We explore the dynamics of artificial one- and two-dimensional Ising-like quantum antiferromagnets with different lattice geometries by using a Rydberg quantum simulator of up to 36 spins in which we dynamically tune the parameters of the Hamiltonian. We observe, in a region in parameter space, the onset of antiferromagnetic (AF) ordering, albeit with only finite-range correlations. We study systematically the influence of the ramp speeds on the correlations and their growth in time. We observe a delay in their buildup associated to the finite speed of propagation of correlations in a system with short-range interactions. We obtain a good agreement between experimental data and numerical simulations, taking into account experimental imperfections measured at the single-particle level. Finally, we develop an analytical model, based on a short-time expansion of the evolution operator, which captures the observed spatial structure of the correlations, and their buildup in time.

Simulating the real-time evolution of quantum spin systems far out of equilibrium poses a major theoretical challenge, especially in more than one dimension. We experimentally explore quench dynamics in a two-dimensional Ising spin system with transverse and longitudinal fields. We realize the system with a near unit-occupancy atomic array of over 200 atoms obtained by loading a spin-polarized band insulator of fermionic lithium into an optical lattice and induce short-range interactions by direct excitation to a low-lying Rydberg state. Using site-resolved microscopy, we probe antiferromagnetic correlations in the system after a sudden quench from a paramagnetic state and compare our measurements to numerical calculations using state-of-the-art techniques. We achieve many-body states with longer-range antiferromagnetic correlations by implementing a near-adiabatic quench of the longitudinal field and study the buildup of correlations as we vary the rate with which we change the field.

The complex structure of the valence band in many semiconductors leads to multifaceted and unusual properties for spin-$3/2$ hole systems compared to common spin-$1/2$ electron systems. In particular, two-dimensional hole systems show a highly anisotropic Zeeman interaction. We have investigated this anisotropy in $\mathrm{GaAs}/\mathrm{AlAs}$ quantum well structures both experimentally and theoretically. By performing time-resolved Kerr rotation measurements, we found a nondiagonal tensor $\mathit{g}$ that manifests itself in unusual precessional motion, as well as distinct dependencies of hole-spin dynamics on the direction of the magnetic field $\mathit{B}$. We quantify the individual components of the tensor $\mathit{g}$ for [113]-, [111]-, and [110]-grown samples. We complement the experiments by a comprehensive theoretical study of Zeeman coupling in in-plane and out-of-plane fields $\mathit{B}$. To this end, we develop a detailed multiband theory for the tensor $\mathit{g}$. Using perturbation theory, we derive transparent analytical expressions for the components of the tensor $\mathit{g}$ that we complement with accurate numerical calculations based on our theoretical framework. We obtain very good agreement between experiment and theory. Our study demonstrates that the tensor $\mathit{g}$ is neither symmetric nor antisymmetric. Opposite off-diagonal components can differ in size by up to an order of magnitude. The tensor $\mathit{g}$ encodes not only the Zeeman energy splitting but also the direction of the axis about which the spins precess in the external field $\mathit{B}$. In general, this axis is not aligned with $\mathit{B}$. Hence our study extends the general concept of optical orientation to the regime of nontrivial Zeeman coupling.

The control of the electron spin by external means is a key issue for spintronic devices. Using spin- and angle-resolved photoemission spectroscopy (SARPES) with three-dimensional spin detection, we demonstrate operando electrostatic spin manipulation in ferroelectric $\alpha \text{−}\mathrm{GeTe}$ and multiferroic ${\mathrm{Ge}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$. We demonstrate for the first time electrostatic spin manipulation in Rashba semiconductors due to ferroelectric polarization reversal. Additionally, we are also able to follow the switching pathway in detail. In multiferroic ${\mathrm{Ge}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ operando SARPES reveals switching of the perpendicular spin component due to electric-field-induced magnetization reversal. This provides firm evidence of magnetoelectric coupling which opens up functionality with a multitude of spin-switching paths in which the magnetic and electric order parameters are coupled through ferroelastic relaxation paths. This work thus provides a new type of magnetoelectric switching intertwined with Rashba-Zeeman splitting in a multiferroic system.

