Electrostatically-defined semiconductor quantum dot arrays offer a promising platform for quantum computation and quantum simulation. However, crosstalk of gate voltages to dot potentials and inter-dot tunnel couplings complicates the tuning of the device parameters. To date, crosstalk to the dot potentials is routinely and efficiently compensated using so-called virtual gates, which are specific linear combinations of physical gate voltages. However, due to exponential dependence of tunnel couplings on gate voltages, crosstalk to the tunnel barriers is currently compensated through a slow iterative process. In this work, we show that the crosstalk on tunnel barriers can be efficiently characterized and compensated for, using the fact that the same exponential dependence applies to all gates. We demonstrate efficient calibration of crosstalk in a quadruple quantum dot array and define a set of virtual barrier gates, with which we show orthogonal control of all inter-dot tunnel couplings. Our method marks a key step forward in the scalability of the tuning process of large-scale quantum dot arrays.
Two main mechanisms dictate the tunneling process in a double quantum dot: overlap of excited wave functions, effectively described as a tunneling rate, and phonon-assisted tunneling. In this paper, we study different regimes of tunneling that arise from the competition between these two mechanisms in a double quantum dot molecule immersed in a unimodal optical cavity. We show how such regimes affect the mean number of excitations in each quantum dot and in the cavity, the spectroscopic resolution and emission peaks of the photoluminescence spectrum, and the second-order coherence function whi…
In Si quantum dots, valley degree of freedom, in particular the generally small valley splitting and the dot-dependent valley-orbit phase, adds complexities to the low-energy electron dynamics and the associated spin qubit manipulation. Here we propose a four-level model to extract tunnel coupling information for a Si double quantum dot (DQD). This scheme is based on a charge sensing measurement on the ground state as proposed in the widely used protocol for a GaAs double dot [DiCarlo et. al., PRL 92. 226801]. Our theory can help determine both intra- and inter-valley tunnel coupling with high…
The long term scaling prospects for solid-state quantum computing architectures relies heavily on the ability to simply and reliably measure and control the coherent electron interaction strength, known as the tunnel coupling, $t_c$. Here, we describe a method to extract the $t_c$ between two quantum dots (QDs) utilising their different tunnel rates to a reservoir. We demonstrate the technique on a few donor triple QD tunnel coupled to a nearby single-electron transistor (SET) in silicon. The device was patterned using scanning tunneling microscopy-hydrogen lithography allowing for a direct me…
Quantum computation based on semiconductor electron-spin qubits requires high control of tunnel-couplings, both across quantum dots and between the quantum dot and the reservoir. The tunnel-coupling to the reservoir sets the qubit detection and initialization bandwidth for energy-resolved spin-to-charge conversion and is essential to tune single-electron transistors commonly used as charge detectors. Potential disorder and the increasing complexity of the two-dimensional gate-defined quantum computing devices sets high demands on the gate design and the voltage tuning of the tunnel barriers. W…
Resonant tunneling through identical potential barriers is a textbook problem in quantum mechanics. Its solution yields total transparency (100% tunneling) at discrete energies. This dramatic phenomenon results from coherent interference among many trajectories, and it is the basis of transport through periodic structures. Resonant tunneling of electrons is commonly seen in semiconducting 'quantum dots'. Here we demonstrate that detecting (distinguishing) electron trajectories in a quantum dot (QD) renders the QD nearly insulating. We couple trajectories in the QD to a 'detector' by employing …
We perform photon-assisted-tunneling (PAT) experiments on a GaAs double quantum dot device under high microwave excitation power. Photon-assisted absorption of up to 14 photons is observed, when electron temperature (>1K) are far above the lattice temperature. Signatures of Landau-Zener-Stückelberg (LZS) interference are found even in this non-equilibrium PAT spectrum. In addition, the charge state relaxation time T_1~8ns measured in this out of thermal equilibrium double quantum dot is in agreement with other previous reports.
