Observation of a Quantum Phase from Classical Rotation of a Single Spin.

The theory of angular momentum connects physical rotations and quantum spins together at a fundamental level. Physical rotation of a quantum system will therefore affect fundamental quantum operations, such as spin rotations in projective Hilbert space, but these effects are subtle and experimentally challenging to observe due to the fragility of quantum coherence. We report on a measurement of a single-electron-spin phase shift arising directly from physical rotation, without transduction through magnetic fields or ancillary spins. This phase shift is observed by measuring the phase difference between a microwave driving field and a rotating two-level electron spin system, and it can accumulate nonlinearly in time. We detect the nonlinear phase using spin-echo interferometry of a single nitrogen-vacancy qubit in a diamond rotating at 200 000 rpm. Our measurements demonstrate the fundamental connections between spin, physical rotation, and quantum phase, and they will be applicable in schemes where the rotational degree of freedom of a quantum system is not fixed, such as spin-based rotation sensors and trapped nanoparticles containing spins.

Microscopic Imaging of the Stress Tensor in Diamond Using in Situ Quantum Sensors.

The precise measurement of mechanical stress at the nanoscale is of fundamental and technological importance. In principle, all six independent variables of the stress tensor, which describe the direction and magnitude of compression/tension and shear stress in a solid, can be exploited to tune or enhance the properties of materials and devices. However, existing techniques to probe the local stress are generally incapable of measuring the entire stress tensor. Here, we make use of an ensemble of atomic-sized in situ strain sensors in diamond (nitrogen-vacancy defects) to achieve spatial mapping of the full stress tensor, with a submicrometer spatial resolution and a sensitivity of the order of 1 MPa (10 MPa) for the shear (axial) stress components. To illustrate the effectiveness and versatility of the technique, we apply it to a broad range of experimental situations, including mapping the stress induced by localized implantation damage, nanoindents, and scratches. In addition, we observe surprisingly large stress contributions from functional electronic devices fabricated on the diamond and also demonstrate sensitivity to deformations of materials in contact with the diamond. Our technique could enable in situ measurements of the mechanical response of diamond nanostructures under various stimuli, with potential applications in strain engineering for diamond-based quantum technologies and in nanomechanical sensing for on-chip mass spectroscopy.

Quantum Bath Control with Nuclear Spin State Selectivity via Pulse-Adjusted Dynamical Decoupling.

Dynamical decoupling (DD) is a powerful method for controlling arbitrary open quantum systems. In quantum spin control, DD generally involves a sequence of timed spin flips (π rotations) arranged to either average out or selectively enhance coupling to the environment. Experimentally, errors in the spin flips are inevitably introduced, motivating efforts to optimize error-robust DD. Here we invert this paradigm: by introducing particular control "errors" in standard DD, namely, a small constant deviation from perfect π rotations (pulse adjustments), we show we obtain protocols that retain the advantages of DD while introducing the capabilities of quantum state readout and polarization transfer. We exploit this nuclear quantum state selectivity on an ensemble of nitrogen-vacancy centers in diamond to efficiently polarize the ^{13}C quantum bath. The underlying physical mechanism is generic and paves the way to systematic engineering of pulse-adjusted protocols with nuclear state selectivity for quantum control applications.

Spatially resolving valley quantum interference of a donor in silicon.

Electron and nuclear spins of donor ensembles in isotopically pure silicon experience a vacuum-like environment, giving them extraordinary coherence. However, in contrast to a real vacuum, electrons in silicon occupy quantum superpositions of valleys in momentum space. Addressable single-qubit and two-qubit operations in silicon require that qubits are placed near interfaces, modifying the valley degrees of freedom associated with these quantum superpositions and strongly influencing qubit relaxation and exchange processes. Yet to date, spectroscopic measurements have only probed wavefunctions indirectly, preventing direct experimental access to valley population, donor position and environment. Here we directly probe the probability density of single quantum states of individual subsurface donors, in real space and reciprocal space, using scanning tunnelling spectroscopy. We directly observe quantum mechanical valley interference patterns associated with linear superpositions of valleys in the donor ground state. The valley population is found to be within 5% of a bulk donor when 2.85 ± 0.45 nm from the interface, indicating that valley-perturbation-induced enhancement of spin relaxation will be negligible for depths greater than 3 nm. The observed valley interference will render two-qubit exchange gates sensitive to atomic-scale variations in positions of subsurface donors. Moreover, these results will also be of interest for emerging schemes proposing to encode information directly in valley polarization.

