Coherent control by means of tailored excitation is a key to versatile experimental schemes for spectroscopic investigation and technological utilization of quantum systems. Here we study a quantum system which consists of a coupled electron-muon spin state, i.e., muonium, a light isotope of hydrogen. We demonstrate the most fundamental coherent control techniques by microwave excitation of spin transitions, namely driven Rabi oscillations and Ramsey fringes upon free evolution. Unprecedented performance is achieved by the microwave hardware devised for these experiments, which enables coherent spin manipulation of individual, isolated, muonium centers. For muonium formed in ${\mathrm{SiO}}_2$ with strong electron-muon hyperfine interaction, a virtually undamped free precession signal is observed up to a $3.5\mu \mathrm{s}$ time window. For muonium formed in Si with weak and anisotropic hyperfine interaction, a strong drive at the multi-quantum transition decouples the muonium center from its magnetic environment formed by the bath of ${}^{29}\mathrm{Si}$ nuclear spins at natural abundance. We expect that these capabilities will provide a powerful tool to investigate the effect of the environment on isolated coupled spins, uncover the details of coupled electron-muon systems in matter and validate quantum electrodynamics in the context of muonium spectroscopy.

Nonlinear dynamics are studied in diverse fields as climate models, avalanches, nanomechanical sensors, optical frequency converters, and electrical quantum amplifiers. A widely studied nonlinear model is the so-called Duffing (or Kerr) resonator, which features a quartic potential term. Two hallmark properties of this model are (i) a shift of a system's resonance frequency as a function of the driving strength, and (ii) monostable or bistable responses, depending on the drive strength and detuning from resonance. Together, these two properties can lead to dynamical phase transitions when several drives are applied simultaneously. Here, we report an experimental and theoretical study of a driven-dissipative nonlinear system with two detuned drives. We observe distinct response regimes characterized by the system's ability to follow the system's time-dependent vector-flow topology. Our work provides an example for understanding dynamical phase transitions in out-of-equilibrium nonlinear systems.

The polarization states of terahertz (THz) radiation generated in a photoionized gas driven by intense two- or multi-frequency fields with locally controlled polarization are studied. We reveal a universal property of the resulting THz waveforms: the ellipticity of their polarization state increases linearly with frequency. This “linear chirp of ellipticity” makes plasma-based THz generation unique among other THz sources. However, it also imposes some constraints on the polarization properties of the generated THz radiation. We derive a general expression for the THz ellipticity and demonstrate how the polarization states of the generated THz waveforms can be manipulated and controlled by the polarization of the pump pulses.

We investigate the hollowing transition of a shell-shaped Bose-Einstein condensate using collective excitations. The shell is created using an immiscible dual-species Bose-Einstein condensate mixture, with its hollowness controlled by tuning the repulsive interspecies interaction via a Feshbach resonance. Our results reveal two distinct monopole modes in which the two condensates oscillate either in phase or out of phase. The spectrum of the out-of-phase mode exhibits a nonmonotonic dependence on the interspecies interaction, providing a clear signature of the topology change from a filled to a hollow condensate. Furthermore, we find that the critical point of the hollowing transition depends strongly on the number ratio of the two species. Our findings provide a detailed understanding of the topology change in shell-shaped quantum gases and pave the way for future study of quantum many-body phenomena in curved spaces.

We diagonalize the quantum two-dimensional spin-1/2 Heisenberg model with Dzyaloshinsky-Moriya interaction (DMI) by applying the variational quantum eigensolver, running on a quantum-computer simulator, which turns out to be a more efficient approach than a classical direct diagonalization for systems with more than 17 sites. The calculated external-magnetic-field dependence of the total energy, of the magnetization, and of the topological charge exhibits a distinctive discontinuity which hints at the existence of zero-temperature magnetic- skyrmion-like structures at the quantum level, controlled by the combination of the exchange-coupling and the DMI parameters. The potentially measurable jump in the magnetization upon changing the field indicates the investigated objects are stable enough for eventual applications in spintronics or even as information carriers.

There are different ways of measuring diversity in complex systems. In particular, in language, lexical diversity is characterized in terms of the type-token ratio and the word entropy. We here investigate both diversity metrics in six massive linguistic data sets in English, Spanish, and Turkish, consisting of books, news articles, and tweets. These gigaword corpora correspond to languages with distinct morphological features and differ in registers and genres, thus constituting a varied testbed for a quantitative approach to lexical diversity. We unveil an empirical functional relation between entropy and type-token ratio of texts of a given corpus and language, which is a consequence of the statistical laws observed in natural language. Further, in the limit of large text lengths we find an analytical expression for this relation relying on both Zipf and Heaps laws that agrees with our empirical findings.

