Bipolar spin blockade and coherent state superpositions in a triple quantum dot

Thermal rectification through the topological states of asymmetrical length armchair graphene nanoribbons heterostructures with vacancies

We present a theoretical investigation of electron heat current in asymmetrical length armchair graphene nanoribbon (AGNR) heterostructures with vacancies, focusing on the topological states (TSs). In particular, we examine the 9-7-9 AGNR heterostructures where the TSs are well-isolated from the conduction and valence subbands. This isolation effectively mitigates thermal noise of subbands arising from temperature fluctuations during charge transport. Moreover, when the TSs exhibit an orbital off-set, intriguing electron heat rectification phenomena are observed, primarily attributed to inter-TS electron Coulomb interactions. To enhance the heat rectification ratio (ηQ), we manipulate the coupling strengths between the heat sources and the TSs by introducing asymmetrical lengths in the 9-AGNRs. This approach offers control over the rectification properties, enabling significant enhancements. Additionally, we introduce vacancies strategically positioned between the heat sources and the TSs to suppress phonon heat current. This arrangement effectively reduces the overall phonon heat current, while leaving the TSs unaffected. Our findings provide valuable insights into the behavior of electron heat current in AGNR heterostructures, highlighting the role of topological states, inter-TS electron Coulomb interactions, and the impact of structural modifications such as asymmetrical lengths and vacancy positioning. These results pave the way for the design and optimization of graphene-based devices with improved thermal management and efficient control of electron heat transport.

Many-body tunneling and nonequilibrium dynamics in double quantum dots with capacitive coupling

Double quantum dots (DQDs) systems may be the minimal setups for realization of QD-based qubits and quantum computation. Pauli spin blockade (PSB) and a kind of novel many-body tunneling (MBT) are identified to play important roles in these systems, and dominate the quantum tunneling at moderate and weak interdot coupling t, respectively. On the other hand, inter-dot Coulomb interaction U' and related inter-dot Coulomb blockade (IDCB) is inevitable in DQDs. However, what would happen on the effect of U' in DQDs has not been touched, in particular for PSB and MBT. Here, we study the tunneling processes and transport properties with various U' in series-coupled DQDs, and find MBT process is rather robust against U' within U'/U < 0.1, where U is the intra-dot Coulomb interaction. Meanwhile, the linearity relationship between the carrier doublon number and MBT current remains valid. These findings enrich the understanding of the many-body tunneling in the DQDs and may shed light on the manipulation of the QD-based qubits.

Long-range overlapping of Kondo clouds in open triple quantum dots

We study the phenomena of overlapping of Kondo clouds in an open triple quantum dots (OTQDs) system by using the dissipaton equation of motion (DEOM) theory. Motivated by the long-rang interaction of the TQDs system demonstrated in Cheng et al (2017 Phys. Rev. B 95 155417), we present a comprehensive picture of the long-range overlapping behavior of Kondo clouds via investigation of the spectral functions, spin-spin correlation, dot occupancies and susceptibility. For the configuration [Formula: see text], a conduction electron peak occurs in the spectral function of intermediate QD in the Kondo regime. This peak results from the overlapping of the two Kondo clouds forming from between the two peripheral QDs and leads, enhances with decreasing temperature and increasing dot-lead coupling. Both the spin-spin correlations between the two adjacent QDs and the two peripheral QDs own negative values. It also confirms the physical picture of the overlapping between left and right Kondo clouds via the intermediate QD. To understand the physical insight, we examine also the electron occupacies and the spectral functions, with their dependence on the temperature and dot-lead coupling. In addition, a distinct nonmonotonic behavior of the susceptibility associated with the Kondo clouds is characterized.

