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  • (2023) Rowlands, Joseph
    Thesis
    Silicon spin qubits are strong candidates in the efforts to build a universal quantum computer. They can be fabricated on the nanometer scale, have low noise and long coherence times. To date, efforts for fabricating donor quantum dots in silicon have only focused on two qubits or less. Presented in this thesis is the design, fabrication, and measurement of a twenty-quantum dot Si:P device, the basis of a 10-qubit singlet-triplet architecture. To individually address each qubit, we designed and manufactured superconducting NbTiN frequency division multiplexing chips. These chips were demonstrated to be reproducible and could be used to readout up to 20 quantum dots using only one input and one output line, an important step for increasing device scalability. This multiplexing chip was characterised under magnetic field and used to demonstrate single shot readout of the 𝑆−𝑇− state with 90% readout fidelity using in-situ gate-based dispersive readout, the highest fidelity readout to date for this system. We then fabricated the largest integrated Si:P qubit circuit using scanning tunnelling microscope (STM) lithography to date, five times larger than previous devices. This scale-up required improvements to the manufacturing process, including extension of electron beam lithography capabilities for defining ohmic structures. A custom cryogenic printed circuit board was designed for the device and demonstrated to have low crosstalk of less than -40 dB up to 4 GHz. The device was characterised at millikelvin in a dilution fridge with charge readout performed on 8 of the 10 double dots. Finally, a scalable measurement system based on the PCI eXtensions for Instrumentation (PXI) platform was created, enabling simultaneous multitone digital signal generation and filtering. This system reduced the hardware requirements of previous analogue setups by 80% and enabled four times better signal to noise (SNR) ratio for charge readout as a result of improved low pass digital filtering. The first demonstration of simultaneous readout of neighbouring qubits in the Si:P platform is presented and used to correlate noise sources in the device showing that noise is strongly correlated across four double dots separated by 300 nm.

  • (2023) Berkman, Ian
    Thesis
    Quantum networks are the quantum analogue of the modern internet, offering the ability to employ more secure protocols than modern communication. At the base of these quantum networks are so-called qubits: physical entities that can be in a simultaneous superposition of two states. For quantum networks, qubits should contain states that can be optically accessed and can store quantum properties for a long time. Nowadays, a number of qubit platforms exist, with spin qubits in Si offering long coherence times due to the low number of nuclear spins in the host crystal. Si is a widely used semiconductor in modern electronic devices and the maturated micro- and nanofabrication techniques can be exploited to miniaturise quantum devices. Additionally, Si and SiO2 form an attractive photonic material system because they provide a large contrast in the refractive index, which is critical for achieving efficient optical confinement. To minimise the photon losses and leverage on the well-established telecommunication networks, the photons excited from the spin states should emit within the telecommunication C-band. In this sense, Er3+:Si is an attractive system because Er3+ ions exhibit a spin transition that can be accessed by photons with frequencies within the telecommunication C-band. Moreover, the optical transition of Er3+ takes place within an inner shell, meaning that the outer shells electrically shield this transition, resulting in narrow and stable optical transitions within the telecommunication C-band. The upper bounds on the coherence times of the optical and spin transitions of Er3+:Si are, thus far, still unknown. In this thesis, these optical and spin properties of Er3+ ions in Si are investigated with the aim to create an interface between a spin qubit and a flying qubit. Here, the optical measurements include the extraction of inhomogeneous and homogeneous broadening of Er3+:Si over various samples, observing linewidths down to less than 100 MHz and 500 kHz, respectively. The low Er3+ density in natural Si samples showed characteristics of long-lived electron spin states for two sites. The electron spin coherence time of an Er3+ site in a nuclear-spin-free Si crystal was measured to be 0.5 ms by employing a Hahn echo sequence, and this was further extended up to 9 ms using a Carr–Purcell Meiboom–Gill sequence. These optical and spin properties establish that Er3+:Si exhibits fundamentally promising properties for quantum networks.

  • (2023) St Medar, Dominique Didier
    Thesis
    Strongly correlated materials can display exotic quantum phenomena relevant to the emergence of quantum technologies. Yet, many questions have remained open because of the difficulty in modelling the underlying physics beyond a few lattice sizes. Therefore, a continuing effort has been made to develop quantum simulation platforms, where these many-body states can be artificially emulated with a great degree of control in bespoke hardware implementations. This thesis focuses on the use of dopant-based atomic-scale devices in silicon to build artificial quantum matter probed by a low-temperature scanning tunnelling microscope (STM). We combine STM hydrogen lithography with phosphine doping for the placement of phosphorus donors in our silicon devices with atomic precision and perform spatially resolved measurements using the STM tip. We first establish the experimental platform by characterising strongly correlated states found in single and pairs of quantum dots made of a few donors each. Using these building blocks, we create devices based on dimerised chains to perform an analogue quantum simulation of the Su-Schrieffer-Hegger model, a topological quantum system that classical computers cannot solve effectively. As a preliminary result, we demonstrate the formation of 25 nm-long electronic bands in chains of 5 and 7 sites. These results demonstrate the viability of using silicon as a base for the realisation of Fermi-Hubbard analogue quantum simulators inside a low-temperature STM, with the tip as a tuneable local probe.