We study phonon-assisted electron tunneling in semiconductor quantum dot molecules. In particular, singlet-singlet relaxation in a two-electron doped structure is considered. The influence of Coulomb interaction is discussed via comparison with a single electron system. We find that the relaxation rate reaches similar values in the two cases but the Coulomb interaction shifts the maximum rates towards larger separations between the dots. The difference in electron-phonon interaction between deformation potential and piezoelectric coupling is investigated. We show that the phonon-induced tunnel…
Graphene double quantum open the possibility to use charge or spin degrees of freedom for storing and manipulating quantum information in this new electronic material. However, impurities and edge disorders in etched graphene nano-structures hinder the ability to control the inter-dot tunnel coupling, tc,the most important property of the artificial molecule. Here we report measurements of tc in an all-metal-gates-tuned graphene DQD. We find that tc can be controlled continuously about a factor of four by employing a single gate. Furthermore, tc, can be changed monotonically about another fact…
QDarts: A Quantum Dot Array Transition Simulator for finding charge transitions in the presence of finite tunnel couplings, non-constant charging energies and sensor dots
Left-handedness with three zero-absorption windows tuned by the incoherent pumping field and inter-dot tunnelings in a GaAs/AlGaAs triple quantum dots system
A scheme based on Coherent Tunneling by Adiabatic Passage (CTAP) of exchange-only spin qubit quantum states in a linearly arranged double quantum dot chain is demonstrated. Logical states for the qubit are defined by adopting the spin state of three electrons confined in a double quantum dot. The possibility to obtain gate operations entirely with electrical manipulations makes this qubit a valuable architecture in the field of quantum computing for the implementation of quantum algorithms. The effect of the external control parameters as well as the effect of the dephasing on the coherent tun…
Localized orbitals and tunnel couplings from general confinement potentials in gate-defined quantum-dot arrays
Institute for Quantum Computing and Department of Physics, University of Waterloo（滑铁卢大学量子计算研究所与物理系）；Institute for Quantum Computing and Department of Chemistry, University of Waterloo（滑铁卢大学量子计算研究所与化学系）
We prepare a gate-defined quadruple quantum dot to study the gate-tunability of single to quadruple quantum dots with finite inter-dot tunnel couplings. The measured charging energies of various double dots suggest that the dot size is governed by gate geometry. For the triple and quadruple dots we study gate-tunable inter-dot tunnel couplings. Particularly for the triple dot we find that the effective tunnel coupling between side dots significantly depends on the alignment of the center dot potential. These results imply that the present quadruple dot device has gate performance relevant for …
We prepare a triple quantum dot with a separate contact lead to each dot to study Pauli spin blockade in the tunnel-coupled three dots in a row. We measure the tunneling current flowing between the center dot and either the left or right dot with the left and right leads as a common source and the center lead as a drain. In the biased stability diagram, we establish Pauli spin blockade in the respective neighboring dots, with features similarly obtained in double quantum dot systems. We further realize Pauli spin blockade with two different conditions by tuning the inter-dot coupling gates: st…
We present measurements of the rates for an electron to tunnel on and off a quantum dot, obtained using a quantum point contact charge sensor. The tunnel rates show exponential dependence on drain-source bias and plunger gate voltages. The tunneling process is shown to be elastic, and a model describing tunneling in terms of the dot energy relative to the height of the tunnel barrier quantitatively describes the measurements.
We review experiments on single electron transport through single quantum dots in the presence of a microwave signal. In the case of a small dot with well-resolved discrete energy states, the applied high-frequency signal allows for inelastic tunnel events that involve the exchange of photons with the microwave field. These photon assisted tunneling (PAT) processes give rise to sideband resonances in addition to the main resonance. Photon absorption can also lead to tunneling via excited states instead of tunneling via the ground state of the quantum dot.
We employ ultrafast pump-probe spectroscopy to directly monitor electron tunneling between discrete orbital states in a pair of spatially separated quantum dots. Immediately after excitation, several peaks are observed in the pump-probe spectrum due to Coulomb interactions between the photo-generated charge carriers. By tuning the relative energy of the orbital states in the two dots and monitoring the temporal evolution of the pump-probe spectra the electron and hole tunneling times are separately measured and resonant tunneling between the two dots is shown to be mediated both by elastic and…
A two-dimensional arrangement of quantum dots with finite inter-dot tunnel coupling provides a promising platform for studying complicated spin correlations as well as for constructing large-scale quantum computers. Here, we fabricate a tunnel-coupled triangular triple quantum dot with a novel gate geometry in which three dots are defined by positively biasing the surface gates. At the same time, the small area in the center of the triangle is depleted by negatively biasing the top gate placed above the surface gates. The size of the small center depleted area is estimated from the Aharonov-Bo…
We demonstrate theoretically that it is possible to use Rabi oscillations to coherently control the electron tunneling in an asymmetric double quantum dot system, a quantum dot molecule. By applying an optical pump pulse we can excite an electron in one of the dots, which can in turn tunnel to the second dot, as controlled by an external voltage. Varying the intensity of the pulse one can suppress or enhance the tunneling between the dots for given level resonance conditions. This approach allows substantial flexibility in the control of the quantum mechanical state of the system.
