A single-atom electron spin qubit in silicon

Traditional electronic and communication devices operate by processing binary information encoded as bits. Such digital devices have led to the most advanced technologies that we encounter in our everyday lives and they influence virtually every aspect of our society. Nonetheless, there exists a much richer way to encode and process information. By encoding information in quantum mechanical states as qubits, phenomena such as coherence and entanglement can be harnessed to execute tasks that are intractable to digital devices. Under this paradigm, it should be possible to realize quantum computers, quantum communication networks and quantum sensors that outperform their classical counterparts. The electronic spin states of color-center defects in the semiconductor silicon carbide have recently emerged as promising qubit candidates. They have long-lived quantum coherence up to room temperature, they can be controlled with mature magnetic resonance techniques, and they have a built-in optical interface operating near the telecommunication bands. In this thesis I will present two of our contributions to this field. The first is the electric-field control of electron spin qubits. This development lays foundation for quantum electronics that operate via electrical gating, much like traditional electronics. The second is the universal control and entanglement of electron and nuclear spin qubits in an ensemble under ambient conditions. This development lays foundation for quantum devices that have a built-in redundancy and can operate in real-world conditions. Both developments represent important steps towards practical quantum devices in an electronic grade material.

Phosphorus atoms in silicon offer a rich quantum computing platform where both nuclear and electron spins can be used to store and process quantum information. While individual control of electron and nuclear spins has been demonstrated, the interplay between them during qubit operations has been largely unexplored. This study investigates the use of exchange-based operation between donor bound electron spins to probe the local magnetic fields experienced by the qubits with exquisite precision at the atomic scale. To achieve this, coherent exchange oscillations are performed between two electron spin qubits, where the left and right qubits are hosted by three and two phosphorus donors, respectively. The frequency spectrum of exchange oscillations shows quantized changes in the local magnetic fields at the qubit sites, corresponding to the different hyperfine coupling between the electron and each of the qubit-hosting nuclear spins. This ability to sense the hyperfine fields of individual nuclear spins using the exchange interaction constitutes a unique metrology technique, which reveals the exact crystallographic arrangements of the phosphorus atoms in the silicon crystal for each qubit. The detailed knowledge obtained of the local magnetic environment can then be used to engineer hyperfine fields in multi-donor qubits for high-fidelity two-qubitgates.

<sec>Spin qubits in silicon-based semiconductor quantum dots have become one of the prominent candidates for realizing fault-tolerant quantum computing due to their long coherence time, good controllability, and compatibility with modern advanced integrated circuit manufacturing processes. In recent years, due to the remarkable advances in silicon-based materials, the structure of quantum dot and its fabrication process, and qubit manipulation technology, the great progress of high-fidelity state preparation and readout, single- and two-qubit gates of spin qubits for silicon based semiconductor quantum computation has been achieved. The control fidelities for single- and two-qubit gates all exceed 99%—fault tolerance threshold required by the surface code known for its exceptionally high tolerance to errors. In this paper, we briefly introduce the basic concepts of silicon-based semiconductor quantum dots, discuss the state-of-art technologies used to improve the fidelities of single- and two-qubit gates, and finally highlight the research directions that should be focused on.</sec><sec>This paper is organized as follows. Firstly, we introduce three major types of quantum dot (QD) devices fabricated on different silicon-based substrates, including Si/SiGe heterojunction and Si/SiO<sub>2</sub>. The spin degree of electron or nucleus hosted in QD can be encoded into spin qubits. Electron spin qubits can be thermally initialized to ground state by using an electron reservoirs, and can be read out by spin-charge conversion mechanism: energy-selective readout (Elzerman readout) with reservoirs or Pauli spin blockade (PSB) without reservoirs. Additionally, high fidelity single-shot readout has been demonstrated by using radio-frequency gate reflectometry combined with the PSB, which has unique advantages in large-scale qubit array. To coherently control the spin qubits, electron dipole resonance (ESR) or electron dipole spin resonance (EDSR) for electron and nuclear magnetic resonance (NMR) for nucleus are introduced. With the help of isotope purification greatly improving the dephasing time of qubit and fast single-qubit manipulation based on EDSR, fidelity above 99.9% can be reached. For the two-qubit gates based on exchange interaction between electron spins, the strength of interaction <inline-formula><tex-math id="M1">\begin{document}$ J $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M1.png"/></alternatives></inline-formula> combined with Zeeman energy difference <inline-formula><tex-math id="M2">\begin{document}$ \Delta {E}_{z} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M2.png"/></alternatives></inline-formula> determines the energy levels of system, which lead to the different two-qubit gates, such as controlled-Z (CZ), controlled-Rotation (CROT), and the square root of the SWAP gate (<inline-formula><tex-math id="M3">\begin{document}$ \sqrt{\rm{S}\rm{W}\rm{A}\rm{P}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M3.png"/></alternatives></inline-formula>) gates. In order to improve the fidelity of two-qubit gates, a series of key technologies is used experimentally, they being isotope purification, symmetry operation, careful Hamiltonian engineering, and gate set tomography. Fidelity of two-qubit gates exceeding 99% has been demonstrated for electron spin qubits in Si/SiGe quantum dots and nuclear spin qubits in donors. These advances have pushed the silicon-based spin qubit platform to become a major stepping stone towards fault-tolerant quantum computation. Finally, we discuss the future study of spin qubits, that is, how to effectively expand the number of qubits, and many other problems to be explored and solved.</sec>