  • (2022) Jones, Michael
    Thesis
    In this thesis we assess the design and optimisation of critical device requirements for the realisation of three qubit parity error detection in donor spin qubits in silicon. Three key results are presented: (i) the capacitative modelling and design of triple donor dot architectures needed to realise a parity device, highlighting the need for multi-donor quantum dots (ii) optimisation of the geometry of the donor charge sensor and noise levels required for reproducible high fidelity spin readout, and (iii) understanding how the configurations of the additional donor nuclear spins in these multi-donor dots impact the electron spin resonance (ESR) spectra observed and how this will affect the operation of the parity measurement. Using electrostatic simulations of the different device geometries we show that either a 1P-2P-1P or 1P-3P-1P configuration of donors in each of the individual quantum dots is needed to achieve the required (1,1)↔(2,0) equivalent interdot charge transitions with the available gate space. Using such a higher donor number ancilla qubit, we then compared the sequence of logical gates required to perform the parity measurement using single qubit rotations and different 2-qubit gates. This analysis highlighted the need for isotopically pure silicon-28 to maintain coherence within the time frame of the measurement and stable, high fidelity single shot spin read-out. We then conducted a series of experiments of how to achieve stable, high fidelity single shot spin read out in our triple dot devices. It is known that read-out fidelity is improved by increasing the signal to noise of the charge sensor and by reducing the electron temperature. As such we investigated two triple dot device designs to investigate the interplay between these two requirements. The first design had the donor dots tunnel coupled to the single electron transistor (SET) charge sensor and the second had the donor dots capacitively coupled to an independent reservoir 50nm away from the SET charge sensor. We showed that under high bias of the SET (1mV) where we achieve a good signal to noise (1nA) of the charge sensor, electron-electron interactions within the tunnel coupled SET lead to heating of the qubits (680mK) compared with the independent reservoir qubits (170mK). Ultimately we showed that this heating limits spin read-out fidelities at high power where the signal to noise of the charge sensor is greatest. We simulated the spin readout fidelity for both designs and found the independent reservoir parity design can achieve above 99% fidelities over a greater range of SET resistances (up to 10MΩ) and tunnel rates (up to 100kHz), whereas the tunnel coupled design is limited to ≈100kΩ SET resistances with tunnel rates below 100Hz. i To further investigate the reproducibility of our SET charge sensors we then investigated the optimal tunnel barrier dimensions in a series of STM-patterned devices to achieve high fidelity single shot spin read-out. We found a simple width dependent exponential model describes the optimal tunnel barrier lengths for different lead widths. For tunnel barriers with 6±0.5nm lead widths, tunnel gap lengths of 11±0.5nm were found to give reliable SET resistances of 100KΩ optimal for providing good S/N. We then measured the charge noise in several SET devices and found that charge noise is correlated with high (> 350W) powers on the SUSI cell giving rise to an increase in pressure in the growth chamber (> 1×10−10mbar). We investigated the impact of charge noise on the ability to perform high fidelity spin readout and determined a noise threshold limit (0.03meV2) to achieve fidelities above 99%. In the final chapter we integrated an antenna on a triple dot device aiming for a 1,3,1 donor dot configuration. Using a detailed analysis of STM image height profiles, charging energies from gate-gate maps, capacitance triangulation and T1 measurements we determined that the final donor number was 0,3,2 indicating that no donor had incorporated in the lefthand dot. Despite this we were able to perform single shot spin read-out of the middle (≈92%) and right dots (92%) and confirmed the donor number of the right dot to be a 2P donor molecule using ESR resonance spectrum. We measured different hyperfine couplings of A1 = 189MHz and A2 = 83MHz to each of the donors within the dot, which under different slightly electric fields of 3.2MV/m and 3.8MV/m gave rise to a Stark shift of 41±31MHz/(MV/m). Using the ESR spectra, Stark shift measurements and tight binding simulations of the donor hyperfine Hamiltonian we are able to locate the exact configuration of the phosphorus atoms within the 2P donor molecule with the second donor being [0.5 1.5 0]a0 from the first donor. From these results we identified that a (3,2) donor configuration for the ancilla/data qubit does provide an equivalent (1,1) ↔ (2,0) interdot charge transitions with the available gate space. We then present a detailed outlook, with specific device recommendations as to how to achieve the parity measurement in donor qubits going forward.