Molecular beam epitaxy is employed to manufacture self-assembled InAs/AlAs quantum-dot resonant tunneling diodes. Resonant tunneling current is superimposed on the thermal current, and they make up the total electron transport in devices. Steps in current-voltage characteristics and peaks in capacitance-voltage characteristics are explained as electron resonant tunneling via quantum dots at 77K or 300K, and this is the first time that resonant tunneling is observed at room temperature in III-V quantum-dot materials. Hysteresis loops in the curves are attributed to hot electron injection/emissi…
Semiconductor quantum dot arrays defined electrostatically in a 2D electron gas provide a scalable platform for quantum information processing and quantum simulations. For the operation of quantum dot arrays, appropriate voltages need to be applied to the gate electrodes that define the quantum dot potential landscape. Tuning the gate voltages has proven to be a time-consuming task, because of initial electrostatic disorder and capacitive cross-talk effects. Here, we report on the automated tuning of the inter-dot tunnel coupling in a linear array of gate-defined semiconductor quantum dots. Th…
We study theoretically the interaction between the charge dynamics of a few-electron double quantum dot and a capacitively-coupled AFM cantilever, a setup realized in several recent experiments. We demonstrate that the dot-induced frequency shift and damping of the cantilever can be used as a sensitive probe of coherent inter-dot tunnelling, and that these effects can be used to quantitatively extract both the magnitude of the coherent interdot tunneling and (in some cases) the value of the double-dot T_1 time. We also show how the adiabatic modulation of the double-dot eigenstates by the cant…
We study electronic transport through quantum dots weakly coupled to ferromagnetic leads with collinear magnetization directions. Tunneling contributions of first and second order in the tunnel-coupling strength are taken into account. We analyze the tunnel magnetoresistance (TMR) for all combinations of linear and nonlinear response, at or off resonance, with an even or odd dot-electron number. Different mechanisms for transport and spin accumulation the various regimes give rise to different TMR behavior.
We theoretically study the effects of bias-controlled interdot tunneling in vertically coupled quantum dots on the emission properties of spin excitons in various bias-controlled tunneling regimes. As a main result, for strongly coupled dots we predict substantial reduction of optical fine structure splitting without any drop in the optical oscillator strength. This special reduction diminishes the distinguibility of polarized decay paths in cascade emission processes suggesting the use of stacked quantum dot molecules as entangled photon-pair sources.
We report on non-linear magneto-tunneling experiments carried out in single GaAs vertical quantum dots. We show that conduction at low voltage bias can be a spectroscopic tool for both the ground state and first excited states of few electrons on the dot. Increasing voltage a large resonant peak is observed and attributed to tunneling across the quasi-continuum of higher excited states.
Tunnel-injection lasers promise advantages in modulation bandwidth and temperature stability in comparison to conventional laser designs. In this paper, we present results of a microscopic theory for laser properties of tunnel-injection devices and a comparison to a conventional quantum-dot laser structure. In general, the modulation bandwidth of semiconductor lasers is affected by the steady-state occupations of electrons and holes via the presence of spectral hole burning. For tunnel-injection lasers with InGaAs quantum dot emitting at the telecom wavelength of 1,55$μ$m, we demonstrate that …
We investigate quantum photovoltaic effect in double quantum dots by applying nonequilibrium quantum master equation. The drastic suppression of the photovoltaic current is observed near the open circuit voltage, which leads to the large filling factor. We find that there always exists an optimal inter-dot tunneling that significantly enhances the photovoltaic current. The maximal output power will also be obtained around the optimal inter-dot tunneling. Moreover, the open circuit voltage approximately behaves as the product of the eigen-level gap and the Carnot efficiency. These results sugge…
Inherent asymmetry in the tunneling barriers of few-electron quantum dots induces intrinsically different tunneling currents for forward and reverse source-drain biases in the non-linear transport regime. Here we show that in addition to spin selection rules, overlap matrix elements between many-body states are crucial for the correct description of tunneling transmission through quantum dots at large magnetic fields. Signatures of excited (N-1)-electron states in the transport process through the N-electron system are clearly identified in the measured transconductances. Our analysis clearly …
We investigate the conductance and zero-frequency shot noise of interacting, multi-level quantum dots coupled to leads. We observe that co-tunneling assisted sequential tunneling (CAST) processes play a dominant role in the transition region from Coulomb blockade to sequential tunneling. We analyze for intermediate coupling strength the dependence of the conductance due to CAST processes on temperature, coupling constant, and gate voltage. Remarkably, the width of the CAST transport feature scales only with temperature, but not with the coupling constant. While the onset of inelastic co-tunnel…
The anomalous low-temperature behavior of the spontaneous magnetization of ordered arrays of In_{1-x}Mn_xAs quantum dots is discussed. It is shown that the experimental results can be well understood, within a mean field approximation, assuming collective response through rather strong spin tunneling processes between neighbouring dots.