We show that absorbing state phase transitions where the absorbing state itself exhibits long-range phase coherence can lead to critical behavior distinct from directed percolation. To do this, we investigate a simple, purely dissipative quantum reaction-diffusion model, which may also be viewed as a dissipative quantum state preparation procedure for the (generalized) $W$ state with errors. The “error” Lindblad jump operators preserve the $W$ state as a dark state, but nonetheless act to decohere the system and induce the phase transition. We find cases where the preparation protocol is either fragile or robust against weak error quantum jump rates and show that local remnants of the coherence persist in the decohering phase. The distinct critical behavior stems from the spreading of coherence throughout the system at the critical point.

Phase reduction is an important tool for studying coupled and driven oscillators. The question of how to generalize phase reduction to stochastic oscillators remains actively debated. In this work, we propose a method to derive a self-contained stochastic phase equation of the form $\mathrm{d}\varphi =a\left(\varphi \right)\mathrm{d}t+\sqrt{2D\left(\varphi \right)}\mathrm{d}W\left(t\right)$ that is valid not only for noise-perturbed limit cycles, but also for noise-induced oscillations. We show that our reduction captures the asymptotic statistics of qualitatively different stochastic oscillators, and use it to infer their phase-response properties.

We propose a new scheme for near-term photonic quantum devices that allows us to increase the expressive power of the quantum models beyond what linear optics can do. This scheme relies upon state injection, a measurement-based technique that can produce states that are more controllable, and solve learning tasks that are believed to be intractable classically. We explain how circuits made of linear optical architectures separated by state injections are well-suited for experimental implementation. In addition, we give theoretical results regarding the evolution of the purity of the resulting states, and we discuss how it impacts the distinguishability of the circuit outputs. Finally, we study a computational subroutine of learning algorithms named probability estimation, and we show that the state injection scheme we propose may offer a potential quantum advantage in a regime that can be more easily achieved than state-of-the-art adaptive techniques. Our analysis offers new possibilities for near-term advantage that rely on overcoming fewer experimental difficulties.

We introduce multiobject operational tasks for measurement incompatibility in the form of multiobject quantum subchannel discrimination and exclusion games with prior information, where a player can simultaneously harness the resources contained within both a quantum state and a set of measurements. We show that any fully or partially resourceful pair of objects is useful for a suitably chosen multiobject subchannel discrimination and exclusion game with prior information. The advantage provided by a fully or partially resourceful object against all possible fully free objects in such a game can be quantified in a multiplicative manner by the resource quantifiers of generalized robustness and the weight of a resource for discrimination and exclusion games, respectively. These results hold for arbitrary properties of quantum states as well as for arbitrary properties of sets of measurements closed under classical pre- and postprocessing and, consequently, include measurement incompatibility as a particular case. We furthermore show that these results are not exclusive to quantum theory, but can also be extended to the realm of general probabilistic theories.

The partial information decomposition (PID) and its extension integrated information decomposition ($\mathrm{\Phi }\mathrm{ID}$) are promising frameworks to investigate information phenomena involving multiple variables. An important limitation of these approaches is the high computational cost involved in their calculation. Here we leverage fundamental algebraic properties of these decompositions to enable a computationally-efficient method to estimate them, which we call the fast Möbius transform. Our approach is based on a formula for estimating the Möbius function that circumvents important computational bottlenecks and can in some cases offer a double-exponential speedup. We showcase the capabilities of this approach by presenting two analyses that would be unfeasible without this method: decomposing the information that neural activity at different frequency bands yields about the brain's macroscopic functional organization and identifying distinctive dynamical properties of the interactions between multiple voices in baroque music. Overall, our proposed approach illuminates the value of algebraic facets of information decomposition and opens the way to a wide range of future analyses.

Quantum machine learning has the potential to computationally outperform classical machine learning, but it is not yet clear whether it will actually be valuable for practical problems. While some artificial scenarios have shown that certain quantum machine learning techniques may be advantageous compared to their classical counterpart, evidence does not yet suggest that quantum machine learning has surpassed conventional approaches in dealing with standard classical datasets, such as the MNIST dataset. In contrast, dealing with quantum data, such as quantum states or circuits, may be the task where we can benefit from quantum methods. Therefore, it is important to develop practically meaningful quantum datasets for which we expect quantum methods to be superior. In this paper, we propose a machine learning task that is likely to soon arise in the real world: clustering and classification of quantum circuits. We provide a dataset of quantum circuits optimized by the variational quantum eigensolver. We utilized six common types of Hamiltonians in condensed matter physics, with a range of 4–20 qubits, and applied ten different ansatz with varying depths (ranging from 3 to 32) to generate a quantum circuit dataset of six distinct classes, each containing 300 samples. We show that this dataset can be easily learned using quantum methods. In particular, we demonstrate a successful classification of our dataset using real four-qubit devices available through IBMQ. By providing a setting and an elementary dataset where quantum machine learning is expected to be beneficial, we hope to encourage and ease the advancement of the field.