The most intriguing properties of non-Hermitian systems are found near the exceptional points (EPs) at which the Hamiltonian matrix becomes defective. Because of the complex topological structure of the energy Riemann surfaces close to an EP and the breakdown of the adiabatic theorem due to non-Hermiticity, the state evolution in non-Hermitian systems is much more complex than that in Hermitian systems. For example, recent experimental work [Doppler et al., Nature (London) 537, 76 (2016)] demonstrated that dynamically encircling an EP can lead to chiral behaviors; i.e., encircling an EP in different directions results in different output states. Here, we propose a coupled ferromagnetic waveguide system that carries two EPs and design an experimental setup in which the trajectory of state evolution can be controlled in situ using a tunable external field, allowing us to dynamically encircle zero, one, or even two EPs experimentally. The tunability allows us to control the trajectory of encircling in the parameter space, including the size of the encircling loop and the starting/end point. We discovered that whether or not the dynamics is chiral actually depends on the starting point of the loop. In particular, dynamically encircling an EP with a starting point in the parity-time-broken phase results in nonchiral behaviors such that the output state is the same no matter which direction the encircling takes. The proposed system is a useful platform to explore the topology of energy surfaces and the dynamics of state evolution in non-Hermitian systems and will likely find applications in mode switching controlled with external parameters.

We discuss the characterization of the polarization for insulators under the periodic boundary condition in terms of the Berry phase, clarifying confusing subtleties. For band insulators, the Berry phase can be formulated in terms of the Bloch function in momentum space. More generally, in the presence of interactions or disorders, one can instead use the many-body ground state as a function of the flux piercing the ring. However, the definition of the Bloch function and the way of describing the flux are not unique. As a result, the value of the Berry phase and its behavior depend on how precisely it is defined. In particular, identifying the Berry phase as a polarization, its change represents a polarization current, which also depends on the definition. We demonstrate this by elucidating mutual relations among different definitions of the Berry phase and showing that they correspond to currents measured differently in real space. Despite the nonuniqueness of the polarization current, the total charge transported during a Thouless pumping process is independent of the definition, reflecting its topological nature.

The main thread that links classical thermodynamics and the thermodynamics of small quantum systems is the celebrated Clausius inequality form of the second law. However, its application to small quantum systems suffers from two cardinal problems. (i) The Clausius inequality does not hold when the system and environment are initially correlated—a commonly encountered scenario in microscopic setups. (ii) In some other cases, the Clausius inequality does not provide any useful information (e.g., in dephasing scenarios). We address these deficiencies by developing the notion of global passivity and employing it as a tool for deriving thermodynamic inequalities on observables. For initially uncorrelated thermal environments the global passivity framework recovers the Clausius inequality. More generally, global passivity provides an extension of the Clausius inequality that holds even in the presences of strong initial system-environment correlations. Crucially, the present framework provides additional thermodynamic bounds on expectation values. To illustrate the role of the additional bounds, we use them to detect unaccounted heat leaks and weak feedback operations (“Maxwell demons”) that the Clausius inequality cannot detect. In addition, it is shown that global passivity can put practical upper and lower bounds on the buildup of system-environment correlations for dephasing interactions. Our findings are highly relevant for experiments in various systems such as ion traps, superconducting circuits, atoms in optical cavities, and more.

Group-IV vacancy color centers in diamond are fast emerging qubits that can be harnessed in quantum communication and sensor applications. There is an immediate quest for understanding their magneto-optical properties, in order to select the appropriate qubits for varying needs of particular quantum applications. Here we present results from cutting-edge ab initio calculations about the charge state stability, zero-phonon-line energies, and spin-orbit and electron-phonon couplings for group-IV vacancy color centers. Based on the analysis of our results, we develop a novel spin Hamiltonian for these qubits which incorporates the interaction of the electron spin and orbit coupled with phonons beyond perturbation theory. Our results are in good agreement with previous data and predict a new defect for qubit applications with thermally initialized ground state spin and long spin coherence time.