We present a diagrammatic real-time approach to adiabatic pumping of electrons through interacting quantum dots. Performing a systematic perturbation expansion in the tunnel-coupling strength, we compute the charge pumped through a single-level quantum dot per pumping cycle. The combination of Coulomb interaction and quantum fluctuations, accounted for in contributions of higher order in the tunnel coupling, modifies the pumping characteristics via an interaction-dependent renormalization of the quantum-dot level. The latter is even responsible for the {\em dominant} contribution to the pumped…
Coupling a quantum system to a bosonic environment always give rise to inelastic processes, which reduce the coherency of the system. We measure energy dependent rates for inelastic tunneling processes in a fully controllable two-level system of a double quantum dot. The emission and absorption rates are well repro-duced by Einstein's coefficients, which relate to the spontaneous emission rate. The inelastic tunneling rate can be comparable to the elastic tunneling rate if the boson occupation number becomes large. In the specific semiconductor double dot, the energy dependence of the inelasti…
We report both photon- and phonon-assisted tunneling transitions in a linear array of three quantum dots, which can only be understood by considering the full three-dimensionality of the charge stability diagram. Such tunneling transitions potentially contribute to leakage of qubits defined in this system. A detailed understanding of these transitions is important as they become more abundant and complex to analyze as quantum dot arrays are scaled up.
Employing the Anderson impurity model, we study tunneling properties through an ideal quantum dot near the conductance minima. Considering the Coulomb blockade and the quantum confinement on an equal footing, we have obtained current contributions from various types of tunneling processes; inelastic cotunneling, elastic cotunneling, and resonant tunneling of thermally activated electrons. We have found that the inelastic cotunneling is suppressed in the quantum confinement limit, and thus the conductance near its minima is determined by the elastic cotunneling at low temperature ($k_BT \ll Γ$,…
We study the loading of electrons into a quantum dot with dynamically controlled tunnel barriers. We introduce a method to measure tunneling rates for individual discrete states and to identify their relaxation paths. Exponential selectivity of the tunnel coupling enables loading into specific quantum dot states by tuning independently energy and rates. While for the single-electron case orbital relaxation leads to fast transition into the ground state, for electron pairs triplet-to-singlet relaxation is suppressed by long spin-flip times. This enables the fast gate-controlled initialization o…
In situ tunable radio-frequency charge detection is used for the determination of the tunneling rates into and out of a graphene single quantum dot connected to only one lead. An analytical model for calculating these rates in the multi-level tunneling regime is presented and found to correspond very well to our experimental observations.
