We show that a many-body system of single-electron quantum dots, whose orbital states are dressed by a global magnetic field, can be described by an effective Hamiltonian with an anisotropic $\mathit{XZ}$ spin-spin interaction which is proportional to the Zeeman splitting. We show that these interaction potentials give rise to spin-dependent Hubbard models with tunable nearest neighbor two-body and three-body interactions. The two-body interactions can even be switched off via the external electric field, and hence the three-body interaction plays a dominant role. The derivation of these effective interaction potentials follows from a well-controlled and systematic expansion into many-body interaction terms. Models of this type have appeared in the recent discussion of exotic quantum phases, in particular in the context of topological quantum phases and quantum computing, and we show that quantum dots can be regarded as a realistic experimental route which provides the basic building blocks and techniques toward the study of these phenomena. The main application of this derived model is to develop topological quantum computation.
We show that a many-body system of single-electron quantum dots, whose orbital states are dressed by a global magnetic field, can be described by an effective Hamiltonian with an anisotropic XZ spin-spin interaction which is proportional to the Zeeman splitting. We show that these interaction potentials give rise to spin-dependent Hubbard models with tunable nearest neighbor two-body and three-body interactions. The two-body interactions can even be switched off via the external electric field, and hence the three-body interaction plays a dominant role. The derivation of these effective interaction potentials follows from a well-controlled and systematic expansion into many-body interaction terms. Models of this type have appeared in the recent discussion of exotic quantum phases, in particular in the context of topological quantum phases and quantum computing, and we show that quantum dots can be regarded as a realistic experimental route which provides the basic building blocks and techniques toward the study of these phenomena. The main application of this derived model is to develop topological quantum computation.
In the last years, the electron spin in quantum dots has become a most promising candidate for the realization of qubits, the basic element for quantum computation. In quantum dot spin qubits the exchange interaction implements a fundamental two qubit gate, which originates in the Coulomb interaction and the Pauli principle. Compared to single qubit gates, the exchange based gates are much faster and easier to control locally, motivating the solely exchange energy based quantum computation. The control is based on the exponential sensitivity of the exchange energy on the interparticle distance. Manipulation then can proceed, for example, shifting the single particle states electrically or compressing them magnetically. The practical manipulation schemes require quantitative knowledge of the exchange energy. The spin-orbit interaction plays an important role in this nano-system. Indeed the usual exchange interaction changes its magnitude, while a new term, called anisotropic exchange, appears. In this thesis we propose an accurate effective spin Hamiltonian for modeling spin-orbit-induced spin dynamics in the presence of the magnetic field. We have also performed numerically exact calculations of the isotropic and anisotropic exchange coupling in realistic two-electron GaAs coupled quantum dots in the presence of both Dresselhaus and Bychkov-Rashba spin-orbit interactions. The numerics allow us to establish the goodness of our model and to see the limits of previous statements. Furthermore we find that in zero magnetic field the second-order spin-orbit effects are absent at all interdot couplings.
In this thesis, I present a microscopic theory of quantum circuits based on interacting electron spins in quantum dot molecules. We use the Linear Combination of Harmonic Orbitals-Configuration Interaction (LCHO-CI) formalism for microscopic calculations. We then derive effective Hubbard, t-J, and Heisenberg models. These models are used to predict the electronic, spin and transport properties of a triple quantum dot molecule (TQDM) as a function of topology, gate configuration, bias and magnetic field. With these theoretical tools and fully characterized TQDMs, we propose the following applications: 1. Voltage tunable qubit encoded in the chiral states of a half-filled TQDM. We show how to perform single qubit operations by pulsing voltages. We propose the "chirality-to-charge" conversion as the measurement scheme and demonstrate the robustness of the chirality-encoded qubit due to charge fluctuations. We derive an effective qubit-qubit Hamiltonian and demonstrate the two-qubit gate. This provides all the necessary operations for a quantum computer built with chirality-encoded qubits. 2. Berry's phase. We explore the prospect of geometric quantum computing with chirality-encoded qubit. We construct a Herzberg circuit in the voltage space and show the accumulation of Berry's phase. 3. Macroscopic quantum states on a semiconductor chip. We consider a linear chain of TQDMs, each with 4 electrons, obtained by nanostructuring a metallic gate in a field effect transistor. We theoretically show that the low energy spectrum of the chain maps onto that of a spin-1 chain. Hence, we show that macroscopic quantum states, protected by a Haldane gap from the continuum, emerge. In order to minimize decoherence of electron spin qubits, we consider using electron spins in the p orbitals of the valence band (valence holes) as qubits. We develop a theory of valence hole qubit within the 4-band k.p model. We show that static magnetic fields can be used to perform single qubit operations. We also show that the qubit-qubit interactions are sensitive to the geometry of a quantum dot network. For vertical qubit arrays, we predict that there exists an optimal qubit separation suitable for the voltage control of qubit-qubit interactions.