  • (2023) Geng, Helen
    Thesis
    In the pursuit of realising a full-scale universal quantum computer, the phosphorus donor in silicon platform provides a simple, low magnetic and low charge noise environment. In this thesis we consider the singlet-triplet (T0) qubit encoding in this system which allows for fast all electrical control. In a first scalable, double quantum dot design, we optimised the readout circuit to achieve single-shot single-gate RF dispersive readout of the singlet and triplet (T-) states with a fidelity of 90% at 5 kHz bandwidth. By atomic engineering of the donor number and positions, we optimised the tunnel coupling between the two dots to 3 GHz, ideal to observe coherent interaction of the qubit states. However surprisingly this was not observed due to the fast relaxation rate (>1 MHz) of the triplet T0 to the singlet ground state. This fast rate is a result of the large difference in Zeeman energy between the two electrons (ΔEZ ~ 200 MHz) present which induces mixing between the triplet T0 and singlet states, exceeding the readout bandwidth of the dispersive sensor. Motivated by this discovery, we designed 2 different charges sensors to map the short-lived triplet (1,1)T0 state to a longer lived (2,1) charge state in a process called latched readout. In the first device, we designed a novel single lead quantum dot (SLQD) sensor. Despite realising an operational sensor, the charge noise in this device was found to be too high. In the second device, we used an single electron transistor (SET) charge sensor where we were able to demonstrate latched readout for the first time in the Si:P platform with a fidelity of 99.7%. We showed that the latched method is robust at higher temperatures, with a 97.1% fidelity measured at 3.7 K. Using this sensor we were able to observe coherent oscillations around the Z-axis of an all donor singlet-triplet qubit with a coherence time of T2*~ 23 ns. Finally the role of phosphorus donor nuclear spins on X-gate operations are discussed.

  • (2022) Donnelly, Matthew
    Thesis
    In this thesis we investigate quantum tunnelling of electrons in nanoscale tunnel junctions made from STM-patterned highly phosphorus doped silicon monolayers. Whilst the devices are monolayer doped, they are encapsulated in epitaxial silicon to form atomically abrupt 3D crystalline junctions that have multiple use cases in the manipulation of spin states in silicon for quantum information. First we investigate how to control the tunnelling resistance in these simple junctions by precision engineering of the junction length with STM lithography. By patterning the hydrogen resist with the tunnel junction edges along a dimer row in the [-110] crystalline direction we achieved a lithography accuracy of ±0.38nm. This precision patterning allowed us to increase the reproducibility of tunnel junction resistances to within 5% and demonstrate the exponential scaling of tunnelling resistance with junction length L. Second we investigated the tunnelling resistance as a function of lead width. By precision patterning the hydrogen resist along the dimer row in the [110] crystalline direction we reduced the lithographic accuracy of the junction length to ±0.77nm but increased the accuracy of the lead width to ±0.38nm. We observed a four order of magnitude change in the resistance of a 15nm long junction as the lead width changed from 7 to 15nm. To understand this variability, we conducted atomistic NEMO calculations and showed that the density of the states in these heavily phosphorus doped silicon wires is very sensitive to lead width. For thinner leads, where the width, W is <7nm the variability in the density of states is 0.7x108 meV-1 compared to 3.0x108 meV-1 at W~15nm. By plotting the resistances of all junctions as a function of lead width we observed an unexpected four order-of-magnitude change in the tunnelling resistance at W∼10 nm. Whilst this this could not be understood using current modelling, we speculate that it is related to size effects of the junction where the width of the leads matches the electron mean free path. We developed two unique atomic precision patterning techniques to realise 3D epitaxial gating. The first used kinetic growth manipulation to reduce the thermal budget during growth to minimise phosphorus diffusion to 0.66nm whilst achieving surfaces with 20nm2 island sizes, suitable for precision STM lithography. The second was to use the topographic height differential of the surface between STM-patterned doped surfaces and those with no underlying phosphorus atoms. Here despite ~100nm epitaxial silicon growth it was possible to observe a 0.4nm height differential. Using these two new techniques we were able to pattern 30nm wide vertically separated 3D epitaxial gates directly above tunnel junctions of size 9nm(W) x 17nm (L) and 9nm(W) x 30nm (L) with ±5nm accuracy. For the short junction we demonstrated strong capacitive coupling (a~0.36) – three times higher than for in-plane gates and showed we could tune the tunnel junction from 0.1 MOhm to 3.1 MOhm changing the barrier height from ∼0meV to 186 meV. Since the gate was more than three times narrower than previous 3D epitaxial gates, we were able to integrate two independent gates above two tunnel junctions in series within a single device. Using this device we demonstrated classical logic with an on/off ratio of ∼1000-2000. Finally we investigated the control of single electron tunnelling between a donor quantum dot qubit and an electron reservoir using a 3D epitaxial gate. We demonstrated that the tunnel rate Γ of electrons between the qubit and reservoir can be tuned from 5Hz to 10kHz which is notable since in-plane gates have not been shown to date to tune tunnel rates. This therefore represents a new capability in Si:P quantum computing devices. We discuss how future optimisation of device design will allow control of electron tunnelling for high fidelity qubit readout and controllable exchange coupling.