Tunneling through two vertically coupled quantum dots is studied by means of a Pauli master equation model. The observation of double peaks in the current-voltage characteristic in a recent experiment is analyzed in terms of the tunnel coupling between the quantum dots and the coupling to the contacts. Different regimes for the emitter chemical potential indicating different peak scenarios in the tunneling current are discussed in detail. We show by comparison with a density matrix approach that the interplay of coherent and incoherent effects in the stationary current can be fully described b…
We explore the full counting statistics of single electron tunneling through a quantum dot using a quantum point contact as non-invasive high bandwidth charge detector. The distribution of counted tunneling events is measured as a function of gate and source-drain-voltage for several consecutive electron numbers on the quantum dot. For certain configurations we observe super-Poissonian statistics for bias voltages at which excited states become accessible. The associated counting distributions interestingly show a bimodal characteristic. Analyzing the time dependence of the number of electron …
We report integrated charge sensing measurements on a Si/SiGe double quantum dot. The quantum dot is shown to be tunable from a single, large dot to a well-isolated double dot. Charge sensing measurements enable the extraction of the tunnel coupling, t, between the quantum dots as a function of the voltage on the top gates defining the device. Control of the voltage on a single such gate tunes the barrier separating the two dots. The measured tunnel coupling is an exponential function of the gate voltage. The ability to control t is an important step towards controlling spin qubits in silicon …
Using real-time charge sensing and gate pulsing techniques we measure the ratio of the rates for tunneling into the excited and ground spin states of a single-electron AlGaAs/GaAs quantum dot in a parallel magnetic field. We find that the ratio decreases with increasing magnetic field until tunneling into the excited spin state is completely suppressed. However, we find that by adjusting the voltages on the surface gates to change the orbital configuration of the dot we can restore tunneling into the excited spin state and that the ratio reaches a maximum when the dot is symmetric.
The transport properties of a metal core/semiconductor shell quantum dot molecule (QDM) embedded in a matrix connected to metallic electrodes are theoretically studied in the framework of Keldysh Green function technique. The effects of the electron plasmon interactions (EPIs) on the tunneling current spectra of QDM are examined. The energy levels of the QDs, intradot and interdot Coulomb interactions, electron interdot hopping strengths, and tunneling rates of QDs are renormalized by the EPIs. The differential conductance spectra show peaks arising from the plasmon assisted tunneling process,…
Recent demonstrations using electron spins stored in quantum dots array as qubits are promising for developing a scalable quantum computing platform. An ongoing effort is therefore aiming at the precise control of the quantum dots parameters in larger and larger arrays which represents a complex challenge. Partitioning of the system with the help of the inter-dot tunnel barriers can lead to a simplification for tuning and offers a protection against unwanted charge displacement. In a triple quantum dot system, we demonstrate a nanosecond control of the inter-dot tunnel rate permitting to reach…
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.
Exciton levels and fine-structure splitting in laterally-coupled quantum dot molecules are studied. The electron and hole tunneling energies as well as the direct Coulomb interaction are essential for the exciton levels. It is found that fine-structure splitting of the two-lowest exciton levels is contributed from the intra- and inter-dot exchange interactions, both of which are largely influenced by the symmetry and tunnel-coupling between the two dots. As the inter-dot separation is reduced, fine-structure splitting of the exciton ground state is largely increased while those of the excited …
We study non-linear phenomena in quantum dots. Non linearities are reflected in the I-V characteristic curve as bistabilities, instabilities and time dependent oscillations of the currents. The nature of the non-linear behavior depends upon the parameters that define the system.
We propose a quantum dot (QD) implementation of a quantum state transfer channel. The proposed channel consists of N vertically stacked QDs with the nearest neighbor tunnel coupling, placed in an axial electric field. We show that the system supports high-fidelity transfer of the state of a terminal dot both by free evolution and by adiabatic transfer. The protocol is to a large extent insensitive to inhomogeneity of the energy parameters of the dots and requires only a global electric field.
We investigated the size dependence of the ground state energy in self-assembled InAs quantum dots embedded in resonant tunneling diodes. Individual current steps observed in the current-voltage characteristics are attributed to resonant single-electron tunneling via the ground state of individual InAs quantum dots. The onset voltage of the first step observed is shown to decrease systematically from 200 mV to 0 with increasing InAs coverage. We relate this to a coverage-dependent size of InAs dots grown on AlAs. The results are confirmed by atomic force micrographs and photoluminescence exper…
We study coherent charge tunneling through a one-dimensional interacting ring with a one-dimensional quantum dot embedded in one of its arms through bosonisation. The symmetries of the effective action explain many of the features such as phase change between resonances, in-phase successive resonances and phase-locking, which have been observed in experiments of coherent transport in mesoscopic rings, with a quantum dot. We also predict changes in the behaviour of the tunneling conductance in the presence of an Aharanov-Bohm flux through the ring. We argue that these results hold true in gener…
We report on the importance of resonant-tunneling processes on quantum transport through interacting quantum-dot spin valves. To include Coulomb interaction in the calculation of the tunneling magnetoresistance (TMR), we reformulate and generalize the recently-developed, numerically-exact method of iterative summation of path integrals (ISPI) to account for spin-dependent tunneling. The ISPI scheme allows us to investigate weak to intermediate Coulomb interaction in a wide range of gate and bias voltage and down to temperatures at which a perturbative treatment of tunneling severely fails.