Arrays of neutral-atom qubits in optical tweezers are a promising platform for quantum computation. Despite experimental progress, a major roadblock for realizing neutral-atom quantum computation is the qubit initialization. Here we propose that supersymmetry, a theoretical framework developed in particle physics, can be used for ultrahigh-fidelity initialization of neutral-atom qubits. We show that a single atom can be deterministically prepared in the vibrational ground state of an optical tweezer by adiabatically extracting all excited atoms to a supersymmetric auxiliary tweezer. The scheme works for both bosonic and fermionic atom qubits trapped in realistic Gaussian optical tweezers and may pave the way for realizing large-scale quantum computation, simulation, and information processing with neutral atoms.

Building scalable quantum information systems is a central challenge facing modern science. Single spins in diamond are a promising platform for distributed quantum information networks and precision measurements. I will discuss recent progress in this field demonstrating coherent operations with coupled electron-nuclear spin quantum registers and nanoscale precision magnetometry. Our experiments demonstrate addressing, preparation, and coherent control of individual nuclear spin qubits in the diamond lattice at room temperature. We have measured spin coherence times exceeding milliseconds, and observed coherent coupling to nearby electronic and nuclear spins. Robust initialization of a two-qubit register and transfer of arbitrary quantum states between electron and nuclear spin qubits has been achieved. Our results show that coherent operations are possible with individual solid-state qubits whose coherence properties approach those for isolated atoms and ions. The resulting electron-nuclear few-qubit registers can potentially serve as small processor nodes in a quantum network where the electron spins are coupled by optical photons.

The recent decade has witnessed substantial advancements in silicon quantum computing. Important milestones include demonstrations of quantum gates exceeding the fault-tolerance threshold, high-fidelity single-shot spin readout, hot quantum bits (hot qubits), and compact scalable spin arrays. Silicon qubits hold promise to leverage semiconductor industry technologies into scalable qubit manufacturing. Both the academic and industry communities are striving to push this advantage into reality. However, formidable challenges persist in the quest to develop a fully operational universal quantum computer. This review focuses on single-spin qubits in silicon. First, we start with foundational spin qubit theory. Then, we discuss gate-defined quantum dots and donor dot systems, with a particular emphasis on two-qubit gate operations and the scalability of qubit arrays. Lastly, we address long-distance coupling, highlighting key areas for future research and potential scale-up strategies for this rapidly evolving field.

