We theoretically study formation of gain without inversion and resonant enhancement of refractive index with suppressed absorption in a system consisting of a monolayer of transition metal dichalcogenide (${\mathrm{WS}}_2$) and a metallic nanoantenna. We show that these processes happen when the hybrid system interacts with a right-circularly polarized laser beam, allowing quantum coherence transfer to happen from the K to ${\mathrm{K}}^{\prime }$ valley. Our results show that the quantum coherence transfer can convert the ${\mathrm{K}}^{\prime }$ valley into a conjugated system wherein the real and imaginary parts of its polarization become similar to the imaginary and real parts of the K valley polarization, respectively. This allows the maximum refractive index in the ${\mathrm{K}}^{\prime }$ valley to occur as the absorption becomes zero. We characterize the conjugated valley system by inspecting the evolution of its Bloch vector as the incident laser frequency varies. The theoretical approach includes density matrix formalism while considering a pure dephasing rate that represents the fast decay of exciton valley polarization in transition metal dichalcogenide monolayers.

Optical nanoantennas, i.e., elements transforming localized light or waveguide modes into freely propagating fields and vice versa, are vital components for modern nanophotonics. Optical antennas have been demonstrated to cause the Dicke superradiance effect, i.e., collective spontaneous emission of quantum sources. However, the impact of coherent excitation on the antenna performance, such as directivity, efficiency, and Purcell effect, remains mostly unexplored. Herein, using full-wave numerical simulations backed by a quantum model, we unveil that coherent excitation allows controlling antenna multipoles, on-demand excitation of nonradiative states, enhanced directivity, and improving antenna radiation efficiency. This collective excitation corresponds to the states with nonzero dipole moment in the quantum picture, where the quantum phase is well defined. The results of this work bring another degree of freedom––the collective phase of an ensemble of quantum emitters––to control optical nanoantennas and, as such, pave the way to the use of collective excitations for nanophotonic devices with superb performance. To make the discussion independent of the frequency range, we consider the all-dielectric design and use dimensionless units.

We present results of a numerical experiment in which a neutral spin-1/2 particle subjected to a static magnetic vortex field passes through a double slit barrier. We demonstrate that the resulting interference pattern on a detection screen exhibits fringes reminiscent of Aharonov-Bohm scattering by a magnetic flux tube. To gain better understanding of the observed behavior, we provide analytic solutions for a neutral spin-1/2 rigid planar rotor in the aforementioned magnetic field. We demonstrate how that system exhibits a generalized Aharonov-Bohm effect [Wu and Yang, Phys. Rev. D 12, 3845 (1975)], due to the emergence of an effective SU(2) Wu-Yang (WY) flux tube. We study the behavior of the gauge invariant partition function and demonstrate a topological phase transition for the spin-1/2 planar rotor. We provide an expression for the partition function in which its dependence on the Wilson loop integral of the WY gauge potential is explicit. We generalize to a spin-1 system in order to explore the Wilczek-Zee (WZ) mechanism in a full quantum setting. We show how degeneracy is lifted by higher-order gauge corrections that alter the semiclassical WZ phase. Models that allow analytic description provide a foil to objections that question the fidelity of predictions based on the generalized Born-Oppenheimer approximation in atomic and molecular systems. Though the primary focus of this paper concerns the emergence of gauge structure in neutral systems, the theory is also applicable to systems that possess electric charge. In that case, we explore interference between fundamental gauge fields (i.e., electromagnetism) with effective gauge potentials. We propose a possible laboratory demonstration for the latter in an ion trap setting. We illustrate how effective gauge potentials influence wave-packet revivals in the said ion trap.

