 5 orders of magnitude longer than the single-qubit gate time. Two-qubit coupling is discussed, both within a single chip by means of exchange coupling of nearby spins and optically induced geometric phases, as well as over longer-distances. Long-distance spin-spin entanglement can be generated if each spin can emit a photon that is entangled with the spin, and these photons are then interfered. We review recent work demonstrating entanglement between a stationary spin qubit and a flying photonic qubit. These experiments utilize the polarization- and frequency-dependent spontaneous emission from the lowest charged exciton state to single spin Zeeman sublevels.

Estimating the hyperfine coupling parameters of the avian compass by comprehensively considering the available experimental results

Migratory birds can utilize the geomagnetic field for orientation and navigation through a widely accepted radical-pair mechanism. Although many theoretical works have been done, the available experimental results have not been fully considered, especially the temporary disorientation induced by the field which is increased by 30% of the geomagnetic field and the disorientation of the very weak resonant field of 15 nT. In this paper, we consider the monotonicity of the singlet yield angular profile as the prerequisite of direction sensitivity, and find that for some optimal values of the hyperfine coupling parameters (that is, the order of 10^{-7}∼10^{-6} meV) the experimental results available so far can be satisfied. We also investigate the effects of two decoherence environments and demonstrate that, in order to satisfy the available experimental results, the decoherence rate should be lower than the recombination rate. Finally, we investigate the effects of the fluctuating magnetic noises and find that the vertical noise destroys the monotonicity of the profile completely, but the parallel noise preserves the monotonicity perfectly and even can enhance the direction sensitivity.

Nondestructive real-time measurement of charge and spin dynamics of photoelectrons in a double quantum dot

We demonstrate one and two photoelectron trapping and the subsequent dynamics associated with interdot transfer in double quantum dots over a time scale much shorter than the typical spin lifetime. Identification of photoelectron trapping is achieved via resonant interdot tunneling of the photoelectrons in the excited states. The interdot transfer enables detection of single photoelectrons in a nondestructive manner. When two photoelectrons are trapped at almost the same time we observed that the interdot resonant tunneling is strongly affected by the Coulomb interaction between the electrons. Finally the influence of the two-electron singlet-triplet state hybridization has been detected using the interdot tunneling of a photoelectron.

The role of heavy-light-hole mixing on the optical initialization of hole spin in InAs quantum dots

The initialization of a resident hole spin by the absorption of a circularly polarized light at resonance involves the formation of an excited state called a trion state. For a pure heavy hole, this optical initialization is mediated by the hyperfine electron-nuclear coupling in the trion state. We show here that for a mixed-hole spin an additional mechanism for the optical initialization appears, associated to 'crossed transitions'; it becomes dominant and keeps a high level of hole spin polarization when the magnetic field screens the electron-nuclear interaction. Finally, using a simple model, we obtain a good theoretical agreement with pulsed pump-probe experiments.

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.

Topological blockade and measurement of topological charge

The fractionally charged quasiparticles appearing in the 5/2 fractional quantum Hall plateau are predicted to have an extra nonlocal degree of freedom, known as topological charge. We show how this topological charge can block the tunneling of these particles, and how such topological blockade can be used to read out their topological charge. We argue that the short time scale required for this measurement is favorable for the detection of the non-Abelian anyonic statistics of the quasiparticles. We also show how topological blockade can be used to measure braiding statistics, and to couple a topological qubit with a conventional one.

Role of nuclear quadrupole coupling on decoherence and relaxation of central spins in quantum dots

Strain-induced gradients of local electric fields in semiconductor quantum dots can couple to the quadrupole moments of nuclear spins. We develop a theory describing the influence of this quadrupolar coupling on the spin correlators of electron and hole "central" spins localized in such dots. We show that when the quadrupolar coupling strength is comparable to or larger than the hyperfine coupling strength between nuclei and the central spin, the relaxation rate of the central spin is strongly enhanced and can be exponential. We demonstrate a good agreement with recent experiments on spin relaxation in hole-doped (In,Ga)As self-assembled quantum dots.

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.