Quantum networks require quantum nodes with coherent optical interfaces and multiple stationary qubits. In terms of optical properties, semiconductor quantum dots are highly compelling, but their adoption as quantum nodes has been impaired by the lack of auxiliary qubits. Here, we demonstrate a functional quantum register in a semiconductor quantum dot leveraging the dense, always-present nuclear spin ensemble. We prepare 13,000 host nuclear spins into a single many-body dark state to operate as the register logic state
∣0⟩. The logic state
∣1⟩ is defined as a single nuclear magnon excitation, enabling controlled quantum-state transfer between the electron spin qubit and the nuclear magnonic register. Using 130-ns SWAP gates, we implement a full write-store-retrieve-readout protocol with 68.6(4)% raw overall fidelity and a storage time of 130(16)
μs in the absence of dynamical decoupling. Our work establishes how many-body physics can add step-change functionality to quantum devices, in this case transforming quantum dots into multi-qubit quantum nodes with deterministic registers.
Abstract Quantum networks require quantum nodes with coherent optical interfaces and several stationary qubits. In terms of optical properties, semiconductor quantum dots are highly compelling, but their adoption as quantum nodes has been impaired by the lack of auxiliary qubits. Here we demonstrate that the dense, always-present, nuclear spin ensemble surrounding a gallium arsenide quantum dot can be used as a functional quantum register. We prepared 13,000 host nuclear spins in a single many-body dark state that acts as a logical state of the register. A second logical state is defined as a single nuclear-magnon excitation, enabling controlled quantum-state transfer between an electron spin qubit in the quantum dot and the nuclear magnonic register. Using SWAP gates, we implemented a full write–store–retrieve-read-out protocol with 68.6(4)% raw overall fidelity and a storage time of 130(16) μs, which could be extended to 20 ms or beyond using dynamical decoupling techniques. Our work establishes how many-body physics can add functionality to quantum devices, in this case transforming quantum dots into multi-qubit quantum nodes with deterministic registers.
The motivating background for this thesis lies in the recent development in the coherent optical control of electron spin states in semiconductor quan- tum dots. One possible and attractive application for these achievements is a physical implementation of a quantum computer based on spin qubits (quan- tum bit) in quantum dots. However, one of the obstacles in building such quantum computer is decoherence caused by the interaction of the electron spins with nuclear spins of the host material. In this thesis we theoretically investigate the effects caused by the hyperfine interaction in optically active semiconductor quantum dots. In Chapter 2 we assume optically induced rotations of single electron spins in semiconductor quantum dots. The optical control of the electron spin states is considered to be conducted by means of Raman type optical transitions between electron spin states. We investigate the influence of nuclear spins on the performance of the single-qubit gates by incorporating the additional effect of the Overhauser field into the electron spin dynamics. To calculate the errors caused by the hyperfine interaction, we determine average fidelities of rotations around characteristic axes in the Bloch sphere in the presence of nuclear spins analytically with perturbation theory up to second order in the Overhauser field. By applying numerical averaging over the nuclear field distribution we find the average fidelity to the arbitrary orders of the hyper- fine interaction. In Chapter 3 we investigate the dynamics of spin qubits interacting by means of an optical cavity. The qubits are represented by a single electron spin each confined to a quantum dot. Knowing that electron spins in III-V semiconduc- tor quantum dots are affected by the decoherence due to the hyperfine inter- action with nuclear spins, we find that the interaction between two qubits is consequently influenced by the Overhauser field. Assuming an unpolarizied nuclear ensemble, we investigate the fidelities for two-qubit gates depending on the Overhauser field. We include the hyperfine interaction perturbatively to second order in our analytical results, and to arbitrary precision numeri cally. Quantum dots can be used not only as physical systems for qubits, but also as sources for entangled photons. In chapter 4 we consider an emission of entangled photons by spontaneous decay of the biexciton state to the ground state. Due to electron-hole exchange interaction, the intermediate excitonic states have a finite fine structure splitting. The electron spins of the excitons also interact via hyperfine interaction with the nuclear spins. We study the temporal and fine structure splitting dependance of the coherence measures considering the effect of the nuclear magnetic field. We find that the hy perfine interaction contributes considerably to the reduction of the photon coherence. One of the possibilities to minimize the decoherence effects of the hyperfine interaction is to polarize the nuclear spins to 100%. However, up to date it was not possible to reach such degree of the nuclear polarization in experi- ments. In a recent experiment by Chekhovich et al. it was shown that high nuclear spin polarization can be achieved in self-assembled quantum dots by exploiting an optically forbidden transition between a heavy hole and a trion state. A fully polarized state in this case was predicted by a classical rate equation, but could not be obtained experimentally. Therefore we theoret- ically investigate this problem with the help of a quantum master equation in Chapter 5, and we show that a fully polarized state cannot be achieved due to formation of a nuclear dark state. Moreover, we demonstrate that the maximal degree of polarization depends on the form of the electron wave function inside of the quantum dot.