We present a framework for understanding the dynamics of operator size, and bounding the growth of out-of-time-ordered correlators, in models of large-$S$ spins. Focusing on the dynamics of a single spin, we show the finiteness of the Lyapunov exponent in the large-$S$ limit; our bounds are tighter than the best known Lieb-Robinson-type bounds on these systems. We numerically find our upper bound on Lyapunov exponents is within an order of magnitude of numerically computed values in classical and quantum kicked top models. Generalizing our results to coupled large-$S$ spins on lattices, we show that the butterfly velocity, which characterizes the spatial speed of quantum information scrambling, is finite as $S\to \infty$. We emphasize qualitative differences between operator growth in semiclassical large-spin models and quantum holographic systems including the Sachdev-Ye-Kitaev model.

Spectral clustering is a powerful unsupervised machine learning algorithm for clustering data with nonconvex or nested structures [A. Y. Ng, M. I. Jordan, and Y. Weiss, On spectral clustering: Analysis and an algorithm, in Advances in Neural Information Processing Systems 14: Proceedings of the 2001 Conference (MIT Press, Cambridge, MA, 2002), pp. 849–856]. With roots in graph theory, it uses the spectral properties of the Laplacian matrix to project the data in a low-dimensional space where clustering is more efficient. Despite its success in clustering tasks, spectral clustering suffers in practice from a fast-growing running time of $O\left(n^3\right)$, where $n$ is the number of points in the data set. In this work we propose an end-to-end quantum algorithm performing spectral clustering, extending a number of works in quantum machine learning. The quantum algorithm is composed of two parts: the first is the efficient creation of the quantum state corresponding to the projected Laplacian matrix, and the second consists of applying the existing quantum analog of the $k$-means algorithm [I. Kerenidis, J. Landman, A. Luongo, and A. Prakash, $q$-means: A quantum algorithm for unsupervised machine learning, in Advances in Neural Information Processing Systems 32: Proceedings of the 2019 Conference (Curran Associates, Red Hook, NY, 2020), pp. 4136–4146]. Both steps depend polynomially on the number of clusters, as well as precision and data parameters arising from quantum procedures, and polylogarithmically on the dimension of the input vectors. Our numerical simulations show an asymptotic linear growth with $n$ when all terms are taken into account, significantly better than the classical cubic growth. This work opens the path to other graph-based quantum machine learning algorithms, as it provides routines for efficient computation and quantum access to the incidence, adjacency, and projected Laplacian matrices of a graph.

We present an extension to the robust phase estimation protocol, which can identify incorrect results that would otherwise lie outside the expected statistical range. Robust phase estimation is increasingly a method of choice for applications such as estimating the effective process parameters of noisy hardware, but its robustness is dependent on the noise satisfying certain threshold assumptions. We provide consistency checks that can indicate when those thresholds have been violated, which can be difficult or impossible to test directly. We test these consistency checks for several common noise models, and identify two possible checks with high accuracy in locating the point in a robust phase estimation run at which further estimates should not be trusted. One of these checks may be chosen based on resource availability, or they can be used together in order to provide additional verification.

Loosely bound van der Waals dimers of lanthanide atoms, as might be obtained in ultracold atom experiments, are investigated. These molecules are known to exhibit a degree of quantum chaos due to the strong anisotropic mixing of their angular spin and rotation degrees of freedom. Within a model of these molecules, we identify different realms of this anisotropic mixing, depending on whether the spin, the rotation, or both are significantly mixed by the anisotropy. These realms are in turn generally correlated with the resulting magnetic moments of the states.

We study optical cycling in the polar free radical calcium monohydroxide (CaOH) and establish an experimental path towards scattering $\sim {10}^4$ photons. We report rovibronic branching ratio measurements with precision at the $\sim {10}^{-4}$ level and observe weak symmetry-forbidden decays to bending modes with nonzero vibrational angular momentum. Calculations are in excellent agreement with these measurements and predict additional decay pathways. Additionally, we perform high-resolution spectroscopy of the $\tilde{X}{}^2{\mathrm{\Sigma }}^{+}\left({12}^{0}0\right)$ and $\tilde{X}{}^2{\mathrm{\Sigma }}^{+}\left({12}^{2}0\right)$ hybrid vibrational states of CaOH. These advances establish a path towards radiative slowing, three-dimensional magneto-optical trapping, and sub-Doppler cooling of CaOH.