Silicon devices form the backbone of modern computers. It turns out that they might also be a natural hardware platform for a new era of computing technology that uses the principles of quantum physics. See Letter p.541 Because silicon devices already form the basis for integrated electronic circuits, it would be ideal if future quantum-computing architectures could also be silicon-based, thus making use of the same well-developed fabrication technologies. A promising approach to constructing silicon qubits (quantum bits), first proposed more than a decade ago, is to make use of single dopant atoms in silicon. Jarryd Pla et al. have now made a nanoelectronic silicon device in which they can read out and control the electron spin of a single phosphorous donor atom, and demonstrate exceptionally long spin coherence times (of 200 microseconds). The combination of good qubit performance and practical fabrication approach opens the door to building scalable quantum-computing circuits.

The creation, coherent manipulation, and measurement of spins in nanostructures open up completely new possibilities for electronics and information processing, among them quantum computing and quantum communication. We review our theoretical proposal for using electron spins in quantum dots as quantum bits, explaining why this scheme satisfies all the essential requirements for quantum computing. We include a discussion of the recent measurements of surprisingly long spin coherence times in semiconductors. Quantum gate mechanisms in laterally and vertically tunnel-coupled quantum dots and methods for single-spin measurements are introduced. We discuss detection and transport of electronic EPR pairs in normal and superconducting systems.

Current status of the research on the use of single neutral atoms, captured in optical traps, as a quantum computer's qubits, is briefly reviewed. The specifics of qubits based on cold atoms and t quantum logical operations via dipole interaction by short-time laser excitation in a Rydberg state are discussed. The latest experimental results of the observation of dipole interaction between two Rydberg atoms and of atoms' entangled states in a ground state are given.

Quantum computers could solve problems insurmountable to conventional computers. The missing ingredient for quantum computing with electron spins is now available — the rotation of a single spin. One of the most promising approaches to realizing a practical quantum bit is to use spin states of single electrons in semiconductor quantum dots. A detailed proposal for such spin qubits was published about ten years ago; since then, all the necessary ingredients to realize it, such as long-lived spin states and the initialization of electron spins, have been reported one by one. Now the last, most difficult step has been accomplished, that of driving coherent spin oscillations for individual electrons, which is necessary to carry out quantum operations. This is achieved by applying oscillating magnetic fields that are resonant with the precession frequencies of the electron spins, generated on-chip near a double quantum dot system. All is now ready to design universal quantum logic gates.

In order to generate a submicron localized hollow laser beam and realize the more efficient laser cooling and trapping of a single atom, a simple and promising scheme with using the system of a single mode fiber a circle binary phase plate and a microlens is proposed in this paper. From Rayleigh-Sommerfeld diffraction theory, the intensity distribution of the generated localized hollow laser beam near the focal plane and its propagating properties in free space are calculated. Also, the dependences of the dark-spot size of the localized hollow beam on the mode radius of single mode fiber and the focal length of the mocrolens are studied. The calculated results show that the intensity distribution of the localized hollow beam presents approximately symmstrical distribution near the focal plane. In the center of the focal plane, the light intensity is 0 and increases gradually around it. So a closed spherical light field (i.e., localized hollow laser beam) with a radius of 0.4 m is generated. The calculated results also show that the dark-spot size of the localized hollow laser beam decreases with the increasing of the microlens focal length and the decreasing of the single mode fiber mode radius. So proper parameters of this optical system can be chosen to generate localized hollow laser beams with different sizes for various applications. When the localized hollow laser beam is blue detuned, atoms will be trapped in the minimum light filed. If a repumping laser beam is applied, the trapped atoms will be also cooled by the intensity-gradient Sisyphus cooling. In this paper, we build a device for trapping and cooling a single atom by using the generated blue detuned submicron localized hollow laser beam. We study the dynamical process of intensity-gradient cooling of a single 87Rb atom trapped in the localized hollow beam by Monte-Carlo method. Our study shows that a single 87Rb atom with a temperature of 120 K (the corresponding momentum is 30ħk) from a magneto-optical trap (MOT) can be directly cooled to a final tempreture of ～ 5.8 K (the corresponding momentum is ～ 6.6ħk). So an ultracold single atom is generated and trapped in our submicro localized hollow beam. This device for obtaining ultralcold single atom can be widely uesd in the regions of the optical physics, the atom and molecule optics, such as the detecting of the fundamental physical parameters, realizing the quantum computer, studying the cold collision of singe atoms, and realizing the single atom laser.