Semiconductor quantum computation

Semiconductors, a significant type of material in the information era, are becoming more and more powerful in the field of quantum information. In recent decades, semiconductor quantum computation was investigated thoroughly across the world and developed with a dramatically fast speed. The research varied from initialization, control and readout of qubits, to the architecture of fault-tolerant quantum computing. Here, we first introduce the basic ideas for quantum computing, and then discuss the developments of single- and two-qubit gate control in semiconductors. Up to now, the qubit initialization, control and readout can be realized with relatively high fidelity and a programmable two-qubit quantum processor has even been demonstrated. However, to further improve the qubit quality and scale it up, there are still some challenges to resolve such as the improvement of the readout method, material development and scalable designs. We discuss these issues and introduce the forefronts of progress. Finally, considering the positive trend of the research on semiconductor quantum devices and recent theoretical work on the applications of quantum computation, we anticipate that semiconductor quantum computation may develop fast and will have a huge impact on our lives in the near future.

Fast long-range charge transfer in quantum dot arrays

Charge, spin and quantum states transfer in solid state devices is an important issue in quantum information. Adiabatic protocols, such as coherent transfer by adiabatic passage have been proposed for direct charge transfer, also denoted as long-range transfer, between the outer dots in a QD array without occupying the intermediate ones. However adiabatic protocols are prone to decoherence. With the aim of achieving direct charge transfer between the outer dots of a QD array with high fidelity, we propose a protocol to speed up the adiabatic transfer, in order to increase the fidelity of the process. Based on adiabaticity shortcuts, by properly engineering the pulses, fast adiabatic-like direct charge transfer between the outer dots can be obtained. We also discuss the impact of transfer fidelity on the operation time in the presence of dephasing. The proposed protocols for accelerating long-range charge and state transfer in a QD array offer a robust mechanism for quantum information transfer, by minimizing the decoherence and relaxation processes.

Two-qubit logical operations in three quantum dots system

We consider a model of two interacting always-on, exchange-only qubits for which controlled phase (CPHASE), controlled NOT (CNOT), quantum Fourier transform (QFT) and SWAP operations can be implemented only in a few electrical pulses in a nanosecond time scale. Each qubit is built of three quantum dots (TQD) in a triangular geometry with three electron spins which are always kept coupled by exchange interactions only. The qubit states are encoded in a doublet subspace and are fully electrically controlled by a voltage applied to gate electrodes. The two qubit quantum gates are realized by short electrical pulses which change the triangular symmetry of TQD and switch on exchange interaction between the qubits. We found an optimal configuration to implement the CPHASE gate by a single pulse of the order 2.3 ns. Using this gate, in combination with single qubit operations, we searched for optimal conditions to perform the other gates: CNOT, QFT and SWAP. Our studies take into account environment effects and leakage processes as well. The results suggest that the system can be implemented for fault tolerant quantum computations.

Ferromagnetic Phase in Nonequilibrium Quantum Dots

By nonperturbatively solving the nonequilibrium Anderson two-impurity model with the hierarchical equations of motion approach, we report a robust ferromagnetic (FM) phase in series-coupled double quantum dots, which can suppress the antiferromagnetic (AFM) phase and dominate the phase diagram at finite bias and detuning energy in the strongly correlated limit. The FM exchange interaction origins from the passive parallel spin arrangement caused by the Pauli exclusion principle during the electrons transport. At very low temperature, the Kondo screening of the magnetic moment in the FM phase induces some nonequilibrium Kondo effects in magnetic susceptibility, spectral functions and current. In the weakly correlated limit, the AFM phase is found still stable, therefore, a magnetic-field-free internal control of spin states can be expected through the continuous FM–AFM phase transition.

