Breaking reflection symmetry: evolving long dynamical cycles in Boolean systems.

In interacting dynamical systems, specific local interaction rules for system components give rise to diverse and complex global dynamics. Long dynamical cycles are a key feature of many natural interacting systems, especially in biology. Examples of dynamical cycles range from circadian rhythms regulating sleep to cell cycles regulating reproductive behavior. Despite the crucial role of cycles in nature, the properties of network structure that give rise to cycles still need to be better understood. Here, we use a Boolean interaction network model to study the relationships between network structure and cyclic dynamics. We identify particular structural motifs that support cycles, and other motifs that suppress them. More generally, we show that the presence of dynamical reflection symmetry in the interaction network enhances cyclic behavior. In simulating an artificial evolutionary process, we find that motifs that break reflection symmetry are discarded. We further show that dynamical reflection symmetries are over-represented in Boolean models of natural biological systems. Altogether, our results demonstrate a link between symmetry and functionality for interacting dynamical systems, and they provide evidence for symmetry's causal role in evolving dynamical functionality.

Red Emission from Copper-Vacancy Color Centers in Zinc Sulfide Colloidal Nanocrystals.

Copper-doped zinc sulfide (ZnS:Cu) exhibits down-conversion luminescence in the UV, visible, and IR regions of the electromagnetic spectrum; the visible red, green, and blue emission is referred to as R-Cu, G-Cu, and B-Cu, respectively. The sub-bandgap emission arises from optical transitions between localized electronic states created by point defects, making ZnS:Cu a prolific phosphor material and an intriguing candidate material for quantum information science, where point defects excel as single-photon sources and spin qubits. Colloidal nanocrystals (NCs) of ZnS:Cu are particularly interesting as hosts for the creation, isolation, and measurement of quantum defects, since their size, composition, and surface chemistry can be precisely tailored for biosensing and optoelectronic applications. Here, we present a method for synthesizing colloidal ZnS:Cu NCs that emit primarily R-Cu, which has been proposed to arise from the CuZn-VS complex, an impurity-vacancy point defect structure analogous to well-known quantum defects in other materials that produce favorable optical and spin dynamics. First-principles calculations confirm the thermodynamic stability and electronic structure of CuZn-VS. Temperature- and time-dependent optical properties of ZnS:Cu NCs show blueshifting luminescence and an anomalous plateau in the intensity dependence as temperature is increased from 19 K to 290 K, for which we propose an empirical dynamical model based on thermally activated coupling between two manifolds of states inside the ZnS bandgap. Understanding of R-Cu emission dynamics, combined with a controlled synthesis method for obtaining R-Cu centers in colloidal NC hosts, will greatly facilitate the development of CuZn-VS and related complexes as quantum point defects in ZnS.

Template-Assisted Self-Assembly of Fluorescent Nanodiamonds for Scalable Quantum Technologies.

Milled nanodiamonds containing nitrogen-vacancy (NV) centers are nanoscale quantum sensors that form colloidal dispersions. However, variations in their size, shape, and surface chemistry limit the ability to position individual nanodiamonds and statistically study properties that affect their optical and quantum characteristics. Here, we present a scalable strategy to form ordered arrays of nanodiamonds using capillary-driven, template-assisted self-assembly. We demonstrate the precise spatial arrangement of isolated nanodiamonds with diameters below 50 nm across millimeter-scale areas. Measurements of over 200 assembled nanodiamonds yield a statistical understanding of their structural, optical, and quantum properties. The NV centers' spin and charge properties are uncorrelated with nanodiamond size but rather are consistent with heterogeneity in their nanoscale environment.

Direct Imaging of Antiferromagnetic Domains and Anomalous Layer-Dependent Mirror Symmetry Breaking in Atomically Thin MnPS_{3}.

We have developed a sensitive cryogenic second-harmonic generation microscopy to study a van der Waals antiferromagnet MnPS_{3}. We find that long-range Néel antiferromagnetic order develops from the bulk crystal down to the bilayer, while it is absent in the monolayer. Before entering the long-range antiferromagnetic ordered phase in all samples, an upturn of the second harmonic generation below 200 K indicates the formation of the short-range order and magnetoelastic coupling. We also directly image the two antiphase (180°) antiferromagnetic domains and thermally induced domain switching down to bilayer. An anomalous mirror symmetry breaking shows up in samples thinner than ten layers for the temperature both above and below the Néel temperature, which indicates a structural change in few-layer samples. Minimal change of the second harmonic generation polar patterns in strain tuning experiments indicate that the symmetry crossover at ten layers is most likely an intrinsic property of MnPS_{3} instead of an extrinsic origin of substrate-induced strain. Our results show that second harmonic generation microscopy is a direct tool for studying antiferromagnetic domains in atomically thin materials, and opens a new way to study two-dimensional antiferromagnets.