A key goal of quantum chaos is to establish a relationship between widely observed universal spectral fluctuations of clean quantum systems and random matrix theory (RMT). Most prominent features of such RMT behavior with respect to a random spectrum, both encompassed in the spectral pair correlation function, are statistical suppression of small level spacings (correlation hole) and enhanced stiffness of the spectrum at large spectral ranges. For single-particle systems with fully chaotic classical counterparts, the problem has been partly solved by Berry [Proc. R. Soc. A 400, 229 (1985)] within the so-called diagonal approximation of semiclassical periodic-orbit sums, while the derivation of the full RMT spectral form factor $K(t)$ (Fourier transform of the spectral pair correlation function) from semiclassics has been completed by Müller et al. [Phys. Rev. Lett. 93, 014103 (2004)]. In recent years, the questions of long-time dynamics at high energies, for which the full many-body energy spectrum becomes relevant, are coming to the forefront even for simple many-body quantum systems, such as locally interacting spin chains. Such systems display two universal types of behaviour which are termed the “many-body localized phase” and “ergodic phase.” In the ergodic phase, the spectral fluctuations are excellently described by RMT, even for very simple interactions and in the absence of any external source of disorder. Here we provide a clear theoretical explanation for these observations. We compute $K(t)$ in the leading two orders in $t$ and show its agreement with RMT for nonintegrable, time-reversal invariant many-body systems without classical counterparts, a generic example of which are Ising spin-$1/2$ models in a periodically kicking transverse field. In particular, we relate $K(t)$ to partition functions of a class of twisted classical Ising models on a ring of size $t$; hence, the leading-order RMT behavior $K(t)\simeq 2t$ is a consequence of translation and reflection symmetry of the Ising partition function.

Streaking of photoelectrons with optical lasers has been widely used for temporal characterization of attosecond extreme ultraviolet pulses. Recently, this technique has been adapted to characterize femtosecond x-ray pulses in free-electron lasers with the streaking imprinted by far-infrared and terahertz (THz) pulses. Here, we report successful implementation of THz streaking for time stamping of an ultrashort relativistic electron beam, whose energy is several orders of magnitude higher than photoelectrons. Such an ability is especially important for MeV ultrafast electron diffraction (UED) applications, where electron beams with a few femtosecond pulse width may be obtained with longitudinal compression, while the arrival time may fluctuate at a much larger timescale. Using this laser-driven THz streaking technique, the arrival time of an ultrashort electron beam with a 6-fs (rms) pulse width has been determined with 1.5-fs (rms) accuracy. Furthermore, we have proposed and demonstrated a noninvasive method for correction of the timing jitter with femtosecond accuracy through measurement of the compressed beam energy, which may allow one to advance UED towards a sub-10-fs frontier, far beyond the approximate 100-fs (rms) jitter.

Verification is a task to check whether a given quantum state is close to an ideal state or not. In this paper, we show that a variety of many-qubit quantum states can be verified with only sequential single-qubit measurements of Pauli operators. First, we introduce a protocol for verifying ground states of Hamiltonians. We next explain how to verify quantum states generated by a certain class of quantum circuits. We finally propose an adaptive test of stabilizers that enables the verification of all polynomial-time-generated hypergraph states, which include output states of the Bremner-Montanaro-Shepherd-type instantaneous quantum polynomial time (IQP) circuits. Importantly, we do not make any assumption that the identically and independently distributed copies of the same states are given: Our protocols work even if some highly complicated entanglement is created among copies in any artificial way. As applications, we consider the verification of the quantum computational supremacy demonstration with IQP models, and verifiable blind quantum computing.

Quantum systems can be exquisite sensors thanks to their sensitivity to external perturbations. This same characteristic also makes them fragile to external noise. Quantum control can tackle the challenge of protecting a quantum sensor from environmental noise, while strongly coupling the sensor with the field to be measured. As the compromise between these two conflicting requirements does not always have an intuitive solution, optimal control based on a numerical search could prove very effective. Here, we adapt optimal control theory to the quantum-sensing scenario by introducing a cost function that, unlike the usual fidelity of operation, correctly takes into account both the field to be measured and the environmental noise. We experimentally implement this novel control paradigm using a nitrogen vacancy center in diamond, finding improved sensitivity to a broad set of time-varying fields. The demonstrated robustness and efficiency of the numerical optimization, as well as the sensitivity advantage it bestows, will prove beneficial to many quantum-sensing applications.