Three-electron spin qubits

The goal of this article is to review the progress of three-electron spin qubits from their inception to the state of the art. We direct the main focus towards the exchange-only qubit (Bacon et al 2000 Phys. Rev. Lett. 85 1758-61, DiVincenzo et al 2000 Nature 408 339) and its derived versions, e.g. the resonant exchange (RX) qubit, but we also discuss other qubit implementations using three electron spins. For each three-spin qubit we describe the qubit model, the envisioned physical realization, the implementations of single-qubit operations, as well as the read-out and initialization schemes. Two-qubit gates and decoherence properties are discussed for the RX qubit and the exchange-only qubit, thereby completing the list of requirements for quantum computation for a viable candidate qubit implementation. We start by describing the full system of three electrons in a triple quantum dot, then discuss the charge-stability diagram, restricting ourselves to the relevant subsystem, introduce the qubit states, and discuss important transitions to other charge states (Russ et al 2016 Phys. Rev. B 94 165411). Introducing the various qubit implementations, we begin with the exchange-only qubit (DiVincenzo et al 2000 Nature 408 339, Laird et al 2010 Phys. Rev. B 82 075403), followed by the RX qubit (Medford et al 2013 Phys. Rev. Lett. 111 050501, Taylor et al 2013 Phys. Rev. Lett. 111 050502), the spin-charge qubit (Kyriakidis and Burkard 2007 Phys. Rev. B 75 115324), and the hybrid qubit (Shi et al 2012 Phys. Rev. Lett. 108 140503, Koh et al 2012 Phys. Rev. Lett. 109 250503, Cao et al 2016 Phys. Rev. Lett. 116 086801, Thorgrimsson et al 2016 arXiv:1611.04945). The main focus will be on the exchange-only qubit and its modification, the RX qubit, whose single-qubit operations are realized by driving the qubit at its resonant frequency in the microwave range similar to electron spin resonance. Two different types of two-qubit operations are presented for the exchange-only qubits which can be divided into short-ranged and long-ranged interactions. Both of these interaction types are expected to be necessary in a large-scale quantum computer. The short-ranged interactions use the exchange coupling by placing qubits next to each other and applying exchange-pulses (DiVincenzo et al 2000 Nature 408 339, Fong and Wandzura 2011 Quantum Inf. Comput. 11 1003, Setiawan et al 2014 Phys. Rev. B 89 085314, Zeuch et al 2014 Phys. Rev. B 90 045306, Doherty and Wardrop 2013 Phys. Rev. Lett. 111 050503, Shim and Tahan 2016 Phys. Rev. B 93 121410), while the long-ranged interactions use the photons of a superconducting microwave cavity as a mediator in order to couple two qubits over long distances (Russ and Burkard 2015 Phys. Rev. B 92 205412, Srinivasa et al 2016 Phys. Rev. B 94 205421). The nature of the three-electron qubit states each having the same total spin and total spin in z-direction (same Zeeman energy) provides a natural protection against several sources of noise (DiVincenzo et al 2000 Nature 408 339, Taylor et al 2013 Phys. Rev. Lett. 111 050502, Kempe et al 2001 Phys. Rev. A 63 042307, Russ and Burkard 2015 Phys. Rev. B 91 235411). The price to pay for this advantage is an increase in gate complexity. We also take into account the decoherence of the qubit through the influence of magnetic noise (Ladd 2012 Phys. Rev. B 86 125408, Mehl and DiVincenzo 2013 Phys. Rev. B 87 195309, Hung et al 2014 Phys. Rev. B 90 045308), in particular dephasing due to the presence of nuclear spins, as well as dephasing due to charge noise (Medford et al 2013 Phys. Rev. Lett. 111 050501, Taylor et al 2013 Phys. Rev. Lett. 111 050502, Shim and Tahan 2016 Phys. Rev. B 93 121410, Russ and Burkard 2015 Phys. Rev. B 91 235411, Fei et al 2015 Phys. Rev. B 91 205434), fluctuations of the energy levels on each dot due to noisy gate voltages or the environment. Several techniques are discussed which partly decouple the qubit from magnetic noise (Setiawan et al 2014 Phys. Rev. B 89 085314, West and Fong 2012 New J. Phys. 14 083002, Rohling and Burkard 2016 Phys. Rev. B 93 205434) while for charge noise it is shown that it is favorable to operate the qubit on the so-called '(double) sweet spots' (Taylor et al 2013 Phys. Rev. Lett. 111 050502, Shim and Tahan 2016 Phys. Rev. B 93 121410, Russ and Burkard 2015 Phys. Rev. B 91 235411, Fei et al 2015 Phys. Rev. B 91 205434, Malinowski et al 2017 arXiv: 1704.01298), which are least susceptible to noise, thus providing a longer lifetime of the qubit.

