We demonstrate single-charge occupation of ambipolar quantum dots in silicon via charge sensing. We have fabricated ambipolar quantum dot (QD) devices in a silicon metal-oxide-semiconductor heterostructure comprising a single-electron transistor next to a single-hole transistor. Both QDs can be tuned to simultaneously sense charge transitions of the other. We further detect the few-electron and few-hole regimes in the QDs of our ambipolar device by active charge sensing.
We report on ambipolar gate-defined quantum dots in silicon on insulator (SOI) nanowires fabricated using a customised complementary metal-oxide-semiconductor (CMOS) process. The ambipolarity was achieved by extending a gate over an intrinsic silicon channel to both highly doped n-type and p-type terminals. We utilise the ability to supply ambipolar carrier reservoirs to the silicon channel to demonstrate an ability to reconfigurably define, with the same electrodes, double quantum dots with either holes or electrons. We use gate-based reflectometry to sense the inter-dot charge transition(IDT…
We integrate ambipolar quantum dots in silicon fin field-effect transistors using exclusively standard complementary metal-oxide-semiconductor fabrication techniques. We realize ambipolarity by replacing conventional highly-doped source and drain electrodes by a metallic nickel silicide with Fermi level close to the silicon mid-gap position. Such devices operate in a dual mode, either as classical field-effect or single-electron transistor. We implement a classical logic NOT gate at low temperature by tuning two interconnected transistors into opposite polarities. In the quantum regime, we dem…
We electrically measure intrinsic silicon quantum dots with electrostatically defined tunnel barriers. The presence of both p-type and n-type ohmic contacts enables the accumulation of either electrons or holes. Thus we are able to study both transport regimes within the same device. We investigate the effect of the tunnel barriers and the electrostatically defined quantum dots. There is greater localisation of charge states under the tunnel barriers in the case of hole conduction leading to higher charge noise in the p-regime.
In this Report we show the role of charge defects in the context of the formation of electrostatically defined quantum dots. We introduce a barrier array structure to probe defects at multiple locations in a single device. We measure samples both before and after an annealing process which uses an Al$_2$O$_3$ overlayer, grown by atomic layer deposition. After passivation of the majority of charge defects with annealing we can electrostatically define hole quantum dots up to 180 nm in length. Our ambipolar structures reveal amphoteric charge defects that remain after annealing with charging ene…
We study the steady-state characteristics and the transient behavior of the nonequilibrium double-dot Aharonov-Bohm interferometer using analytical tools and numerical simulations. Our simple setup includes noninteracting degenerate quantum dots that are coupled to two biased metallic leads at the same strength. A magnetic flux $Φ$ is piercing the setup perpendicularly. As we tune the degenerate dots energies away from the symmetric point we observe four nontrivial magnetic flux control effects: (i) flux dependency of the dots occupation, (ii) magnetic flux induced occupation difference betwee…
An ambipolar $n$-$p$ double quantum dot defined by potential variation along a semiconducting carbon-nanotube is considered. We focus on the (1e,1h) charge configuration with a single excess electron in the conduction band state confined in the $n$-type dot and a single missing electron in the valence band state of the $p$-dot for which lifting of the Pauli blockade of the current was observed in the electric-dipole spin resonance [E. A. Laird et al. Nat. Nanotech. 8 , 565 (2013)]. The dynamics of the system driven by periodic electric field is studied with the Floquet theory and the time-depe…
We study the occupation of two electrostatically-coupled single-level quantum dots with spinless electrons as a function of gate voltage. While the total occupation of the double-dot system varies monotonically with gate voltage, we predict that the competition between tunneling and Coulomb interaction can give rise to a nonmonotonic filling of the individual quantum dots. This non-monotonicity is a signature of the correlated nature of the many-body wavefunction in the reduced Hilbert space of the dots. We identify two mechanisms for this nonmonotonic behavior, which are associated with chang…
We have studied the dissipative dynamics of a solid-state qubit with an extra electron confined to either one of two coupled quantum dots. Previous theoretical work based on Bloch-type rate equations gave an unphysical uniform occupation probability of the electron in the quantum dots even for non-identical dots. We show that this is due to neglecting higher order interactions in the analysis. By including higher order terms, we obtain expected asymmetric occupation probabilities for non-identical dots. Our work demonstrates that the high order interaction terms can lead to important qualitati…
We describe the conditional and unconditional dynamics of two coupled quantum dots when one dot is subjected to a measurement of its occupation number using a single electron transistor (SET). The measurement is made when the bare tunneling rate though the SET is changed by the occupation number of one of the dots. We show that there is a difference between the time scale for the measurement-induced decoherence between the localized states of the dots and the time scale on which the system becomes localized due to the measurement. A comparison between theory and current experiments is made.
