Quantum computation holds the promise of efficient solutions to currently formidable problems. A prospective technology is that of computing using quantum states, which may dramatically speed up or otherwise reduce the complexity for the solution of some hard problems. Of the many different schemes proposed, shallow substitutional donors in Silicon hold great attractiveness for the detailed study of the medium, high industrial capacity, and ubiquity of raw materials. We develop control over the quantum orbital and spin states of bound electrons using the THz ultrafast laser FELIX. \nManipulation of orbital states is studied using interferometric methods to produce Ramsey fringes, read out using optical and electrical methods. Contactless electrical measurement of free charge carriers is implemented, and the details of its advantages and limitations are explored. Both types of readout are used to demonstrate a coherent 3-level orbital manipulation, otherwise known as a quantum beat. The work constitutes a nontrivial control over the spatial distribution of the wavefunction of the atom which may enable error correcting surface code implementations. \nSpin dynamics are then explored in the presence of FELIX using donor-bound exciton techniques, which allow a sensitive and fast control over the electron spin states. The implementation is used to probe whether orbital excitation has a strong effect upon the spin states of the donor electrons, and it is shown that any modification of the spin is negligible. Experimental measurements of optically gated spin-exchange coupling are enabled by this methodology, and a roadmap to future implementation is discussed in the context of the present work. \nOverall, the work advances the state of spin and orbital control of neutral donor states for the purposes of optically gated quantum computing. Combined spin and orbital manipulations are now possible in the system, which will allow a more advanced implementation of quantum computation using orbital states than was previously possible.
Quantum computation holds the promise of efficient solutions to currently formidable problems. A prospective technology is that of computing using quantum states, which may dramatically speed up or otherwise reduce the complexity for the solution of some hard problems. Of the many different schemes proposed, shallow substitutional donors in Silicon hold great attractiveness for the detailed study of the medium, high industrial capacity, and ubiquity of raw materials. We develop control over the quantum orbital and spin states of bound electrons using the THz ultrafast laser FELIX. \nManipulation of orbital states is studied using interferometric methods to produce Ramsey fringes, read out using optical and electrical methods. Contactless electrical measurement of free charge carriers is implemented, and the details of its advantages and limitations are explored. Both types of readout are used to demonstrate a coherent 3-level orbital manipulation, otherwise known as a quantum beat. The work constitutes a nontrivial control over the spatial distribution of the wavefunction of the atom which may enable error correcting surface code implementations. \nSpin dynamics are then explored in the presence of FELIX using donor-bound exciton techniques, which allow a sensitive and fast control over the electron spin states. The implementation is used to probe whether orbital excitation has a strong effect upon the spin states of the donor electrons, and it is shown that any modification of the spin is negligible. Experimental measurements of optically gated spin-exchange coupling are enabled by this methodology, and a roadmap to future implementation is discussed in the context of the present work. \nOverall, the work advances the state of spin and orbital control of neutral donor states for the purposes of optically gated quantum computing. Combined spin and orbital manipulations are now possible in the system, which will allow a more advanced implementation of quantum computation using orbital states than was previously possible.
It has long been known that shallow donors such as phosphorous and the other group-V elements, have a hydrogen-like optical spectrum. The main difference is that while the spectrum of atomic hydrogen lies in the visible band, the spectrum of shallow donors in silicon is downshifted to the THz frequency band. This is a direct consequence of the reduced Coulomb attraction seen by the loosely bound electron because the core electrons shield the positive donor atom nucleus, and because the electron is now moving in a dielectric material. While spectroscopy has already revealed much about the energy level structure, very little was known about the temporal dynamics of the system until now. We have used THz pulses from the FELIX free electron laser to probe these hydrogen-like levels. By exploiting the well-known pump-probe technique we have measured the characteristic lifetimes of the excited Rydberg states and found them to be of the order 200 ps. Then, by making subtle changes to the geometry of the pump-probe experimental setup we demonstrate the existence of a THz photon echo. The photon echo is a purely quantum phenomenon with no classical analogue, and it allows us to study the quantum state of the donor electron. We then show, using the photon echo, that it is possible to create a coherent superposition of the ground and excited state of the donor. Measuring the photon echo is important because it can also be used to measure a second important characteristic lifetime of the silicon-donor system, the phase decoherence time.
