It has been experimentally shown that negative exchange interactions can arise in a linear three-dot system when a two-electron double quantum dot is exchange coupled to a larger quantum dot containing on the order of one hundred electrons. The origin of this negative exchange can be traced to the larger quantum dot exhibiting a spin tripletlike rather than singletlike ground state. Here we show using a microscopic model based on the configuration interaction (CI) method that both tripletlike and singletlike ground states are realized depending on the number of electrons. In the case of only four electrons, a full CI calculation reveals that tripletlike ground states occur for sufficiently large dots. These results hold for symmetric and asymmetric quantum dots in both Si and GaAs, showing that negative exchange interactions are robust in few-electron double quantum dots and do not require large numbers of electrons.
It has been experimentally shown that negative exchange interactions can arise in a linear three-dot system when a two-electron double quantum dot is exchange coupled to a larger quantum dot containing on the order of one hundred electrons. The origin of this negative exchange can be traced to the larger quantum dot exhibiting a spin tripletlike rather than singletlike ground state. Here we show using a microscopic model based on the configuration interaction (CI) method that both tripletlike and singletlike ground states are realized depending on the number of electrons. In the case of only four electrons, a full CI calculation reveals that tripletlike ground states occur for sufficiently large dots. These results hold for symmetric and asymmetric quantum dots in both Si and GaAs, showing that negative exchange interactions are robust in few-electron double quantum dots and do not require large numbers of electrons.
Semiconductor quantum dot systems offer a promising platform for quantum computation. And these quantum computation candidates are normally based on spin or charge properties of electrons. In these systems, we focus on quantum computation based on electron spins since these systems has good scalability, long coherence times, and rapid gate operations. And this thesis focuses on building a theoretical description of quantum dot systems and the link between theory and experiments. In many quantum dot systems, exchange interactions are the primary mechanism used to control spins and generate entanglement. And exchange energies are normally positive, which limits control flexibility. However, recent experiments show that negative exchange interactions can arise in a linear three-dot system when a two-electron double quantum dot is exchange coupled to a larger quantum dot containing on the order of one hundred electrons. The origin of this negative exchange can be traced to the larger quantum dot exhibiting a spin triplet-like rather than singlet-like ground state. Here we show using a microscopic model based on the configuration interaction (CI) method that both triplet-like and singlet-like ground states are realized depending on the number of electrons. In the case of only four electrons, a full CI calculation reveals that triplet-like ground states occur for sufficiently large dots. These results hold for symmetric and asymmetric quantum dots in both Si and GaAs, showing that negative exchange interactions are robust in few-electron double quantum dots and do not require large numbers of electrons. Recent experiments also show the potential to utilize large quantum dots to mediate superexchange interaction and generate entanglement between distant spins. This opens up a possible mechanism for selectively coupling pairs of remote spins in a larger network of quantum dots. Taking advantage of this opportunity requires a deeper understanding of how to control superexchange interactions in these systems. Here, we consider a triple-dot system arranged in linear and triangular geometries. We use CI calculations to investigate the interplay of superexchange and nearest-neighbor exchange interactions as the location, detuning, and electron number of the mediating dot are varied. We show that superexchange processes strongly enhance and increase the range of the net spin-spin exchange as the dots approach a linear configuration. Furthermore, we show that the strength of the exchange interaction depends sensitively on the number of electrons in the mediator. Our results can be used as a guide to assist further experimental efforts towards scaling up to larger, two-dimensional quantum dot arrays.
Recent experiments on semiconductor quantum dots have demonstrated the ability to utilize a large quantum dot to mediate superexchange interactions and generate entanglement between distant spins. This opens up a possible mechanism for selectively coupling pairs of remote spins in a larger network of quantum dots. Taking advantage of this opportunity requires a deeper understanding of how to control superexchange interactions in these systems. Here, we consider a triple-dot system arranged in linear and triangular geometries. We use configuration interaction calculations to investigate the interplay of superexchange and nearest-neighbor exchange interactions as the location, detuning, and electron number of the mediating dot are varied. We show that superexchange processes strongly enhance and increase the range of the net spin-spin exchange as the dots approach a linear configuration. Furthermore, we show that the strength of the exchange interaction depends sensitively on the number of electrons in the mediator. Our results can be used as a guide to assist further experimental efforts towards scaling up to larger, two-dimensional quantum dot arrays.
Superexchange is one of the vital resources to realize long-range interaction between distant spins for large-scale quantum computing. Recent experiments have demonstrated coherent oscillations between logical states defined by remote spins whose coupling is given by the superexchange interaction mediated by central spins. Excavating the potential of superexchange requires a full understanding of the interaction in terms of control parameters, which is still lacking in literature. Here, using full configuration interaction calculations, we study a two-electron system in a linear triple-quantum-dot device in which the left and right dots are occupied by a single electron each, whose spin states are defined as qubits. The numerical nature of the full configuration interaction calculations allows access to the microscopic details of the quantum-dot confining potential and electronic wave functions, some of which are overlooked in the celebrated Hubbard model but turn out to be critical for the behavior of superexchange. Following experimental demonstrations of superexchange interactions, we focus on the detuning regime where the charge ground state yields an empty middle dot. We have found that, when the detunings at the left and right dots are leveled, the superexchange can exhibit a nonmonotonic behavior, which ranges from positive to negative values as a function of the middle-dot detuning. We further show that a larger relative detuning between the left and right dots causes the magnitude of the superexchange to increase (decrease) for an originally positive (negative) superexchange. We then proceed to show the results for a much larger left-right dot detuning. Using a Hubbard-like model, we present analytical expressions of the superexchange and have found that they conform well qualitatively with the numerical results. Our results suggest that even a simple configuration of delocalized two-electron states in a linear triple-quantum-dot device exhibits superexchange energy with nontrivial behaviors, which could have important applications in spin-based quantum computing.
We discuss the microscopic modeling of exchange interactions between double semiconductor quantum dots used as spin qubits. Starting from a reference full configuration interaction (CI) calculation for the two-particle wave functions, we build a reduced basis set of dressed states that can describe the ground-state singlets and triplets over the whole operational range with as few as 100 basis functions (as compared to a few thousands for the full CI). This enables fast explorations of the exchange interactions landscape as well as efficient time-dependent simulations. We apply this methodology to a double hole quantum dot in germanium and discuss the physics of exchange interactions in this system. We show that the net exchange splitting results from a complex interplay among interdot tunneling, Coulomb exchange, and correlations. We analyze, moreover, the effects of confinement, strains, and Rashba interactions on the anisotropic exchange and singlet-triplet mixings at finite magnetic field. We finally illustrate the relevance of this methodology for time-dependent calculations on a singlet-triplet qubit.
We describe in detail a full configuration interaction (CI) method designed to analyze systems of quantum dots. This method is capable of exploring large regions of parameter space, like more approximate approaches such as Heitler London and Hund Mulliken, though it is not limited to weakly coupled dots. In particular, this method is well-suited to the analysis of solid state quantum-dot-based qubits, and we consider the case of a double quantum dot (DQD) singlet-triplet qubit. Past analyses have used techniques which are either substantially restricted in the regimes they can be used, or device specific and unsuited to exploration of a large regions of parameter space. We analyze how the DQD exchange energy, which is central to the operation of qubit rotation gates, depends on a generic set of system parameters including magnetic field, DQD detuning, dot size, and dot separation. We discuss the implications of these results to the construction of real devices. We provide a benchmark of the CI by directly comparing results from the CI method with exact results for two electrons in a single parabolic potential (dot).
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.