Nanowire double quantum dots occupied by an even number of electrons are investigated in the context of energy level structure revealed by electric dipole spin resonance measurements. We use numerically exact configuration interaction approach up to 6 electrons for systems tuned to Pauli spin blockade regime. We point out the differences between the spectra of systems with two and a greater number of electrons. For two-electrons the unequal length of the dots results in a different effective $g$-factors in the dots as observed by the recent experiments. For an increased number of electrons the…
Nonlocal entanglement between two quantum dots can be generated through Majorana fermions. The two Majorana fermions at the ends of an one-dimensional topological superconductor form a nonlocal fermion level, coupling to the occupation states of two quantum dots put close to the two ends, and the entire system will come into an entangled state. After introducing a charging energy by a capacitor, entanglement of the entire system can manifest itself through the nonlocal entanglement between the two quantum dots. That is, when measuring the electron occupations of the quantum dots, the measureme…
Measuring phase in coherent electron systems (mesoscopic systems) provides ample information not easily revealed by conductance measurements. Phase measurements in relatively large quantum dots (QDs) recently demonstrated a universal like phase evolution independent of dot size, shape, and occupancy. Explicitly, in Coulomb blockaded QDs the transmission phase increased monotonically by pi throughout each conductance peak, thereafter, in the conductance valleys the phase returned sharply to its base value. Expected mesoscopic features in the phase, related to spin degeneracy or to exchange effe…
We introduce a model of quantum teleportation on a channel built on a quantum dot chain. Quantum dots are coupled through hopping and each dot can accept zero, one or two electrons. Vacuum and double occupation states have the same potential energy, while single occupation states are characterized by a lower potential energy. A single dot initially decoupled from the others is weakly coupled with an external element (Bob), where a pair of electrons has been previously localized. Because of hopping after a suitable time the two dots charge states become maximally entangled. Another chain dot (A…
The charge transport properties of zero-temperature multi-orbital quantum dot systems with one dot coupled to leads and the other dots coupled only capacitatively are studied within density functional theory. It is shown that the setup is equivalent to an effective single impurity Anderson model. This allows to understand the level occupation switching effect as transitions between ground states of different integer occupations in the uncoupled dots. Level occupation switching is very sensitive to small energy differences and therefore also to the details of the parametrized exchange-correlati…
Indirect exchange interaction between itinerant electrons and nano-structures with non-trivial geometrical configurations manifests a plethora of unexpected results. These configurations can be realized either in quantum dots with several potential valleys or in real complex molecules with strong correlations. Here we demonstrate that the Kondo effect may be suppressed under certain conditions in triple quantum dots with mirror symmetry at odd electron occupation. First, we show that the indirect exchange has ferromagnetic sign in the ground state of triple quantum dot in a two-terminal cross …
We report measurements of the nonlinear conductance of InAs nanowire quantum dots coupled to superconducting leads. We observe a clear alternation between odd and even occupation of the dot, with sub-gap-peaks at $|V_{sd}|=Δ/e$ markedly stronger(weaker) than the quasiparticle tunneling peaks at $|V_{sd}|=2Δ/e$ for odd(even) occupation. We attribute the enhanced $Δ$-peak to an interplay between Kondo-correlations and Andreev tunneling in dots with an odd number of spins, and substantiate this interpretation by a poor man's scaling analysis.