  • (2023) Huq, Abu Mohammad Saffat-Ee
    Thesis
    Motivated by the advancement in phosphorus donor atom qubits in silicon over the last decade, the semiconductor quantum computing community has begun investigating a variety of dopant species as well as more complex dopant structures for embedding enhanced quantum functionalities into quantum processors. The atomistic tight-binding method can simulate such systems capturing the wavefunctions of these substitutional atoms over a 1-30 nm domain without any apriori assumptions about the electronic structure. It has been hugely successful in describing the phosphorus atom qubits in silicon with atomistic detail. In this thesis, we extend this methodology to a variety of dopants in Group IV semiconductors (Si and Ge), including both donor and acceptor species. We achieve excellent calibration with known experimental data and obtain insights about the interplay between multiple bands, orbitals, spins, and valley states. We show how these features modify the critical spin qubit properties, such as hyperfine couplings, g-factors, energy splittings, magnetic and electric field dependencies, and discuss the ultimate limits of the modeling capability. We apply the simulation framework to investigate more complex dopant structures, such as phosphorus donor quantum dots (QD), which arise from the deterministic placement of a few dopant atoms within a small lithographic patch of 1-3 nm by Scanning Tunneling Microscope. High tunability in electronic confinement can be achieved in these systems by varying the number and arrangement of the donors inside the dot. We show that atomic confinement engineering enables control of qubit properties crucial for quantum operations, including contact hyperfine coupling, g-factors, relaxation time, decoherence time, and tunnel coupling strengths. In addition, we develop a Broyden mixing scheme with exchange-correlation corrections to self-consistently obtain tight-binding states and wavefunctions with different electron filling in the donor QDs. This provides us with a knob to engineer quantum confinement and the spin qubit properties post-fabrication. We assess the metrics of these multi-electron donor QDs as spin qubits and compare them with relevant experimental measurements. In summary, this thesis has generalized the simulation capabilities to investigate more complex dopant species and structures as potential high-performance qubits.

  • (2023) Munia, Mushita Masud
    Thesis
    Donor-based quantum computing in silicon has flourished in the last decade after the atomic precision placement of individual atoms has been demonstrated using Scanning Tunneling Microscope (STM) lithography. To facilitate effective design and characterization of the STM devices, predictive theoretical models are required that are multi-scale, multi-physics, self-consistent, and free of fitting parameters. The models need to capture quantum electronics at the nanoscale with corresponding electrostatics at nano- to micro-meter length scales. Here, we develop and apply such a framework involving atomistic tight-binding, non-linear Poisson, non-equilibrium Green’s function, and full configuration interaction (FCI) to investigate designs of STM devices for quantum computing. The methods are applied to investigate 1) electrical properties of semi-metallic degenerately doped phosphorus leads, 2) device electrostatics extending over multiple leads, gates, qubits, and SET regions, 3) current flow through atomically engineered tunnel barriers across leads/channels, 4) and long-range spin coupling between donor qubits. Each of these systems presents unique modeling challenges which we overcome in this thesis. We compute the conduction properties of the STM leads atomistically as a function of their dimensions and predict the optimum width for better reproducibility in the experiments. We then combine the properties of these semi-metallic phosphorus structures to solve the electrostatics of the extended device regions including the leads, gates, and qubits. We find agreement with experimentally measured lever arms and charging energies, which provide insight into the electrical tunability of the devices. We use the device electrostatics to tune the nearest and non-nearest neighbor exchange couplings between phosphorus donor qubits, extending the FCI method to handle more electrons than previously considered. The simulations predict robust spin coupling to the third-nearest neighbors in a donor chain, with qubits spaced out by about 40 nm or more. Finally, we combine calculations of the extended device electrostatics with Green’s function method of quantum transport at low temperatures to describe the current flow between two leads as a function of their separation and obtain good agreement with the tunneling resistance measured in experiments. The methodology and the results lay a foundation to design more complex donor devices for scaling up the quantum processors.