Donors in silicon, which combine an electron and nuclear spin, are some of the most promising candidates for quantum information. The electron spin has been proposed as a register with fast manipulation and the nuclear spin as a memory with long coherence times. However, this division reduces the complexity of the donor system, in particular behaviors emerging from their interaction. In natural silicon, there is also the presence of 29Si nuclear spins in the donor environment; though they are generally seen as a source of decoherence, they are quantum systems that can be investigated too. The main subject of this thesis is the study of the interactions between these various spins, using different methods to probe and control them. I first concentrate on the coupling between the donor and the 29Si spins. This coupling can be perturbed by the application of dynamical decoupling on the donor electron spin, whose evolution can be made sensitive to the number of 29Si spins interacting together. I then propose an error correction scheme using the donor and 29Si spins, showing key requirements such as coherence times and methods for manipulation and initialization. Secondly, I focus on the donor itself, in a regime where the hyperfine and Zeeman couplings compete with each other. Here, the spin transitions can have different sensitivities to the magnetic environment, and can even be suppressed to first order, resulting in coherence times up to seconds with electron spin-like manipulation times. Controlling this sensitivity was also used to probe the effect of the donor on the 29Si spin bath evolution. Finally, I use electric fields to modulate the hyperfine coupling within the donor. I first characterize the spins’ sensitivity to the electric field, and then demonstrate electrical switching of the nuclear spin response to an external magnetic excitation.
Coherent spin-photon interfaces are essential for scalable quantum networks, but their realization requires optically bright transitions, long-lived spin coherence, and complete coherent control. Donor-bound electron spins in II-VI semiconductors offer an attractive platform for optically active spin qubits because they combine strong donor-bound exciton transitions in a direct-bandgap material with a potentially nuclear-spin-free environment. However, coherent control of an individual optically active donor spin has remained elusive. Here we demonstrate optical initialization, coherent control, and readout of a single donor-bound electron spin in ZnSe. Using spin-selective donor-bound exciton optical transitions, we initialize the electron spin and directly resolve its spin-relaxation dynamics. We achieve coherent spin control with off-resonant picosecond optical pulses, as demonstrated by spin Rabi oscillations and Ramsey interference. We further coherently drive two spin-selective optical transitions and observe high-contrast coherent population trapping, demonstrating the formation of an optically controlled dark state. At higher driving strengths, multiple dark resonances reveal the hyperfine interaction between the electron and the I = 3/2 Cl nucleus. These results establish the first coherent optical control of a single donor electron spin in a II-VI semiconductor and identify isolated optical donors as a promising platform for solid-state optically active qubits.
The discovery of efficient quantum algorithms a decade ago has shown that a quantum computer encoding and processing information quantum mechanically, can solve important problems intractable with conventional computers. The invention of quantum error correction principle, makes quantum computation possibly fault-tolerant against the decoherence of information carriers. Thereafter, intensive research activities have been made toward the implementation of quantum computation with various realistic quantum systems. Among them, the most attractive implementation proposals are using silicon-based materials, which have the advantage of borrowing the existing ingenuity and resources accumulated during the development of modern microelectronics. In this dissertation we investigate several theoretical aspects of a silicon- based quantum computer in which qubits are represented by the spins of electrons bound to phosphorous donors in silicon. Encoding each qubit in terms of three neighboring donor electron spins, we can realize universal quantum gate operations with only the Heisenberg exchange coupling J S1 •S2 between neighboring donors. Therefore, studying the exchange coupling for a phosphorous donor pair in silicon is of central importance for providing the experimentalists with qualitative insights and quantitative guidance for building such a silicon quantum computer. After giving some general considerations on the quantum computer architecture, we develop the necessary theoretical tools. A multi-valley effective mass equation is derived and discussed, to handle impurities in a multi-valley semiconductor. Then we apply it to solve a single Si:P donor embedded in our quantum computer architecture. We show that the width of the silicon quantum well can significantly influence the energy splitting and charge distributions of the ground state. Oscillation of level splitting is observed as the