We formulate the theory of electron transport through coupled-quantum dots by extending the auxiliary operator representation. By using the generating functional technique, we derive the exact expressions for currents, dot-occupation numbers and spin correlations, and examine them based on the non-equilibrium Green's function method under the non-crossing approximation (NCA). Our formulation generalizes the previous NCA approaches by allowing full occupation numbers with a finite Coulomb repulsion.
We report highly tunable control of holes in Ge/Si core/shell nanowires (NWs). We demonstrate the ability to create single quantum dots (QDs) of various sizes, with low hole occupation numbers and clearly observable excited states. For the smallest dot size we observe indications of single-hole occupation. Moreover, we create double and triple tunnel-coupled quantum dot arrays. In the double quantum dot configuration we observe Pauli spin blockade (PSB). These results open the way to perform hole spin qubit experiments in these devices.
We analyze the local level occupation of a spinless, interacting two-level quantum dot coupled to two leads by means of Wilson's numerical renormalization group method. A gate voltage sweep, causing a rearrangement of the charge such that the system's energy is minimized, leads to oscillations, and sometimes even inversions, in the level occupations. These charge oscillations can be understood qualitatively by a simple Hartree analysis. By allowing a relative sign in one tunneling matrix element between dot and leads, we extend our findings to more generic models.
The valley-orbit coupling in a few-electron Si quantum dot is expected to be a function of its occupation number N. We study the spectrum of multivalley Si quantum dots for 2 <= N <= 4, showing that, counterintuitively, electron-electron interaction effects on the valley-orbit coupling are negligible. For N=2 they are suppressed by valley interference, for N=3 they vanish due to spinor overlaps, and for N = 4 they cancel between different pairs of electrons. To corroborate our theoretical findings, we examine the experimental energy spectrum of a few-electron metal-oxide-semiconductor quantum …
We study an accumulation mode Si/SiGe double quantum dot (DQD) containing a single electron that is dipole coupled to microwave photons in a superconducting cavity. Measurements of the cavity transmission reveal dispersive features due to the DQD valley states in Si. The occupation of the valley states can be increased by raising temperature or applying a finite source-drain bias across the DQD, resulting in an increased signal. Using cavity input-output theory and a four-level model of the DQD, it is possible to efficiently extract valley splittings and the inter- and intra-valley tunnel coup…
We demonstrate a reconfigurable quantum dot gate architecture that incorporates two interchangeable transport channels. One channel is used to form quantum dots and the other is used for charge sensing. The quantum dot transport channel can support either a single or a double quantum dot. We demonstrate few-electron occupation in a single quantum dot and extract charging energies as large as 6.6 meV. Magnetospectroscopy is used to measure valley splittings in the range of 35-70 microeV. By energizing two additional gates we form a few-electron double quantum dot and demonstrate tunable tunnel …
We analyze tunneling-induced quantum fluctuations in a single-level quantum dot with arbitrarily strong onsite Coulomb interaction, generating cotunneling processes and renormalizing system parameters. For a perturbative analysis of these quantum fluctuations, we remove off-shell parts of the Hamiltonian via a canonical transformation. We find that the tunnel couplings for the transitions connecting empty and single occupation and connecting single and double occupation of the dot renormalize with the same magnitude but with opposite signs. This has an important impact on the shape of the reno…
Quantum dots are gate-defined within InSb nanowires, in proximity to NbTiN superconducting contacts. As the coupling between the dot and the superconductor is increased, the odd-parity occupations become non-discernible (erased) both above and below the induced superconducting gap. Above the gap, conductance in the odd Coulomb valleys increases until the valleys are lifted. Below the gap, Andreev bound states undergo quantum phase transitions to singlet ground states at odd occupancy. We observe that the apparent erasure of odd-parity regimes coincides at low-bias and at high-bias. This observ…
We investigate quantum dots in semiconductor PbTe nanowire devices. Due to the accessibility of ambipolar transport in PbTe, quantum dots can be occupied both with electrons and holes. Owing to a very large dielectric constant in PbTe of order 1000, we do not observe Coulomb blockade which typically obfuscates the orbital and spin spectra. We extract large and highly anisotropic effective Lande g-factors, in the range 20-44. The absence of Coulomb blockade allows direct readout, at zero source-drain bias, of spin-orbit hybridization energies of up to 600 microelectronvolt. These spin propertie…
The electronic spin precession in semiconductor dots is strongly affected by the spin-orbit coupling. We present a theory of the electronic spin resonance at low magnetic fields that predicts a strong dependence on the dot occupation, the magnetic field and the spin-orbit coupling strength. Coulomb interaction effects are also taken into account in a numerical approach.