Ab Initio electronic properties of monolayer phosphorus nanowires in silicon.

Epitaxial circuitry offers a revolution in silicon technology, with components that can be fabricated on atomic scales. We perform the first ab initio calculation of atomically thin epitaxial nanowires in silicon, investigating the fundamental electronic properties of wires two P atoms thick, similar to those produced this year by Weber et al. For the first time, we catch a glimpse of disorder-related effects in the wires--a prerequisite for understanding real fabricated systems. Interwire interactions are made negligible by including 40 ML of silicon in the vertical direction (and the equivalent horizontally). Accurate pictures of band splittings and the electronic density are presented, and for the first time the effective masses of electrons in such device components are calculated.

Measurable quantum geometric phase from a rotating single spin.

We demonstrate that the internal magnetic states of a single nitrogen-vacancy defect, within a rotating diamond crystal, acquire geometric phases. The geometric phase shift is manifest as a relative phase between components of a superposition of magnetic substates. We demonstrate that under reasonable experimental conditions a phase shift of up to four radians could be measured. Such a measurement of the accumulation of a geometric phase, due to macroscopic rotation, would be the first for a single atom-scale quantum system.

Lifetime-enhanced transport in silicon due to spin and valley blockade.

We report the observation of lifetime-enhanced transport (LET) based on perpendicular valleys in silicon by transport spectroscopy measurements of a two-electron system in a silicon transistor. The LET is manifested as a peculiar current step in the stability diagram due to a forbidden transition between an excited state and any of the lower energy states due to perpendicular valley (and spin) configurations, offering an additional current path. By employing a detailed temperature dependence study in combination with a rate equation model, we estimate the lifetime of this particular state to exceed 48 ns. The two-electron spin-valley configurations of all relevant confined quantum states in our device were obtained by a large-scale atomistic tight-binding simulation. The LET acts as a signature of the complicated valley physics in silicon: a feature that becomes increasingly important in silicon quantum devices.

Demonstration of non-Markovian process characterisation and control on a quantum processor.

In the scale-up of quantum computers, the framework underpinning fault-tolerance generally relies on the strong assumption that environmental noise affecting qubit logic is uncorrelated (Markovian). However, as physical devices progress well into the complex multi-qubit regime, attention is turning to understanding the appearance and mitigation of correlated - or non-Markovian - noise, which poses a serious challenge to the progression of quantum technology. This error type has previously remained elusive to characterisation techniques. Here, we develop a framework for characterising non-Markovian dynamics in quantum systems and experimentally test it on multi-qubit superconducting quantum devices. Where noisy processes cannot be accounted for using standard Markovian techniques, our reconstruction predicts the behaviour of the devices with an infidelity of 10-3. Our results show this characterisation technique leads to superior quantum control and extension of coherence time by effective decoupling from the non-Markovian environment. This framework, validated by our results, is applicable to any controlled quantum device and offers a significant step towards optimal device operation and noise reduction.

Valley interference and spin exchange at the atomic scale in silicon.

Tunneling is a fundamental quantum process with no classical equivalent, which can compete with Coulomb interactions to give rise to complex phenomena. Phosphorus dopants in silicon can be placed with atomic precision to address the different regimes arising from this competition. However, they exploit wavefunctions relying on crystal band symmetries, which tunneling interactions are inherently sensitive to. Here we directly image lattice-aperiodic valley interference between coupled atoms in silicon using scanning tunneling microscopy. Our atomistic analysis unveils the role of envelope anisotropy, valley interference and dopant placement on the Heisenberg spin exchange interaction. We find that the exchange can become immune to valley interference by engineering in-plane dopant placement along specific crystallographic directions. A vacuum-like behaviour is recovered, where the exchange is maximised to the overlap between the donor orbitals, and pair-to-pair variations limited to a factor of less than 10 considering the accuracy in dopant positioning. This robustness remains over a large range of distances, from the strongly Coulomb interacting regime relevant for high-fidelity quantum computation to strongly coupled donor arrays of interest for quantum simulation in silicon.

Nano-manipulation of diamond-based single photon sources.