We study the electronic structure of a single self-assembled InAs quantum dot by probing elastic single-electron tunneling through a single pair of weakly coupled dots. In the region below pinch-off voltage, the non-linear threshold voltage behavior provides electronic addition energies exactly as the linear, Coulomb blockade oscillation does. By analyzing it, we identify the s and p shell addition spectrum for up to six electrons in the single InAs dot, i.e. one of the coupled dots. The evolution of shell addition spectrum with magnetic field provides Fock-Darwin spectra of s and p shell.
We examine the shot noise spectrum properties of coherent resonant tunneling in coupled quantum dots in both series and parallel arrangements by means of quantum rate equations and MacDonald's formula. Our results show that, for a series-CQD with a relatively high dot-dot hopping $Ω$, $Ω/Γ\gtrsim 1$ ($Γ$ denotes the dot-lead tunnel-coupling strength), the noise spectrum exhibits a dip at the Rabi frequency, $2Ω$, in the case of noninteracting electrons, but the dip is supplanted by a peak in the case of strong Coulomb repulsion; furthermore, it becomes a dip again for a completely symmetric pa…
We present Coulomb Blockade measurements of two few-electron quantum dots in series which are configured such that the electrochemical potential of one of the two dots is aligned with spin-selective leads. The charge transfer through the system requires co-tunneling through the second dot which is $not$ in resonance with the leads. The observed amplitude modulation of the resulting current is found to reflect spin blockade events occurring through either of the two dots. We also confirm that charge redistribution events occurring in the off-resonance dot are detected indirectly via changes in …
We report on a novel Kondo phenomenon of interacting quantum dots coupled asymmetrically to a normal and a superconducting lead. The effects of intradot Coulomb interaction and Andreev tunneling give rise to Andreev bound resonances. As a result, a new type of co-tunneling process which we term Andreev-normal co-tunneling, is predicted. At low temperatures, coherent superposition of these co-tunneling processes induces a Kondo effect in which Cooper pairs directly participate formation of a spin singlet, leading to four Kondo resonance peaks in the local density of states, and enhancing the tu…
Spin-dependent transport through two coupled single-level quantum dots weakly connected to ferromagnetic leads with collinear magnetizations is considered theoretically. Transport characteristics, including the current, linear and nonlinear conductance, and tunnel magnetoresistance are calculated using the real-time diagrammatic technique in the parallel, serial, and intermediate geometries. The effects due to virtual tunneling processes between the two dots via the leads, associated with off-diagonal coupling matrix elements, are also considered. Negative differential conductance and negative…
We study the influence of the phonon environment on the electron dynamics in a doped quantum dot molecule. A non-perturbative quantum kinetic theory based on correlation expansion is used in order to describe both diagonal and off-diagonal electron-phonon couplings representing real and virtual processes with relevant acoustic phonons. We show that the relaxation is dominated by phonon-assisted electron tunneling between constituent quantum dots and occurs on a picosecond time scale. The dependence of the time evolution of the quantum dot occupation probabilities on the energy mismatch between…
We are pursuing a capability to perform time resolved manipulations of single spins in quantum dot circuits involving more than two quantum dots. In this paper, we demonstrate full counting statistics as well as averaging techniques we use to calibrate the tunnel barriers. We make use of this to implement the Delft protocol for single shot single spin readout in a device designed to form a triple quantum dot potential. We are able to tune the tunnelling times over around three orders of magnitude. We obtain a spin relaxation time of 300 microseconds at 10T.
Resonant tunneling through a quantum dot weakly coupled to Tomonaga-Luttinger liquids is discussed. The linear conductance due to sequential tunneling is calculated by solving a master equation for temperatures below and above the average level spacing in the dot. When the parameter g characterizing the Tomonaga-Luttinger liquid is smaller than 1/2, the resonant tunneling process is incoherent down to zero temperature. At low temperature T the height and width of the conductance peaks in the Coulomb blockade oscillations are proportional to T^{(1/g)-2} and T, respectively. The contribution fro…