The effect of an ac electric field on quantum transport properties in a system of three quantum dots, two of which are connected in parallel while the third is coupled to one of the other two, is investigated theoretically. Based on the Keldysh nonequilibrium Green's function method, the spin-dependent current, occupation number and spin accumulation can be obtained in our model. An external magnetic flux, Rashba spin orbit coupling (SOC) and intradot Coulomb interactions are considered. The magnitude of the spin-dependent average current and the positions of the photon assisted tunneling (PAT…
Electrostatic confinement of charge carriers in bilayer graphene provides a unique platform for carbon-based spin, charge or exchange qubits. By exploiting the possibility to induce a band gap with electrostatic gating, we form a versatile and widely tunable multi-quantum dot system. We demonstrate the formation of single, double and triple quantum dots that are free of any sign of disorder. In bilayer graphene we have the possibility to form tunnel barriers using different mechanisms. We can exploit the ambipolar nature of bilayer graphene where pn-junctions form natural tunnel barriers. Alte…
We study the effects of intraband relaxation processes on optical manipulation protocols for sp biexcitons hosted by CdTe disk-shaped quantum dots. The many-body states are calculated within the configuration interaction method starting from single-particle states given by the kp theory. The time-dependent occupations of relevant many-body states are extracted from the von Neumann-Lindblad equation for the density operator. We mainly investigate the generation of sp biexcitons with two pulses of different polarizations sigma_{+} and sigma_{-}. The fast hole relaxation processes prevent a high-…
This Chapter contains a review of the recent results, both experimental and theoretical, related to optical control of carriers confined in semiconductor quantum dots. The physics of Rabi oscillations of exciton and biexciton occupations, as well as time-domain interference experiments are discussed. Next, the impact of carrier--phonon interaction in a semiconductor structure is described and modern methods of theoretical description of the carrier--phonon kinetics and of the resulting dephasing are presented.
We theoretically investigate transport signatures of quantum interference in highly symmetric double quantum dots in a parallel geometry and demonstrate that extremely weak symmetry-breaking effects can have a dramatic influence on the current. Our calculations are based on a master equation where quantum interference enters as non-diagonal elements of the density matrix of the double quantum dots. We also show that many results have a physically intuitive meaning when recasting our equations as Bloch-like equations for a pseudo spin associated with the dot occupation. In the perfectly symmetr…
Weakly coupled quantum dots in the Pauli spin blockade regime are considered with respect to spin-dependent transport. By attaching one half-metallic and one non-magnetic lead, the Pauli spin blockade if formed by a pure triplet state with spin moment $S_z=1$ or -1. Furthermore, additional spin blockade regimes emerge because of full occupation in states with opposite spin to that of the half-metallic lead.
It is demonstrated that parallel weakly coupled quantum dots exhibit non-equilibrium blockade regimes caused by a full occupation in the spin triplet state, in analogy to the Pauli spin blockade in serially weakly coupled quantum dots. Charge tends to accumulate in the two-electron triplet for bias voltages that support transitions between the singlet and three-electron states.