We design a logical qubit consisting of a linear array of quantum dots, we analyze error correction for this linear architecture, and we propose a sequence of experiments to demonstrate components of the logical qubit on near-term devices. To avoid the difficulty of fully controlling a two-dimensional array of dots, we adapt spin control and error correction to a one-dimensional line of silicon quantum dots. Control speed and efficiency are maintained via a scheme in which electron spin states are controlled globally using broadband microwave pulses for magnetic resonance, while two-qubit gates are provided by local electrical control of the exchange interaction between neighboring dots. Error correction with two-, three-, and four-qubit codes is adapted to a linear chain of qubits with nearest-neighbor gates. We estimate an error correction threshold of ${10}^{-4}$. Furthermore, we describe a sequence of experiments to validate the methods on near-term devices starting from four coupled dots.

Spin-orbit-coupled cold-atom systems, governed by Hamiltonians that contain quadratic kinetic energy terms typical for a particle’s motion in the usual Schrödinger equation and linear kinetic energy terms typical for a particle’s motion in the usual Dirac equation, have attracted a great deal of attention recently since they provide an alternative route for realizing fractional quantum Hall physics, topological insulators, and spintronics physics. The present work focuses on the three-boson system in the presence of 1D spin-orbit coupling, which is most relevant to ongoing cold-atom experiments. In the absence of spin-orbit-coupling terms, the three-boson system exhibits the Efimov effect: the entire energy spectrum is uniquely determined by the $s$-wave scattering length and a single three-body parameter; i.e., using one of the energy levels as input, the other energy levels can be obtained via Efimov’s radial scaling law, which is intimately tied to a discrete scaling symmetry. It is demonstrated that the discrete scaling symmetry persists in the presence of 1D spin-orbit coupling, implying the validity of a generalized radial scaling law in five-dimensional space. The dependence of the energy levels on the scattering length, spin-orbit-coupling parameters, and center-of-mass momentum is discussed. It is conjectured that three-body systems with other types of spin-orbit-coupling terms are also governed by generalized radial scaling laws, provided the system exhibits the Efimov effect in the absence of spin-orbit coupling.

We use inelastic neutron scattering to study acoustic phonons and spin excitations in single crystals of NaFeAs, a parent compound of iron-pnictide superconductors. NaFeAs exhibits a tetragonal-to-orthorhombic structural transition at $T_s\approx 58\mathrm{K}$ and a collinear antiferromagnetic order at $T_N\approx 45\mathrm{K}$. While longitudinal and out-of-plane transverse acoustic phonons behave as expected, the in-plane transverse acoustic phonons reveal considerable softening on cooling to $T_s$ and then harden on approaching $T_N$ before saturating below $T_N$. In addition, we find that spin-spin correlation lengths of low-energy magnetic excitations within the FeAs layer and along the $c$ axis increase dramatically below $T_s$ and show a weak anomaly across $T_N$. These results suggest that the electronic nematic phase present in the paramagnetic tetragonal phase is closely associated with dynamic spin-lattice coupling, possibly arising from the one-phonon–two-magnon mechanism.

The pentatellurides ${\mathrm{ZrTe}}_5$ and ${\mathrm{HfTe}}_5$ are layered compounds with one-dimensional transition-metal chains that show a not-yet-understood temperature-dependent transition in transport properties as well as recently discovered properties suggesting topological semimetallic behavior. Here, we report magnetotransport properties for two kinds of ${\mathrm{ZrTe}}_5$ single crystals grown with the chemical vapor transport (CVT) and the flux method (Flux), respectively. They show distinct transport properties at zero field: The CVT crystal displays a metallic behavior with a pronounced resistance peak and a sudden sign reversal in thermopower at approximately 130 K, consistent with previous observations of the electronic transition; in striking contrast, the Flux crystal exhibits a semiconducting-like behavior at low temperatures and a positive thermopower over the whole temperature range. For both samples, strong effects on the transport properties are observed when the magnetic field is applied along the orthorhombic $b$ and $c$ axes, i.e., perpendicular to the chain direction. Refinements on the single-crystal x-ray diffraction and the measurements of energy dispersive spectroscopy reveal the presence of noticeable Te vacancies in the CVT samples, while the Flux samples are close to the stoichiometry. Analyses on the magnetotransport properties confirm that the carrier densities of the CVT sample are about two orders higher than those of the Flux sample. Our results thus indicate that the widely observed anomalous transport behaviors in pentatellurides actually take place in the Te-deficient samples. For the stoichiometric pentatellurides, our electronic structure calculations show narrow-gap semiconducting behavior, with different transport anisotropies for holes and electrons. For the degenerately doped $n$-type samples, our transport calculations can result in a resistivity peak and crossover in thermopower from negative to positive at temperatures close to those observed experimentally due to a combination of bipolar effects and different anisotropies of electrons and holes. Our present work resolves the long-standing puzzle regarding the anomalous transport behaviors of pentatellurides, as well as the electronic structure in favor of a semiconducting state.

