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arXiv:1702.07991 · Physical review. B./Physical review. B

Coherent control via weak measurements in P31 single-atom electron and nuclear spin qubits

Juha T. Muhonen, Juan Pablo Dehollain, Arne Laucht, Stephanie Simmons, Rachpon Kalra, Fay E. Hudson, Andrew S. Dzurak, Andrea Morello, David N. Jamieson, Jeffrey Colin McCallum, Kohei M. Itoh

Published Oct 5, 2018• 22 citations
arXivHTMLPDF

Abstract

At the heart of quantum mechanics is the idea that we cannot observe a physical system without affecting it. This is normally taken to mean that the act of measurement produces uncontrolled disturbances, and ``collapses'' quantum superposition states. Here, the authors demonstrate the preparation of arbitrary quantum states of the nuclear spin of a single ${}^{31}$P donor in silicon, while operating and measuring only the donor-bound electron. The ``partial collapse'' resulting from a sequence of weak nuclear spin measurement is shown to be a fully coherent process, which can even be reversed. The change in the nuclear spin state can also be used as a physical meter to probe the measurement strength, proportional to the electron tunnel rate, by analyzing events where no tunneling occurs.

DOI
10.1103/physrevb.98.155201

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At the heart of quantum mechanics is the idea that we cannot observe a physical system without affecting it. This is normally taken to mean that the act of measurement produces uncontrolled disturbances, and collapses'' quantum superposition states. Here, the authors demonstrate the preparation of arbitrary quantum states of the nuclear spin of a single ${}^{31}$P donor in silicon, while operating and measuring only the donor-bound electron. The partial collapse'' resulting from a sequence of weak nuclear spin measurement is shown to be a fully coherent process, which can even be reversed. The change in the nuclear spin state can also be used as a physical meter to probe the measurement strength, proportional to the electron tunnel rate, by analyzing events where no tunneling occurs.
Spin is a quantum mechanical property that describes the magnetic orientation of elementary and composite particles such as electrons and nuclei. For spin-half particles placed in a magnetic field, two states with differing energies are defined. Proposals exist for developing a revolutionary kind of computer that encodes bits of information on the states of a simple quantum two-level system - like those of a spin in a magnetic field. These quantum computers exploit the fundamental principles of quantum mechanics in order to perform certain calculations exponentially faster than their classical counterparts. Key to the development of such a device is the identification of potential systems that are suitable for employment as a quantum bit (qubit). This thesis explores quantum bits constructed from the spin states of single atoms hosted in silicon semiconductor devices. Silicon is an exceptional platform for spin-based quantum computing - in addition to being the dominant material in the microelectronic industry, it is also predominantly composed of nuclear spin-zero isotopes, providing very little background magnetic disturbance. The donor-atom phosphorus (31P) is investigated here. It possesses a nucleus that binds an additional electron to its positive charge, providing two distinct spin qubits. Here, several world-first experimental milestones in spin-based quantum information processing are reported. First, the readout of the electron spin is demonstrated in single-shot, using a silicon device which combines implanted phosphorus donors with a sensitive nanoscale electrometer. Then, the electron spin is coherently operated as a qubit by delivering on-chip microwave excitations. Combining the electron spin detection and control capabilities enables a quantum non-demolition measurement of the single 31P nuclear spin. Experiments yield exceptional nuclear readout fidelities - the highest for any solid-state qubit. Through an application of nuclear magnetic resonance, high-fidelity quantum control of the nuclear spin qubit is demonstrated. Finally, a single spin-bearing silicon nucleus (29Si) coupled to the electron spin is detected in single-shot and operated as a qubit. These results, along with the clear pathways identified for improving device performance, illustrate that single-atom electron and nuclear spin qubits in silicon constitute an excellent basis on which to construct a quantum computer.
Phosphorus donor nuclear spins in silicon couple weakly to the environment, making them promising candidates for high-fidelity qubits. The state of a donor nuclear spin qubit can be manipulated and read out using its hyperfine interaction with the electron confined by the donor potential. Here we use a master-equation-based approach to investigate how the backaction from this electron-mediated measurement affects the lifetimes of single and multidonor qubits. We analyze this process as a function of electric and magnetic fields and hyperfine interaction strength. Apart from single nuclear spin flips, we identify an additional measurement-related mechanism, the nuclear spin flip-flop, which is specific to multidonor qubits. Although this flip-flop mechanism reduces qubit lifetimes, we show that it can be effectively suppressed by the hyperfine Stark shift. We show that using atomic precision donor placement and engineered Stark shift, we can minimize the measurement backaction in multidonor qubits, achieving larger nuclear spin lifetimes than single donor qubits.
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.
Projective quantum measurement is fundamental for quantum technologies. Here we propose a method for construction of projective measurement of nonconserved quantity of nuclear spin via a weakly coupled auxiliary electron spin. The key idea is to apply suitable quantum control on the electron to construct a weak quantum nondemolition (QND) measurement on the nuclear spin and then cascade a sequence of such measurements into a projective one. We identify a set of tunable parameters to select the QND observables and control the strength of the weak QND measurement. We also find that the QND measurement can be stabilized against realistic experimental control errors. As a demonstration of our method, we design projective measurement on a 13C{}^{13}\mathrm{C}13C nuclear spin weakly coupled to a nitrogen-vacancy center electron spin in diamond.
Abstract Long coherence times and fast gate operations are desirable but often conflicting requirements for physical qubits. This conflict can be resolved by resorting to fast qubits for operations, and by storing their state in a ‘quantum memory’ while idle. The 31 P donor in silicon comes naturally equipped with a fast qubit (the electron spin) and a long-lived qubit (the 31 P nuclear spin), coexisting in a bound state at cryogenic temperatures. Here, we demonstrate storage and retrieval of quantum information from a single donor electron spin to its host phosphorus nucleus in isotopically enriched 28 Si. The fidelity of the memory process is characterised via both state and process tomography. We report an overall process fidelity F p ≈ 81 %, and memory storage times up to 80 ms. These values are limited by a transient shift of the electron spin resonance frequency following high-power radiofrequency pulses.
The theory of weak quantum measurements is developed for quantum-dot spin qubits. Building on recent experiments, we propose a control cycle to prepare, manipulate, weakly measure, and perform quantum state tomography. This is accomplished using a combination of the physics of electron spin resonance, spin blockade, and Coulomb blockade, resulting in a charge transport process. We investigate the influence of the surrounding nuclear spin environment, and find a regime where this environment significantly simplifies the dynamics of the weak-measurement process, making this theoretical proposal realistic with existing experimental technology. We further consider spin-echo refocusing to combat dephasing, as well as discuss a realization of ``quantum undemolition,'' whereby the effects of quantum state disturbance are undone.