The ability to manipulate nano-particles at the nano-scale is critical for the development of active quantum systems. This paper presents a technique to manipulate diamond nano-crystals at the nano-scale using a scanning electron microscope, nano-manipulator and custom tapered optical fibre probes. The manipulation of a approximately 300 nm diamond crystal, containing a single nitrogen-vacancy centre, onto the endface of an optical fibre is demonstrated. The emission properties of the single photon source post manipulation are in excellent agreement with those observed on the original substrate.

Sensing of fluctuating nanoscale magnetic fields using nitrogen-vacancy centers in diamond.

New magnetometry techniques based on nitrogen-vacancy (NV) defects in diamond allow for the detection of static (dc) and oscillatory (ac) nanoscopic magnetic fields, yet are limited in their ability to detect fields arising from randomly fluctuating (FC) environments. We show here that FC fields restrict dc and ac sensitivities and that probing the NV dephasing rate in a FC environment should permit the characterization of FC fields inaccessible to dc and ac techniques. FC sensitivities are shown to be comparable to those of ac magnetometry and require no additional experimental overhead or sample control.

Coherent tunneling adiabatic passage with the alternating coupling scheme.

The use of adiabatic passage techniques to mediate particle transport through real space, rather than phase space, is becoming an interesting possibility. We have investigated the properties of coherent tunneling adiabatic passage (CTAP) with alternating tunneling matrix elements. This coupling scheme, not previously considered in the donor in silicon paradigm, provides an interesting route to long-range quantum transport. We introduce simplified coupling protocols and transient eigenspectra as well as a realistic gate design for this transport protocol. Using a pairwise treatment of the tunnel couplings for a five-donor device with 30 nm donor spacings, 120 nm total chain length, we estimate the timescale required for adiabatic operation to be approximately 70 ns, a time well within the measured electron spin and estimated charge relaxation times for phosphorus donors in silicon.

Two-electron spin correlations in precision placed donors in silicon.

Substitutional donor atoms in silicon are promising qubits for quantum computation with extremely long relaxation and dephasing times demonstrated. One of the critical challenges of scaling these systems is determining inter-donor distances to achieve controllable wavefunction overlap while at the same time performing high fidelity spin readout on each qubit. Here we achieve such a device by means of scanning tunnelling microscopy lithography. We measure anti-correlated spin states between two donor-based spin qubits in silicon separated by 16 ± 1 nm. By utilising an asymmetric system with two phosphorus donors at one qubit site and one on the other (2P-1P), we demonstrate that the exchange interaction can be turned on and off via electrical control of two in-plane phosphorus doped detuning gates. We determine the tunnel coupling between the 2P-1P system to be 200 MHz and provide a roadmap for the observation of two-electron coherent exchange oscillations.

Ab initio calculation of energy levels for phosphorus donors in silicon.

The s manifold energy levels for phosphorus donors in silicon are important input parameters for the design and modeling of electronic devices on the nanoscale. In this paper we calculate these energy levels from first principles using density functional theory. The wavefunction of the donor electron's ground state is found to have a form that is similar to an atomic s orbital, with an effective Bohr radius of 1.8 nm. The corresponding binding energy of this state is found to be 41 meV, which is in good agreement with the currently accepted value of 45.59 meV. We also calculate the energies of the excited 1s(T 2) and 1s(E) states, finding them to be 32 and 31 meV respectively.

A quantum spin-probe molecular microscope.

Imaging the atomic structure of a single biomolecule is an important challenge in the physical biosciences. Whilst existing techniques all rely on averaging over large ensembles of molecules, the single-molecule realm remains unsolved. Here we present a protocol for 3D magnetic resonance imaging of a single molecule using a quantum spin probe acting simultaneously as the magnetic resonance sensor and source of magnetic field gradient. Signals corresponding to specific regions of the molecule's nuclear spin density are encoded on the quantum state of the probe, which is used to produce a 3D image of the molecular structure. Quantum simulations of the protocol applied to the rapamycin molecule (C51H79NO13) show that the hydrogen and carbon substructure can be imaged at the angstrom level using current spin-probe technology. With prospects for scaling to large molecules and/or fast dynamic conformation mapping using spin labels, this method provides a realistic pathway for single-molecule microscopy.

Spatial metrology of dopants in silicon with exact lattice site precision.