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 study the spin-spin coupling between two single-electron quantum dots due to the Coulomb and spin-orbit interactions, in the absence of tunneling between the dots. We find an anisotropic XY spin-spin interaction that is proportional to the Zeeman splitting produced by the external magnetic field. This interaction is studied both in the limit of weak and strong Coulomb repulsion with respect to the level spacing of the dot. The interaction is found to be a nonmonotonic function of interdot distance a0 and external magnetic field and, moreover, vanishes for some special values of a0 and/or magnetic field orientation. This mechanism thus provides a new way to generate and tune spin interaction between quantum dots. We propose a scheme to measure this spin-spin interaction based on the spin-relaxation-measurement technique.
We propose altermagnetic semiconductors as a platform for field-free, all-electrically controlled spin qubits in gate-defined quantum dots. The momentum-dependent spin splitting of an altermagnet produces a Zeeman-like qubit splitting whose magnitude and sign are set by the dot ellipticity, enabling local frequency tunability without external magnetic fields or micromagnets. Because the splitting is tied to a fixed altermagnetic quantization axis, electric-field noise is longitudinally suppressed at leading order, while quantization-axis fluctuations couple transversely and therefore cause relaxation rather than pure dephasing. The compensated magnetic order also avoids stray fields, making the platform naturally compatible with superconducting resonators and dispersive circuit-QED readout through the qubit's spin-dependent electric dipole. Starting from an effective quantum-dot model, supported by a microscopic lattice model, we derive the single- and two-dot Hamiltonian models. We show that electric-dipole spin resonance enables single-qubit control, while tunable exchange and electrically addressable qubit frequencies realize fSim two-qubit gates. The same double-dot architecture also supports singlet-triplet qubits with electrical control of both exchange and splitting gradients, removing the need for micromagnets or nuclear-polarization gradients. These results establish altermagnetic quantum dots as a route to field-free spin qubits with intrinsic electrical tunability and enhanced dephasing protection.
Quantum-mechanical correlations of interacting fermions result in the emergence of exotic phases.Magnetic phases naturally arise in the Mott-insulator regime of the Fermi-Hubbard model, where charges are localized and the spin degree of freedom remains.In this regime, the occurrence of phenomena such as resonating valence bonds, frustrated magnetism, and spin liquids is predicted.Quantum systems with engineered Hamiltonians can be used as simulators of such spin physics to provide insights beyond the capabilities of analytical methods and classical computers.To be useful, methods for the preparation of intricate many-body spin states and access to relevant observables are required.Here, we show the quantum simulation of magnetism in the Mott-insulator regime with a linear quantum-dot array.We characterize the energy spectrum for a Heisenberg spin chain, from which we can identify when the conditions for homogeneous exchange couplings are met.Next, we study the multispin coherence with global exchange oscillations in both the singlet and triplet subspace of the Heisenberg Hamiltonian.Last, we adiabatically prepare the low-energy global singlet of the homogeneous spin chain and probe it with two-spin singlettriplet measurements on each nearest-neighbor pair and the correlations therein.The methods and control presented here open new opportunities for the simulation of quantum magnetism benefiting from the flexibility in tuning and layout of gate-defined quantum-dot arrays.