Colloidal Quantum Dots as Platforms for Quantum Information Science.

Colloidal quantum dots (QDs) are nanoscale semiconductor crystals with surface ligands that enable their dispersion in solvents. Quantum confinement effects facilitate wave function engineering to sculpt the spatial distribution of charge and spin states and thus the energy and dynamics of QD optical transitions. Colloidal QDs can be integrated in devices using solution-based assembly methods to position single QDs and to create ordered QD arrays. Here, we describe the synthesis, assembly, and photophysical properties of colloidal QDs that have captured scientific imagination and have been harnessed in optical applications. We focus especially on the current understanding of their quantum coherent effects and opportunities to exploit QDs as platforms for quantum information science. Freedom in QD design to isolate and control the quantum mechanical properties of charge, spin, and light presents various approaches to create systems with robust, addressable quantum states. We consider the attributes of QDs for optically addressable qubits in emerging quantum computation, sensing, simulation, and communication technologies, e.g., as robust sources of indistinguishable, single photons that can be integrated into photonic structures to amplify, direct, and tune their emission or as hosts for isolated, coherent spin states that can be coupled to light or to other spins in QD arrays.

Dangling Bonds in Hexagonal Boron Nitride as Single-Photon Emitters.

Hexagonal boron nitride has been found to host color centers that exhibit single-photon emission, but the microscopic origin of these emitters is unknown. We propose boron dangling bonds as the likely source of the observed single-photon emission around 2 eV. An optical transition where an electron is excited from a doubly occupied boron dangling bond to a localized B p_{z} state gives rise to a zero-phonon line of 2.06 eV and emission with a Huang-Rhys factor of 2.3. This transition is linearly polarized with the absorptive and emissive dipole aligned. Because of the energetic position of the states within the band gap, indirect excitation through the conduction band will occur for sufficiently large excitation energies, leading to the misalignment of the absorptive and emissive dipoles seen in experiment. Our calculations predict a singlet ground state and the existence of a metastable triplet state, in agreement with experiment.

A monolithic immersion metalens for imaging solid-state quantum emitters.

Quantum emitters such as the diamond nitrogen-vacancy (NV) center are the basis for a wide range of quantum technologies. However, refraction and reflections at material interfaces impede photon collection, and the emitters' atomic scale necessitates the use of free space optical measurement setups that prevent packaging of quantum devices. To overcome these limitations, we design and fabricate a metasurface composed of nanoscale diamond pillars that acts as an immersion lens to collect and collimate the emission of an individual NV center. The metalens exhibits a numerical aperture greater than 1.0, enabling efficient fiber-coupling of quantum emitters. This flexible design will lead to the miniaturization of quantum devices in a wide range of host materials and the development of metasurfaces that shape single-photon emission for coupling to optical cavities or route photons based on their quantum state.

Magnetic-field-dependent quantum emission in hexagonal boron nitride at room temperature.

Optically addressable spins associated with defects in wide-bandgap semiconductors are versatile platforms for quantum information processing and nanoscale sensing, where spin-dependent inter-system crossing transitions facilitate optical spin initialization and readout. Recently, the van der Waals material hexagonal boron nitride (h-BN) has emerged as a robust host for quantum emitters, promising efficient photon extraction and atom-scale engineering, but observations of spin-related effects have remained thus far elusive. Here, we report room-temperature observations of strongly anisotropic photoluminescence patterns as a function of applied magnetic field for select quantum emitters in h-BN. Field-dependent variations in the steady-state photoluminescence and photon emission statistics are consistent with an electronic model featuring a spin-dependent inter-system crossing between triplet and singlet manifolds, indicating that optically-addressable spin defects are present in h-BN.

Spin Readout Techniques of the Nitrogen-Vacancy Center in Diamond.

The diamond nitrogen-vacancy (NV) center is a leading platform for quantum information science due to its optical addressability and room-temperature spin coherence. However, measurements of the NV center's spin state typically require averaging over many cycles to overcome noise. Here, we review several approaches to improve the readout performance and highlight future avenues of research that could enable single-shot electron-spin readout at room temperature.

Amplified Sensitivity of Nitrogen-Vacancy Spins in Nanodiamonds Using All-Optical Charge Readout.