Electrostatically defined quantum dots in bilayer graphene offer a promising platform for spin qubits with presumably long coherence times due to low spin-orbit coupling and low nuclear spin density. We demonstrate two different experimental approaches to measure the decay times of excited states. The first is based on direct current measurements through the quantum device. Pulse sequences are applied to control the occupation of ground and excited states. We observe a lower bound for the excited state decay on the order of hundred microseconds. The second approach employs a capacitively coupl…
Holes in silicon quantum dots are receiving significant attention due to their potential as fast, tunable, and scalable qubits in semiconductor quantum circuits. Despite this, challenges remain in this material system including difficulties using charge sensing to determine the number of holes in a quantum dot, and in controlling the coupling between adjacent quantum dots. In this work, we address these problems by fabricating an ambipolar complementary metal-oxide-semiconductor (CMOS) device using multilayer palladium gates. The device consists of an electron charge sensor adjacent to a hole …
We propose steady-state electron transport based on coherent transfer by adiabatic passage (CTAP) in a linearly arranged triple quantum dot with leads attached to the outer dots. Its main feature is repeated steering of single electrons from the first dot to the last dot without relevant occupation of the middle dot. The coupling to leads enables a steady-state current, whose shot noise is significantly suppressed provided that the CTAP protocol performs properly. This represents an indication for the direct transfer between spatially separated dots and, thus, may resolve the problem of findin…
We analyze the reading and initialization of a topological qubit encoded by Majorana fermions in one-dimensional semiconducting nanowires, weakly coupled to a single level quantum dot (QD). It is shown that when the Majorana fermions are fused by tuning gate voltage, the topological qubit can be read out directly through the occupation of the QD in an energy window. The initialization of the qubit can also be realized via adjusting the gate voltage on the QD, with the total fermion parity conserved. As a result, both reading and initialization processes can be achieved in an all-electrical way…
We provide an atomistic tight-binding description of a few carriers confined in ambipolar (n-p) double quantum dots defined in a semiconducting carbon nanotube. We focus our attention on the charge state of the system in which Pauli blockade of the current flow is observed [F. Pei et al., Nat. Nanotechnol. 7, 630 (2012); E. A. Laird et al., ibid 8, 565 (2013)] with a single excess electron in the n-dot and a single hole in the p-dot. We use the configuration interaction approach to determine the spin-valley structure of the states near the neutrality point and discuss its consequences for the …
We investigated the peculiarities of non-equilibrium charge configurations in the system of two strongly coupled quantum dots (QDs) weakly connected to the reservoirs in the presence of Coulomb correlations. We revealed that total electron occupation demonstrates in some cases significant decreasing with increasing of applied bias - contrary to the situation when Coulomb correlations are absent and found well pronounced ranges of system parameters where negative tunneling conductivity appears due to the Coulomb correlations.
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.
Tunneling in a quantum coherent structure is not restricted to only nearest neighbours. 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 centre one remains always empty. Superpositions are formed and both charge and spin are exchanged between the outermost dots. Detection of the process is achieved via the observation of narrow reson…
Time evolution of initially prepared entangled state in the system of coupled quantum dots has been analyzed by means of two different theoretical approaches: equations of motion for the all orders localized electron correlation functions, considering interference effects, and kinetic equations for the pseudo-particle occupation numbers with constraint on the possible physical states. Results obtained by means of different approaches were carefully analyzed and compared with each other. Revealed direct link between concurrence (degree of entanglement) and quantum dots pair correlation function…
We present a theoretical study of vacuum-induced coherence in a pair of vertically stacked semiconductor quantum dots. The process consists in a coherent excitation transfer from a single-exciton state localized in one dot to a delocalized state in which the exciton occupation gets trapped. We study the influence of the factors characteristic of quantum dot systems (as opposed to natural atoms): energy mismatch, coupling between the single exciton states localized in different dots, different and non-parallel dipoles due to subband mixing, as well as coupling to phonons. We show that the destr…
The possibility of non-adiabatic electron pumping in the system of three coupled quantum dots attached to the leads is discussed. We have found out that periodical changing of energy level position in the middle quantum dot results in non zero mean tunneling current appeared due to non-adiabatic non-equilibrium processes. The same principle can be used for fabrication of a new class of semiconductor electronic devices based on non-stationary non-equilibrium currents. As an example we propose a nanometer quantum emitter with non-stationary inverse level occupation achieved by electron pumping.