Coherent long-distance displacement of individual electron spins

Controlling nanocircuits at the single electron spin level is a possible route for large-scale quantum information processing. In this context, individual electron spins have been identified as versatile quantum information carriers to interconnect different nodes of a spin-based semiconductor quantum circuit. Despite extensive experimental efforts to control the electron displacement over long distances, maintaining electron spin coherence after transfer remained elusive up to now. Here we demonstrate that individual electron spins can be displaced coherently over a distance of 5 µm. This displacement is realized on a closed path made of three tunnel-coupled lateral quantum dots at a speed approaching 100 ms⁻¹. We find that the spin coherence length is eight times longer than expected from the electron spin coherence without displacement, pointing at a process similar to motional narrowing observed in nuclear magnetic resonance experiments. The demonstrated coherent displacement will open the route towards long-range interaction between distant spin qubits.

The spin states of electrons in quantum dots have well-established potential for use as qubits but some proposed developments require the ability to move the quantum spin state across a larger device. Here, the authors experimentally demonstrate coherent shuttling of spins in a ring of three dots.

Coherent Transport in a Linear Triple Quantum Dot Made from a Pure-Phase InAs Nanowire

A highly tunable linear triple quantum dot (TQD) device is realized in a single-crystalline pure-phase InAs nanowire using a local finger gate technique. The electrical measurements show that the charge stability diagram of the TQD can be represented by three kinds of current lines of different slopes and a simulation performed based on a capacitance matrix model confirms the experiment. We show that each current line observable in the charge stability diagram is associated with a case where a QD is on resonance with the Fermi level of the source and drain reservoirs. At a triple point where two current lines of different slopes move together but show anticrossing, two QDs are on resonance with the Fermi level of the reservoirs. We demonstrate that an energetically degenerated quadruple point at which all three QDs are on resonance with the Fermi level of the reservoirs can be built by moving two separated triple points together via sophistically tuning of energy levels in the three QDs. We also demonstrate the achievement of direct coherent electron transfer between the two remote QDs in the TQD, realizing a long-distance coherent quantum bus operation. Such a long-distance coherent coupling could be used to investigate coherent spin teleportation and superexchange effects and to construct a spin qubit with an improved long coherent time and with spin state detection solely by sensing the charge states.

Manipulation of Pauli spin blockade in double quantum dot systems

Pauli spin blockade (PSB) is a significant physical effect in double quantum dot (DQD) systems. In this paper, we start from the fundamental quantum model of the DQD with the electron-electron interaction being considered and then systematically study the PSB effect in DQD by using a recently developed nonperturbative method, the hierarchical equations of motion approach. By checking the current-voltage and nonequilibrium spectral function features, the physical picture of the PSB is explicitly elucidated. Then, various kinds of manipulation of PSBs are discussed, including gate voltage, exchange interaction, and electron spin resonance. Three main characteristics beyond low-order perturbation theory are demonstrated in detail as follows: (1) the finite leakage current in the strongly correlated limit; (2) the enhancement and lifting of PSB by exchange interaction; and (3) the ON-and-OFF switch of PSB by real-time modulation.

Coherent and incoherent charge transport in linear triple quantum dots

One of the fundamental questions in quantum transport is how charge transfer through complex nanostructures is influenced by quantum coherence. We address this issue for linear triple quantum dots by comparing a Lindblad density matrix description with a Pauli rate equation approach and analyze the corresponding zero-frequency counting statistics of charge transfer. The impact of decaying coherences of the density matrix due to dephasing is also studied. Our findings reveal that the sensitivity to coherence shown by shot noise and skewness, in particular in the limit of large coupling to the drain reservoir, can be used to unambiguously evidence coherent processes involved in charge transport across triple quantum dots. Our analytical results are obtained by using the characteristic polynomial approach to full counting statistics.

Coherent spin-exchange via a quantum mediator

Coherent interactions at a distance provide a powerful tool for quantum simulation and computation. The most common approach to realize an effective long-distance coupling 'on-chip' is to use a quantum mediator, as has been demonstrated for superconducting qubits and trapped ions. For quantum dot arrays, which combine a high degree of tunability with extremely long coherence times, the experimental demonstration of the time evolution of coherent spin-spin coupling via an intermediary system remains an important outstanding goal. Here, we use a linear triple-quantum-dot array to demonstrate a coherent time evolution of two interacting distant spins via a quantum mediator. The two outer dots are occupied with a single electron spin each, and the spins experience a superexchange interaction through the empty middle dot, which acts as mediator. Using single-shot spin readout, we measure the coherent time evolution of the spin states on the outer dots and observe a characteristic dependence of the exchange frequency as a function of the detuning between the middle and outer dots. This approach may provide a new route for scaling up spin qubit circuits using quantum dots, and aid in the simulation of materials and molecules with non-nearest-neighbour couplings such as MnO (ref. 27), high-temperature superconductors and DNA. The same superexchange concept can also be applied in cold atom experiments.