Nanodiamonds containing nitrogen-vacancy (NV) centers offer a versatile platform for sensing applications spanning from nanomagnetism to in vivo monitoring of cellular processes. In many cases, however, weak optical signals and poor contrast demand long acquisition times that prevent the measurement of environmental dynamics. Here, we demonstrate the ability to perform fast, high-contrast optical measurements of charge distributions in ensembles of NV centers in nanodiamonds and use the technique to improve the spin-readout signal-to-noise ratio through spin-to-charge conversion. A study of 38 nanodiamonds with sizes ranging between 20 and 70 nm, each hosting a small ensemble of NV centers, uncovers complex, multiple time scale dynamics due to radiative and nonradiative ionization and recombination processes. Nonetheless, the NV-containing nanodiamonds universally exhibit charge-dependent photoluminescence contrasts and the potential for enhanced spin readout using spin-to-charge conversion. We use the technique to speed up a T1 relaxometry measurement by a factor of 5.

Optical Signatures of Quantum Emitters in Suspended Hexagonal Boron Nitride.

Hexagonal boron nitride (h-BN) is rapidly emerging as an attractive material for solid-state quantum engineering. Analogously to three-dimensional wide-band-gap semiconductors such as diamond, h-BN hosts isolated defects exhibiting visible fluorescence at room temperature, and the ability to position such quantum emitters within a two-dimensional material promises breakthrough advances in quantum sensing, photonics, and other quantum technologies. Critical to such applications is an understanding of the physics underlying h-BN's quantum emission. We report the creation and characterization of visible single-photon sources in suspended, single-crystal, h-BN films. With substrate interactions eliminated, we study the spectral, temporal, and spatial characteristics of the defects' optical emission. Theoretical analysis of the defects' spectra reveals similarities in vibronic coupling to h-BN phonon modes despite widely varying fluorescence wavelengths, and a statistical analysis of the polarized emission from many emitters throughout the same single-crystal flake uncovers a weak correlation between the optical dipole orientations of some defects and h-BN's primitive crystallographic axes, despite a clear misalignment for other dipoles. These measurements constrain possible defect models and, moreover, suggest that several classes of emitters can exist simultaneously throughout free-standing h-BN, whether they be different defects, different charge states of the same defect, or the result of strong local perturbations.

Ultrafast optical control of orbital and spin dynamics in a solid-state defect.

Atom-scale defects in semiconductors are promising building blocks for quantum devices, but our understanding of their material-dependent electronic structure, optical interactions, and dissipation mechanisms is lacking. Using picosecond resonant pulses of light, we study the coherent orbital and spin dynamics of a single nitrogen-vacancy center in diamond over time scales spanning six orders of magnitude. We develop a time-domain quantum tomography technique to precisely map the defect's excited-state Hamiltonian and exploit the excited-state dynamics to control its ground-state spin with optical pulses alone. These techniques generalize to other optically addressable nanoscale spin systems and serve as powerful tools to characterize and control spin qubits for future applications in quantum technology.

All-optical control of a solid-state spin using coherent dark states.

The study of individual quantum systems in solids, for use as quantum bits (qubits) and probes of decoherence, requires protocols for their initialization, unitary manipulation, and readout. In many solid-state quantum systems, these operations rely on disparate techniques that can vary widely depending on the particular qubit structure. One such qubit, the nitrogen-vacancy (NV) center spin in diamond, can be initialized and read out through its special spin-selective intersystem crossing, while microwave electron spin resonance techniques provide unitary spin rotations. Instead, we demonstrate an alternative, fully optical approach to these control protocols in an NV center that does not rely on its intersystem crossing. By tuning an NV center to an excited-state spin anticrossing at cryogenic temperatures, we use coherent population trapping and stimulated Raman techniques to realize initialization, readout, and unitary manipulation of a single spin. Each of these techniques can be performed directly along any arbitrarily chosen quantum basis, removing the need for extra control steps to map the spin to and from a preferred basis. Combining these protocols, we perform measurements of the NV center's spin coherence, a demonstration of this full optical control. Consisting solely of optical pulses, these techniques enable control within a smaller footprint and within photonic networks. Likewise, this unified approach obviates the need for both electron spin resonance manipulation and spin addressability through the intersystem crossing. This method could therefore be applied to a wide range of potential solid-state qubits, including those which currently lack a means to be addressed.

Quantum spintronics: engineering and manipulating atom-like spins in semiconductors.

The past decade has seen remarkable progress in isolating and controlling quantum coherence using charges and spins in semiconductors. Quantum control has been established at room temperature, and electron spin coherence times now exceed several seconds, a nine-order-of-magnitude increase in coherence compared with the first semiconductor qubits. These coherence times rival those traditionally found only in atomic systems, ushering in a new era of ultracoherent spintronics. We review recent advances in quantum measurements, coherent control, and the generation of entangled states and describe some of the challenges that remain for processing quantum information with spins in semiconductors.