We have used a hybrid vertical-lateral double quantum dot to study the excitation energy spectrum for one- and two-electron states, which are effectively formed on top of a certain core shell. We have observed bonding and antibonding states, and exchange coupled singlet and triplet states for the one- and two-electron states, respectively, and derived the interdot tunnel coupling and exchange coupling energies for various parameters of interdot level detuning, central gate voltage and magnetic field. The obtained exchange coupling energy is consistently reproduced by calculation using the Hund-Mulliken method.
We have used a hybrid vertical-lateral double quantum dot to study the excitation energy spectrum for one- and two-electron states, which are effectively formed on top of a certain core shell. We have observed bonding and antibonding states, and exchange coupled singlet and triplet states for the one- and two-electron states, respectively, and derived the interdot tunnel coupling and exchange coupling energies for various parameters of interdot level detuning, central gate voltage and magnetic field. The obtained exchange coupling energy is consistently reproduced by calculation using the Hund-Mulliken method.
The orbital, spin and valley degrees of freedom in silicon quantum dots support many modes of spin qubit operation. However, it is generally challenging to obtain information about the energy level spectrum over large ranges of parameter space. We demonstrate a form of spectroscopy that is capable of mapping the energy level structure of a double quantum dot as a function of level detuning, interdot tunnel coupling, and magnetic field. In the one electron regime, we directly observe the transition from the atom like energy levels of isolated quantum dots to molecular like bonding and anti bonding states with increasing interdot tunnel coupling. We also resolve the Zeeman splitting of ground and excited valley states in a magnetic field. In the two electron regime, we gain access to the detuning dependent singlet triplet splitting. Our work may be extended to a broader class of systems, such as strong spin-orbit materials or proximitized quantum dots, allowing the direct extraction of various energy gaps.
We use Pauli-spin blockade in two-electron vertical double quantum dots to quantitatively estimate the exchange energy J in a wide range of interdot level detuning $\ensuremath{\Delta}$ and fully compare it with calculations. Pauli-spin blockade is lifted via a singlet- (S-)triplet (T) transition mediated by hyperfine coupling, which abruptly occurs in our devices when the $S\mathrm{\text{\ensuremath{-}}}T$ transition energy or J is compensated by the Zeeman energy. We use this feature to derive J depending on $\ensuremath{\Delta}$ between the $S\mathrm{\text{\ensuremath{-}}}S$ and $T\mathrm{\text{\ensuremath{-}}}T$ resonances. The obtained J versus $\ensuremath{\Delta}$ including the resonance effect is perfectly reproduced by Hubbard model calculations.
We present a theoretical study of a four-electron four-quantum-dot system based on molecular-orbital methods, which hosts a pair of singlet-triplet spin qubits. We took into account the admixture of electron wave functions in all dots, and we found that this mixing of wave functions has consequences to the energy spectrum, exchange interaction, and gate crosstalk of the system. Specifically, we found that when the two singlet-triplet qubits are close enough, some of the states are no longer dominated by the computational basis states, and the exchange interaction cannot simply be understood as the energy difference between the singlet and triplet states. Using the Hund-Mulliken calculation of the Hubbard parameters, we characterized the effective exchange interaction of the system, and we found good agreement with results calculated by taking energy differences where applicable. We studied the two commonly conceived schemes coupling two qubits, namely the exchange and capacitive coupling, and we found that when the interqubit distance is at certain intermediate values, the two kinds of coupling are comparable in strength, complicating the analyses of the evolution of the two qubits. We also investigated the gate crosstalk in the system due to the quantum-mechanical mixing of electron states, and we found that while this effect is typically very weak, it should not be ignored if the spacing between the qubits is similar to or less than the distance between the double dots that constitute the qubit.
Exchange energies and charge densities for few electrons in electrically tunable quantum dot (QD) systems are investigated by using the variational Monte Carlo (VMC) method in the presence of magnetic fields. For N = 2 electrons in double QD, the singlet Coulomb energy decreases in magnetic fields as a consequence of magnetic localization in both strongly and weakly coupled QDs. However, the triplet Coulomb energy reaches a maximum value at intermediate magnetic fields before decreasing. We observe good agreement between the results for VMC with s-p orbital trial wavefunction and exact diagonalization (ED) method in the exchange energies. For N = 2 electrons in triple quantum dot (TQD), we observe a discontinuity in the J-derivative with detuning voltage ( dJdVT ) in triangular TQDs at B = 0 T as crossing of the eigenenergy levels leads to abrupt spatial symmetry change of the triplet densities (density rotation) and relocalization. For B ≠ 0 T, the angular momentum provided to the electrons quenches this effect. The density rotation is absent in collinear TQD for all magnetic fields as the lowest excited state remains the px state and as such, no change in symmetry is possible. By varying the triangular TQD configuration, we show the discontinuity in ( dJdVT ) persists for top angle between 20° and 70°. For N = 3 electrons in symmetric triangular TQD, the monotonicity of the exchange curve from B = 0 to 4 T remains intact for decoupled QDs but not for coupled QDs. Finally, additional energy for the triangular TQD system is computed for up to N = 3 electrons.
We determine the spin-exchange coupling J between two electrons located in two vertically tunnel-coupled quantum dots, and its variation when magnetic (B) and electric (E) fields (both in-plane and perpendicular) are applied. We predict a strong decrease of J as the in-plane B field is increased, mainly due to orbital compression. Combined with the Zeeman splitting, this leads to a singlet-triplet crossing, which can be observed as a pronounced jump in the magnetization at in-plane fields of a few T, and perpendicular fields of the order of 10 T for typical self-assembled dots. We use harmonic potentials to model the confining of electrons, and calculate the exchange J using the Heitler-London and Hund-Mulliken techniques, including the long-range Coulomb interaction. With our results we provide experimental criteria for the distinction of singlet and triplet states, and therefore for microscopic spin measurements. In the case where dots of different sizes are coupled, we present a simple method to switch the spin coupling on and off with exponential sensitivity using an in-plane electric field. Switching the spin coupling is essential for quantum computation using electronic spins as qubits.
We investigate the spin of a multielectron GaAs quantum dot in a sequence of nine charge occupancies, by exchange coupling the multielectron dot to a neighboring two-electron double quantum dot.For all nine occupancies, we make use of a leakage spectroscopy technique to reconstruct the spectrum of spin states in the vicinity of the interdot charge transition between a single-and a multielectron quantum dot.In the same regime we also perform time-resolved measurements of coherent exchange oscillations between the singleand multielectron quantum dot.With these measurements, we identify distinct characteristics of the multielectron spin state, depending on whether the dot's occupancy is even or odd.For three out of four even occupancies, we do not observe any exchange interaction with the single quantum dot, indicating a spin-0 ground state.For the one remaining even occupancy, we observe an exchange interaction that we associate with a spin-1 multielectron quantum dot ground state.For all five of the odd occupancies, we observe an exchange interaction associated with a spin-1=2 ground state.For three of these odd occupancies, we clearly demonstrate that the exchange interaction changes sign in the vicinity of the charge transition.For one of these, the exchange interaction is negative (i.e., triplet preferring) beyond the interdot charge transition, consistent with the observed spin-1 for the next (even) occupancy.Our experimental results are interpreted through the use of a Hubbard model involving two orbitals of the multielectron quantum dot.Allowing for the spin correlation energy (i.e., including a term favoring Hund's rules) and different tunnel coupling to different orbitals, we qualitatively reproduce the measured exchange profiles for all occupancies.