We study effects of spin-orbit interaction on quantum states in multiple low-dimensional systems. In the first part we investigate coupling of hybrid qubit with other broadly used types of qubit like singlet-triplet or single spin qubit in quantum dots. In the second part we investigate effects of strong in-plane magnetic field on g-factor renormalization in lateral quantum dots in GaAs, exploiting the symmetry of the underlying lattice. In the third part we analyze the topological phase transition in Majorana nanowires and we show that edge spin along the direction of the external magnetic field can be used as a probe of this elusive transition.

The first quantum revolution provided a microscopic understanding of nature and underpinned the development of transistors, originally made in germanium. The following assembly of silicon transistors into integrated circuits triggered the digital age, which completely changed our daily life. We are now in the midst of the second quantum revolution, in which quantum matter is engineered to develop disruptive technologies beyond the reach of classical understanding. Quantum computing is considered by many the man on the moon goal of such second quantum revolution. How will we get there? In this talk I will discuss, from a materials perspective, how we are turning everyday silicon into the quantum computing wonder material by using quantum dots defined electrostatically in SiGe heterostructures. Group-IV semiconductors Si and Ge offer several advantages for the realization of spin quantum bits. Si and Ge can be isotopically purified into a nuclear spin free materials, which allows long spin coherence time. A quantum dot defined by metallic gates in a strained Si/SiGe heterostructure can trap a single electron, such that the electron spin can be operated as a quantum bit, the elementary unit of quantum computation. Quantum dots in Si/SiGe heterostructure are promising because bear similarities from a materials and integration perspective to the transistors used in advanced semiconductor manufacturing. Advanced quantum control in Si qubits allows to run quantum algorithms on two qubit processors. Strong spin-photon coupling has been achieved in Si, a first step towards realizing large networks of quantum dot based spin qubit registers.[1] Additionally, SiGe heterostructures allows us to explore high mobility holes in strained Ge as a complementary option for fast quantum hardware due to the different band structure properties of Ge compared to Si. Recently, gate-controlled stable quantum dots were demonstrated in planar Ge, a first step towards Ge hole qubits.[2] However, to deploy a qubit into high volume manufacturing in a quantum computer requires stringent control over substrate uniformity and quality. In this talk we will focus on carrier mobility and energetic valley splittings in SiGe heterostructures, which are two key electrical metrics of substrate quality relevant for qubits. To ensure rapid progress in quantum wells development we have implemented fast feedback loops from materials growth, to innovative heterostructure field effect transistor fabrication, and low temperature characterization. In this direction we show progress in developing a cryogenic platform for high-throughput magnetotransport measurements. [1] N. Samkharadze, G. Zheng, N. Kalhor, D. Brousse, A. Sammak, U. C. Mendes, A. Blais, G. Scappucci, and L. M. K. Vandersypen, Science , eaar4054 (2018). [2] N. W. Hendrickx, D.P. Franke, A. Sammak, M. Kouwenhoven, D. Sabbagh, L. Yeoh, R. Li, M. L. V. Tagliaferri, M. Virgilio, G. Capellini, G. Scappucci, M. Veldhorst, arXiv:1801.08869 (2018)