Scaling of Si-based nanoelectronics has reached the regime where device function is affected not only by the presence of individual dopants, but also by their positions in the crystal. Determination of the precise dopant location is an unsolved problem in applications from channel doping in ultrascaled transistors to quantum information processing. Here, we establish a metrology combining low-temperature scanning tunnelling microscopy (STM) imaging and a comprehensive quantum treatment of the dopant-STM system to pinpoint the exact coordinates of the dopant in the Si crystal. The technique is underpinned by the observation that STM images contain atomic-sized features in ordered patterns that are highly sensitive to the STM tip orbital and the absolute dopant lattice site. The demonstrated ability to determine the locations of P and As dopants to 5 nm depths will provide critical information for the design and optimization of nanoscale devices for classical and quantum computing applications.

Quantum simulation of the Hubbard model with dopant atoms in silicon.

In quantum simulation, many-body phenomena are probed in controllable quantum systems. Recently, simulation of Bose-Hubbard Hamiltonians using cold atoms revealed previously hidden local correlations. However, fermionic many-body Hubbard phenomena such as unconventional superconductivity and spin liquids are more difficult to simulate using cold atoms. To date the required single-site measurements and cooling remain problematic, while only ensemble measurements have been achieved. Here we simulate a two-site Hubbard Hamiltonian at low effective temperatures with single-site resolution using subsurface dopants in silicon. We measure quasi-particle tunnelling maps of spin-resolved states with atomic resolution, finding interference processes from which the entanglement entropy and Hubbard interactions are quantified. Entanglement, determined by spin and orbital degrees of freedom, increases with increasing valence bond length. We find separation-tunable Hubbard interaction strengths that are suitable for simulating strongly correlated phenomena in larger arrays of dopants, establishing dopants as a platform for quantum simulation of the Hubbard model.

Detection of nanoscale electron spin resonance spectra demonstrated using nitrogen-vacancy centre probes in diamond.

Electron spin resonance (ESR) describes a suite of techniques for characterizing electronic systems with applications in physics, chemistry, and biology. However, the requirement for large electron spin ensembles in conventional ESR techniques limits their spatial resolution. Here we present a method for measuring ESR spectra of nanoscale electronic environments by measuring the longitudinal relaxation time of a single-spin probe as it is systematically tuned into resonance with the target electronic system. As a proof of concept, we extracted the spectral distribution for the P1 electronic spin bath in diamond by using an ensemble of nitrogen-vacancy centres, and demonstrated excellent agreement with theoretical expectations. As the response of each nitrogen-vacancy spin in this experiment is dominated by a single P1 spin at a mean distance of 2.7 nm, the application of this technique to the single nitrogen-vacancy case will enable nanoscale ESR spectroscopy of atomic and molecular spin systems.

Ohm's law survives to the atomic scale.

As silicon electronics approaches the atomic scale, interconnects and circuitry become comparable in size to the active device components. Maintaining low electrical resistivity at this scale is challenging because of the presence of confining surfaces and interfaces. We report on the fabrication of wires in silicon--only one atom tall and four atoms wide--with exceptionally low resistivity (~0.3 milliohm-centimeters) and the current-carrying capabilities of copper. By embedding phosphorus atoms within a silicon crystal with an average spacing of less than 1 nanometer, we achieved a diameter-independent resistivity, which demonstrates ohmic scaling to the atomic limit. Atomistic tight-binding calculations confirm the metallicity of these atomic-scale wires, which pave the way for single-atom device architectures for both classical and quantum information processing.

High spatial and temporal resolution wide-field imaging of neuron activity using quantum NV-diamond.

A quantitative understanding of the dynamics of biological neural networks is fundamental to gaining insight into information processing in the brain. While techniques exist to measure spatial or temporal properties of these networks, it remains a significant challenge to resolve the neural dynamics with subcellular spatial resolution. In this work we consider a fundamentally new form of wide-field imaging for neuronal networks based on the nanoscale magnetic field sensing properties of optically active spins in a diamond substrate. We analyse the sensitivity of the system to the magnetic field generated by an axon transmembrane potential and confirm these predictions experimentally using electronically-generated neuron signals. By numerical simulation of the time dependent transmembrane potential of a morphologically reconstructed hippocampal CA1 pyramidal neuron, we show that the imaging system is capable of imaging planar neuron activity non-invasively at millisecond temporal resolution and micron spatial resolution over wide-fields.