We investigate the ergodicity-to-localization transition in interacting fermion systems subjected to a spatially uniform electric field. For that, we employ the recently proposed tensorflow equations (TFE), a type of continuous unitary flow equations. This enables us to iteratively determine an approximate diagonal basis of the quantum many-body system. We present improvements to the method, which achieves good accuracy at small to intermediate interaction strengths, even in the absence of an electric field or disorder. Then, we examine two quantities that reveal the fate of Stark MBL in 1D and 2D. First, we investigate the structure of the resulting basis to determine the crossover between ergodic and localized regimes with respect to electric field strength. Second, we simulate long-time dynamics at infinite temperature. Our results in 1D show a localization transition at nonzero field for finite interaction that vanishes with increasing system size leading to localization at infinitesimally small field even in the presence of interactions. In 2D, we find less clear signatures of localization and strong finite-size effects. We establish that the TFE work accurately up to intermediate times but cannot capture higher order effects in interaction strength that lead to delocalization at longer times in finite-size Stark MBL systems.

We observed magnetocapacitance oscillations in InAs/GaSb quantum wells separated by a $20\mathrm{nm}$ AlSb middle barrier. By realizing independent ohmic contacts for electrons in InAs and holes in the GaSb layer, we found an out-of-plane oscillatory response in capacitance representing the density of states of this system. We were able to tune the charge carrier densities by applying a DC bias voltage, identifying the formation of beating signatures for forward bias. The coexistence of two distinguishable two-dimensional ($2\mathrm{D}$) charge carrier systems of unequal densities was verified. By developing a theory to describe the magnetocapacitance response of the system, we were able to validate that we have an electron-hole bilayer system. The Landau phase diagram presents distinct features originating from the bilayer channel with the additional presence of a $2\mathrm{D}$ electron system at the surface of the InAs layer.

Numerous networked systems feature a structure of nontrivial communities, which often correspond to their functional modules. Such communities have been detected in real-world biological, social, and technological systems, as well as in synthetic models thereof. While much effort has been devoted to developing methods for community detection in traditional networks, the study of community structure in networks with higher-order interactions is still not as extensively explored. In this article, we introduce a formalism for the hypermodularity of higher-order networks that allows us to use spectral methods to detect community structures in hypergraphs. We apply this approach to synthetic random networks as well as to real-world data, showing that it produces results that reflect the nature and the dynamics of the interactions modeled, thereby constituting a valuable tool for the extraction of hidden information from complex higher-order data sets.

Allosteric interactions occur when binding at one part of a complex affects the interactions at another part. Allostery offers a high degree of control in multispecies processes, and these interactions play a crucial role in many biological and synthetic contexts. Leveraging allosteric principles in synthetic systems holds great potential for designing materials and systems that can autonomously adapt, reconfigure, or replicate. In this work we establish a basic allosteric model and develop an intuitive design process, which we demonstrate by constructing systems to exhibit four different complex behaviors: controlled fiber growth, shape shifting, sorting, and self-replication. In order to verify that the systems evolve according to the pathways we have developed, we also calculate and measure key length and time scales. Our findings demonstrate that with minimal interaction rules, allosteric systems can be engineered to achieve sophisticated emergent behaviors, opening new avenues for the design of responsive and adaptive materials.

We investigate the ultrafast dynamics of plasma formation by optical breakdown, filamentation, and cavitation in water, using high spatiotemporal resolution offered by x-ray free-electron laser (XFEL) radiation. A femtosecond infrared laser pulse is focused in a water-filled cuvette and probed by a single femtosecond x-ray pulse, with a time delay covering nearly four orders of magnitude. By exploiting the quantitative contrast values obtained by phase retrieval, we can follow the transition from plasma to gas in terms of a continuous decrease of mass density in the cavity. At the same time, we image the emission of a cylindrical shock wave for the scenario of a single elongated breakdown filament with a high degree of symmetry. Contrarily, the regime of multiple breakdown spots deviates from cylindrical symmetry and the idealized picture expected for a Gaussian beam. Here different scenarios of cavitation and (collective) expansion dynamics as well as bubble fusion are observed. Specifically, we quantify the decrease of the expansion velocity with the number of auxiliary cavitation events due to a redistribution of the deposited laser energy. We also report events with (multi)filamentation reflecting instabilities in the initial distribution of the laser intensity upon formation of the plasma. Filaments with submicron diameter and few-micrometer spacing are observed, as well as the phenomena of filament emergence, splitting, and termination. The different regimes of heterogeneous optical breakdown and cavitation can be distinguished depending on the laser pulse energy. Altogether, the experiments demonstrate the potential of single-pulse XFEL imaging for the investigation of optical breakdown and ultrafast hydrodynamics. The future application of the imaging approach to soft matter environments, tissue, glasses, and opaque materials seems straightforward.