We study theoretically a double quantum dot hydrogen molecule in the GaAs conduction band as the basic elementary gate for a quantum computer with the electron spins in the dots serving as qubits. Such a two-dot system provides the necessary two-qubit entanglement required for quantum computation. We determine the excitation spectrum of two horizontally coupled quantum dots with two confined electrons, and study its dependence on an external magnetic field. In particular, we focus on the splitting of the lowest singlet and triplet states, the double occupation probability of the lowest states,…
The particle transport through a chain of quantum dots coupled to two bosonic reservoirs is studied. For the case of reservoirs of non-interacting bosonic particles, we derive an exact set of stochastic differential equations, whose memory kernels and driving noise are characterised entirely by the properties of the reservoirs. Going to the Markovian limit an analytically solvable case is presented. The effect of interparticle interactions on the transient behaviour of the system, when both reservoirs are instantaneously coupled to an empty chain of quantum dots, is approximated by a semiclass…
We report the fabrication and measurement of one-electron single and double quantum dots with fast tunnel rates in a Si/SiGe heterostructure. Achieving fast tunnel rates in few-electron dots can be challenging, in part due to the large electron effective mass in Si. Using charge sensing, we identify signatures of tunnel rates in and out of the dot that are fast or slow compared to the measurement rate. Such signatures provide a means to calibrate the absolute electron number and verify single electron occupation. Pulsed gate voltage measurements are used to validate the approach.
We study non-equilibrium current and occupation probabilities of a two-orbital quantum dot. The couplings to the leads are allowed to be asymmetric and orbital dependent as it is generically the case in transport experiments on molecules and nanowires. Starting from a two-orbital Anderson model, we perform a generalised Schrieffer-Wolff transformation to derive an effective Kondo model. This generates an orbital potential scattering contribution which is of the same order as the spin exchange interaction. In a first perturbative analysis we identify a regime of negative differential conductanc…
We describe in this short review the influence of discrete symmetries in complex quantum dots on the Kondo co-tunneling through these nano-objects. These discrete symmetries stem from the geometrical structure of the tunneling devices (e.g spatial symmetry of multivalley quantum dot in a tunneling contact with leads). They affect the dynamical symmetry of spin multiplets characterizing the ground state and excitations in quantum dots with definite electron number occupation. The influence of external electric and magnetic fields on these symmetries is examined, and analogies with the physics o…
We consider a `quantum dot' in the Coulomb blockade regime, subject to an arbitrarily large source-drain voltage V. When V is small, quantum dots with odd electron occupation display the Kondo effect, giving rise to enhanced conductance. Here we investigate the regime where V is increased beyond the Kondo temperature and the Kondo resonance splits into two components. It is shown that interference between them results in spontaneous oscillations of the current through the dot. The theory predicts the appearance of ``Shapiro steps'' in the current-voltage characteristics of an irradiated quantu…
Time-resolved electron dynamics in coupled quantum dots is directly observed by a pulsed-gate technique. While individual gate voltages are modulated with periodic pulse trains, average charge occupations are measured with a nearby quantum point contact as detector. A key component of our setup is a sample holder optimized for broadband radio frequency applications. Our setup can detect displacements of single electrons on time scales well below a nanosecond. Tunneling rates through individual barriers and relaxation times are obtained by using a rate equation model. We demonstrate the full ch…
The time evolution of a qubit, consisting of two single-level quantum dots, is studied in the presence of telegraph noise. The dots are connected by two tunneling paths, with an Aharonov-Bohm flux enclosed between them. Under special symmetry conditions, which can be achieved by tuning gate voltages, there develops partial decoherence: at long times, the off-diagonal element of the reduced density matrix (in the basis of the two dot states) approaches a non-zero value, generating a circulating current around the loop. The flux dependence of this current contains full information on the initial…