To implement fault-tolerant quantum computation with continuous variables, the Gottesman-Kitaev-Preskill (GKP) qubit has been recognized as an important technological element. However, it is still challenging to experimentally generate the GKP qubit with the required squeezing level, 14.8 dB, of the existing fault-tolerant quantum computation. To reduce this requirement, we propose a high-threshold fault-tolerant quantum computation with GKP qubits using topologically protected measurement-based quantum computation with the surface code. By harnessing analog information contained in the GKP qubits, we apply analog quantum error correction to the surface code. Furthermore, we develop a method to prevent the squeezing level from decreasing during the construction of the large-scale cluster states for the topologically protected, measurement-based, quantum computation. We numerically show that the required squeezing level can be relaxed to less than 10 dB, which is within the reach of the current experimental technology. Hence, this work can considerably alleviate this experimental requirement and take a step closer to the realization of large-scale quantum computation.

We explore the physics of highly frustrated magnets in confined geometries, focusing on the Coulomb phase of pyrochlore spin ices. As a specific example, we investigate thin films of nearest-neighbor spin ice, using a combination of analytic large-$N$ techniques and Monte Carlo simulations. In the simplest film geometry, with surfaces perpendicular to the [001] crystallographic direction, we observe pinch points in the spin-spin correlations characteristic of a two-dimensional Coulomb phase. We then consider the consequences of crystal symmetry breaking on the surfaces of the film through the inclusion of orphan bonds. We find that when these bonds are ferromagnetic, the Coulomb phase is destroyed by the presence of fluctuating surface magnetic charges, leading to a classical $Z_2$ spin liquid. Building on this understanding, we discuss other film geometries with surfaces perpendicular to the [110] or the [111] direction. We generically predict the appearance of surface magnetic charges and discuss their implications for the physics of such films, including the possibility of an unusual $Z_3$ classical spin liquid. Finally, we comment on open questions and promising avenues for future research.

We introduce the “displacemon” electromechanical architecture that comprises a vibrating nanobeam, e.g., a carbon nanotube, flux coupled to a superconducting qubit. This platform can achieve strong and even ultrastrong coupling, enabling a variety of quantum protocols. We use this system to describe a protocol for generating and measuring quantum interference between trajectories of a nanomechanical resonator. The scheme uses a sequence of qubit manipulations and measurements to cool the resonator, to apply two effective diffraction gratings, and then to measure the resulting interference pattern. We demonstrate the feasibility of generating a spatially distinct quantum superposition state of motion containing more than $10^6$ nucleons using a vibrating nanotube acting as a junction in this new superconducting qubit configuration.

Koopmans-compliant functionals have been shown to provide accurate spectral properties for molecular systems; this accuracy is driven by the generalized linearization condition imposed on each charged excitation, i.e., on changing the occupation of any orbital in the system, while accounting for screening and relaxation from all other electrons. In this work, we discuss the theoretical formulation and the practical implementation of this formalism to the case of extended systems, where a third condition, the localization of Koopmans’s orbitals, proves crucial to reach seamlessly the thermodynamic limit. We illustrate the formalism by first studying one-dimensional molecular systems of increasing length. Then, we consider the band gaps of 30 paradigmatic solid-state test cases, for which accurate experimental and computational results are available. The results are found to be comparable with the state of the art in many-body perturbation theory, notably using just a functional formulation for spectral properties and the generalized-gradient approximation for the exchange and correlation functional.