N@C60 and other group V endohedral fullerenes have recently been proposed as quantum bits for a quantum computer due to their long spin relaxation times. So far quantum computing (QC) experiments have been limited to standard relaxation measurements and simple spin rotations. The purpose of the presented work was perform basic quantum computation experiments including entangled states on this system using electron spin resonance (ESR and ENDOR). In order to allow access the full 3/2 spin character, the symmetry of the fullerenes was lowered by encapsulating them in a crystalline matrix. Co-crystallization of endohedral fullerenes with bromophenoxy triazine (BrPOT) afforded two host-guest structures. In the first, hexagonal, structure fullerenes are situated together with solvent molecules in parallel channels formed by BrPOT molecules. The ESR lines are inhomogeneously broadened compared to those of non-encapsulated fullerenes with no observable fine structure in the case of crystals obtained from toluene solution. In the rhombohedral crystal of N@C60 and P@C60 in BrPOT the fullerenes are fully oriented in individual pockets formed by the BrPOT molecules, hence there are no channels and no solvent inclusion is observed. The ESR spectra show significant fine structure (FS) with D = 8.01 MHz and D = 127 MHz for N@C60 and P@C60, respectively. The presence of FS means that the degeneracy of the electron spin S = 3/2 system is lifted so that all Zeeman sublevels can be addressed individually. In order to elucidate the decoherence mechanisms in P@C60, several polycrystalline samples with low spin concentrations were prepared. The phase memory time Tm and the spin-spin relaxation time T2 were measured using the Hahn echo and Carr-Purcell-Meiboom-Gill (CPMG) pulse sequences, respectively. Tm and T2 increase up to 113.25 ms and 417 ms respectively with decreasing spin concentration. It was found that instant diffusion does not significantly influence the spin-spin relaxation and that the phase memory time is determined mainly by spectral diffusion due to coupling between the P@C60 molecules. The spin relaxation of P@C60 in rhombohedral BrPOT was studied at various temperatures in W-band. Two longitudinal relaxation times T1a and T1b with similar temperature dependence were found in bulk P@C60. The encapsulation of P@C60 in BrPOT has shortened the relaxation but not too much to prevent the realization of QC experiments. The coherence time Tm is not equal for the different ESR transitions and increases decreasing the temperature. For the transition with ms = +1/2 to ms = -1/2 Tm has a minimum at T = 210 K. A subsystem of four states from the total eight levels of P@C60 in BrPOT was selected for QC experiments in which pseudo-pure states were prepared and their diagonal matrix elements were measured. The experimental density matrices deviate slightly (about 3 %) from the theoretically calculated ones due to pulse imperfections. Pseudo-entanglement was created in this subsystem with a Hadamard transform. Phase rotations on both electron and nuclear spins were used for the tomography of the entangled state. The lifetime of the entangled state depends on the type of states used for its creation. For two states with |ms| = 1/2, the coherence time was so short that the entanglement between them was partially destroyed during the preparation. If one of the energy levels had |ms| = 3/2, pseudo-entanglement could be prepared with a decay time of Tent = 55 ns, much shorter than the electron spin coherence time at that temperature, Tm = 17 ms. A possible reason for the fast decay is the coupling of the endohedral electrons to protons in the BrPOT matrix.

All conventional methods to laser-cool atoms rely on repeated cycles of optical pumping and spontaneous emission of a photon by the atom. Spontaneous emission in a random direction provides the dissipative mechanism required to remove entropy from the atom. However, alternative cooling methods have been proposed for a single atom strongly coupled to a high-finesse cavity; the role of spontaneous emission is replaced by the escape of a photon from the cavity. Application of such cooling schemes would improve the performance of atom-cavity systems for quantum information processing. Furthermore, as cavity cooling does not rely on spontaneous emission, it can be applied to systems that cannot be laser-cooled by conventional methods; these include molecules (which do not have a closed transition) and collective excitations of Bose condensates, which are destroyed by randomly directed recoil kicks. Here we demonstrate cavity cooling of single rubidium atoms stored in an intracavity dipole trap. The cooling mechanism results in extended storage times and improved localization of atoms. We estimate that the observed cooling rate is at least five times larger than that produced by free-space cooling methods, for comparable excitation of the atom.