Long-range doublon transfer in a dimer chain induced by topology and ac fields

The controlled transfer of particles from one site of a spatial lattice to another is essential for many tasks in quantum information processing and quantum communication. In this work we study how to induce long-range transfer between the two ends of a dimer chain, by coupling states that are localized just on the chain’s end-points. This has the appealing feature that the transfer occurs only between the end-points – the particle does not pass through the intermediate sites–making the transfer less susceptible to decoherence. We first show how a repulsively bound-pair of fermions, known as a doublon, can be transferred from one end of the chain to the other via topological edge states. We then show how non-topological surface states of the familiar Shockley or Tamm type can be used to produce a similar form of transfer under the action of a periodic driving potential. Finally we show that combining these effects can produce transfer by means of more exotic topological effects, in which the driving field can be used to switch the topological character of the edge states, as measured by the Zak phase. Our results demonstrate how to induce long range transfer of strongly correlated particles by tuning both topology and driving.

Quantum interference and structure-dependent orbital-filling effects on the thermoelectric properties of quantum dot molecules

The quantum interference and orbital filling effects on the thermoelectric (TE) properties of quantum dot (QD) molecules with high figure of merit are illustrated via the full solution to the Hubbard-Anderson model in the Coulomb blockade regime. It is found that under certain conditions in the triangular QD molecule (TQDM), destructive quantum interference (QI) can occur, which leads to vanishingly small electrical conductance, while the Seebeck coefficient is modified dramatically. When the TQDM is in the charge localization state due to QI, the Seebeck coefficient is seriously suppressed at low temperature, but is highly enhanced at high temperature. Meanwhile, the behavior of the Lorenz number reveals that it is easier to block charge transport via destructive QI than the electron heat transport at high temperatures. The maximum power factor (PF) in the TQDM occurs under full-filling conditions. Nevertheless, low-filling conditions are preferred for getting the maximum PF in serially coupled triple QDs in general. In double QDs, the maximum PF can be achieved either with orbital-depletion or orbital-filling as a result of electron-hole symmetry. Our theoretical work provides a useful guideline for the advancement of the nanoscale TE technology.

Quantum interference and electron correlation in charge transport through triangular quantum dot molecules

We study the charge transport properties of triangular quantum dot molecules (TQDMs) connected to metallic electrodes, taking into account all correlation functions and relevant charging states. The quantum interference (QI) effect of TQDMs resulting from electron coherent tunneling between quantum dots is revealed and well interpreted by the long distance coherent tunneling mechanism. The spectra of electrical conductance of TQDMs with charge filling from one to six electrons clearly depict the many-body and topological effects. The calculated charge stability diagram for conductance and total occupation numbers matches well with the recent experimental measurements. We also demonstrate that the destructive QI effect on the tunneling current of TQDMs is robust with respect to temperature variation, making the single electron QI transistor feasible at higher temperatures.

Circular-polarization-sensitive metamaterial based on triple-quantum-dot molecules

We propose a new type of chiral metamaterial based on an ensemble of artificial molecules formed by three identical quantum dots in a triangular arrangement. A static magnetic field oriented perpendicular to the plane breaks mirror symmetry, rendering the molecules sensitive to the circular polarization of light. By varying the orientation and magnitude of the magnetic field one can control the polarization and frequency of the emission spectrum. We identify a threshold frequency Ω, above which we find strong birefringence. In addition, Kerr rotation and circular-polarized lasing action can be implemented. We investigate the single-molecule lasing properties for different energy-level arrangements and demonstrate the possibility of circular-polarization conversion. Finally, we analyze the effect of weak stray electric fields or deviations from the equilateral triangular geometry.