quantum well width or donor position is varied at atomic scale. Elementary gate operations for 3-donor-spin qubits involve a neighboring pair of donors at each step. The exchange coupling in Heisenberg model hamiltonian, defined as the energy splitting of the lowest singlet and triplet states, has to be calculated from the realistic two-donor hamiltonian. We discuss several popular methods to solve the two-donor problem and develop an appropriate extended Hartree-Fock method that can give reliable results for a well-separated donor pair subject to tunable coupling. This method is first applied to a Si:P donor pair in the framework of hydrogenic effective mass theory, to study how to tune the exchange coupling with simple gate potentials. A followed study shows that under a parallel electric field the singlet and triplet states exhibit very different polarization behaviors. This difference can be exploited to measure the state of an electron spin. We also show that, a perpendicular electric field cannot tune the exchange coupling efficiently. Then we apply the realistic multi-valley effective mass equation, coupled with a realistic modeling of the potential generated by gate electrodes, to a pair of phosphorous donors in silicon quantum well. By varying the gate electrode voltages, the exchange coupling can be tuned with exponential efficiency in a wide range. We find that, for best performance, we need to set the quantum well width to be around 10 nm, and the donor separation to be around 10 a∗ b---- 24nm in the doping plane. We analyze in detail an adiabatic half-swap operation between neighboring donor spins. The gate operation time is estimated to be 0.2 ns, which satisfies the constraints put by the donor spin decoherence time and by the validity of adiabatic approximation. The interference between different valley components could lead to oscillations of exchange coupling as donor positions are shifted by occasion. We find the exchange oscillation persists even with only two relevant valleys for donors in a strongly-strained silicon quantum well. It is also shown that the oscillation induced by changing donor separation at atomic scale is strongly suppressed as donors approach each other. Finally, we study the entanglement issue in quantum computing context. We analyze the low-energy Hilbert space for a pair of qubits encoded by localized electron spins and suggest a suitable measure to describe the entanglement between qubits involving indistinguishable electrons and in the presence of leakage errors. The dynamics of inter-qubit entanglement during a gate operation is also studied.
Spin qubits of donors in silicon show some of the longest coherence times recorded and hold the promise of scalability with seamless integration of quantum computing into semiconductor fabrication. However, current entangling gate implementations rely on highly challenging precision donor placement and substantial gate tuning, rendering scaling challenging. In this work, we show how to implement placement-insensitive ultrafast entangling gates in deep and shallow donors in silicon by relying on the Rydberg blockade induced by strong interactions between low lying orbital excited states. We calculate multivalley interactions for several donor species using the Finite Element Method, and show that Van der Waals interactions between donors, calculated here for the first time, are important even for low-lying excited states. We show that blockade entangling gate operation is possible within the short lifetime of donor excited states with over 99% fidelity for the creation of a Bell state in the presence of decoherence. This gate substantially relaxes the requirements on single donor placement while allowing for billions of entangling gate operations within the single-qubit lifetime, thus paving the way for large scale quantum computation in silicon.
A quantum-mechanical many-particle system may exhibit nonlocal behavior in that measurements performed on one of the particles can affect a second one that is far apart. These so-called entangled states are crucial for the implementation of quantum information protocols and gates for quantum computation. Here, we use ultrafast optical pulses and coherent pump-probe techniques to create and control spin entangled states in an ensemble of up to three non-interacting electrons bound to donors in a ${\mathrm{Cd}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}$Te quantum well. Our method, relying on the exchange interaction between optically excited excitons and the paramagnetic impurities, can in principle be applied to entangle an arbitrarily large number of electrons. A microscopic theory of impulsive stimulated Raman scattering and a model for multi-spin entanglement are presented. The signature of entanglement is the observation of overtones of donor spin-flips in the differential reflectivity of the probe pulse. Results are shown for resonant excitation of localized excitons below the gap, and above the gap where the signatures of entanglement are significantly enhanced. Data is also presented on the generation of coherent excitations of antiferromagnetically coupled manganese pairs, folded acoustic phonons, exciton Zeeman beats and entanglement involving two Mn+2 ions.