Prediction of quantum dot characteristics through universal scaling relations

We derive scaling relations for the electrochemical potential and addition energy of 2D quantum dots charged with N electrons. In the derivation we apply the Thomas-Fermi theory for the harmonic model of a quantum dot in the effective mass approximation. We demonstrate that the resulting scaling relations yield excellent agreement with measured chemical potentials and addition energies for both lateral and vertical quantum dots. Moreover, we show that the scaling relation has predictive power in estimating the confinement strength and the number of electrons trapped in the quantum dot.

Tunable double and triple quantum dots in carbon nanotube with local side gates

We demonstrate a simple but efficient design for forming tunable single, double and triple quantum dots (QDs) in a sub-μm-long carbon nanotube (CNT) with two major features that distinguish this design from that of traditional CNT QDs: the use of i) Al2Ox tunnelling barriers between the CNT and metal contacts and ii) local side gates for controlling both the height of the potential barrier and the electron-confining potential profile to define multiple QDs. In a serial triple QD, in particular, we find that a stable molecular coupling state exists between two distant outer QDs. This state manifests in anti-crossing charging lines that correspond to electron and hole triple points for the outer QDs. The observed results are also reproduced in calculations based on a capacitive interaction model with reasonable configurations of electrons in the QDs. Our design using artificial tunnel contacts and local side gates provides a simple means of creating multiple QDs in CNTs for future quantum-engineering applications.

Single-electron dynamics of an atomic silicon quantum dot on the H-Si(100)-(2×1) surface

Here we report the direct observation of single electron charging of a single atomic dangling bond (DB) on the H-Si(100)-2×1 surface. The tip of a scanning tunneling microscope is placed adjacent to the DB to serve as a single-electron sensitive charge detector. Three distinct charge states of the dangling bond--positive, neutral, and negative--are discerned. Charge state probabilities are extracted from the data, and analysis of current traces reveals the characteristic single-electron charging dynamics. Filling rates are found to decay exponentially with increasing tip-DB separation, but are not a function of sample bias, while emptying rates show a very weak dependence on tip position, but a strong dependence on sample bias, consistent with the notion of an atomic quantum dot tunnel coupled to the tip on one side and the bulk silicon on the other.

Long-range spin transfer in triple quantum dots

Tunneling in a quantum coherent structure is not restricted to only nearest neighbors. Hopping between distant sites is possible via the virtual occupation of otherwise avoided intermediate states. Here we report the observation of long-range transitions in the transport through three quantum dots coupled in series. A single electron is delocalized between the left and right quantum dots, while the center one remains always empty. Superpositions are formed, and both charge and spin are exchanged between the outermost dots. The delocalized electron acts as a quantum bus transferring the spin state from one end to the other. Spin selection is enabled by spin correlations. The process is detected via the observation of narrow resonances which are insensitive to Pauli spin blockade.

Transport in asymmetrically coupled donor-based silicon triple quantum dots

We demonstrate serial electron transport through a donor-based triple quantum dot in silicon fabricated with nanoscale precision by scanning tunnelling microscopy lithography. From an equivalent circuit model, we calculate the electrochemical potentials of the dots allowing us to identify ground and excited states in finite bias transport. Significantly, we show that using a scanning tunnelling microscope, we can directly demonstrate that a ∼1 nm difference in interdot distance dramatically affects transport pathways between the three dots.

Long-distance coherent coupling in a quantum dot array

Controlling long-distance quantum correlations is central to quantum computation and simulation. In quantum dot arrays, experiments so far rely on nearest-neighbour couplings only, and inducing long-distance correlations requires sequential local operations. Here, we show that two distant sites can be tunnel-coupled directly. The coupling is mediated by virtual occupation of an intermediate site, with a strength that is controlled via the energy detuning of this site. It permits a single charge to oscillate coherently between the outer sites of a triple dot array without passing through the middle, as demonstrated through the observation of Landau-Zener-Stückelberg interference. The long-distance coupling significantly improves the prospects of fault-tolerant quantum computation using quantum dot arrays, and opens up new avenues for performing quantum simulations in nanoscale devices.