An exceptional point (EP) is a singularity in non-Hermitian systems which exhibits exotic functionalities such as high sensitivity to external perturbations and fine selectivity of a laser mode arising due to the abrupt transition in the eigenvalue spectra. To achieve an EP, both the real and imaginary parts of two or several eigenfrequencies should coincide. Perturbations that appeared at the fabrication stage usually lift the degeneracy, and it impedes the experimental observation of EPs. In this work, we reveal that a Kerr-type nonlinearity can compensate for an initial distortion in resonant frequencies that is hardly avoidable in practice using the example of a pair of coupled ring resonators. We analyze the behavior of the eigenvalues and mode amplitudes in the vicinity of the second- and third-order EPs as a function of excitation amplitude. This work can help to improve the characteristics of the systems that support EPs, broadening their application to the domain of nonlinear photonics.

Collective emission behavior is usually described by the decay dynamics of the completely symmetric Dicke states. To study a more realistic scenario, we investigate alternative initial states inducing a more complex time evolution. Superposition states of the fully inverted Dicke state and the Dicke ground state with unequal mutual weights are studied as examples as well as superradiance stemming from atoms in clusters separated by more than one wavelength. The Monte Carlo wave function method serves as a framework to study the dynamics of quantum states, which is determined by quantum jumps, on the one hand, and continuous evolution dynamics, on the other hand. We compare this method with the classical picture of a system of rate equations written for the diagonal components of the density matrix.

Time-resolved buildup of a Fano resonance in a macroscopic gaseous medium is theoretically studied by attosecond transient absorption spectroscopy. An intense near-infrared field is employed as an adjustable gate to confine the temporal dynamics, enabling one to resolve the line-shape formation in real time. Beyond the region where the single-atom approximation holds, we observe the emergence of spectral spikes with narrow linewidths for certain time delays and propagation distances, which represents that the medium can be delicately structured to be an efficient resonant absorber. Spectral substructures appear on the shoulder of the absorption lines after additional pulse propagation. The links between these features imprinted in spectral profiles and the formation of temporal characteristics in the excitation field are identified. The collective response of the medium versus time delay and propagation distance, in this laser-gated case, provides clues to the time-domain information on autoionization state and the microscopic dynamics occurring at each layer of the medium.

In quantum Darwinism, the pointer observable of a system leaves redundant imprints in its environment after decoherence. Each imprint is recorded in a fraction of the environment, which identifies a particular partition of the environment. An ambiguity situation may occur when another observable noncommuting to the pointer observable also leaves redundant imprints with respect to another partition of the environment. We study this problem based on a uniqueness theorem we proved. We find that within a particular subset of all possible partitions of the environment, the observable of the system leaving redundant and nondegenerately recorded imprints in the environment is unique. And, in a typical situation, the partitions outside this particular subset have no physical significance.

Randomness in Bell test data can be device-independently certified by Bell's theorem without placing assumptions about the experimental devices. The device-independent randomness has very demanding requirements about the experimental devices and relatively lower output randomness. With the same Bell test data we can extract substantially more randomness without using Bell's theorem. To achieve this goal, we introduce a remote-state-preparation dimension witness and a semi-device-independent randomness certification model which is based on it. This is one important step towards practical use of the Bell test in randomness generation.

We formulate a three-dimensional semiclassical model to treat three-electron escape dynamics in a strongly driven linear triatomic molecule, ${{\mathrm{HeH}}_2}^{+}$. Our model includes the Coulomb singularities. Hence, to avoid unphysical autoionization, we employ two criteria to switch off the Coulomb repulsive force between two bound electrons and switch it on when the motion of one electron is mostly determined by the laser field. We investigate triple and so-called frustrated triple ionization. In the latter process, two electrons escape while one electron remains bound in a Rydberg state. We find that two pathways prevail in frustrated triple ionization, as in frustrated double ionization. We also find that the electron that remains in a Rydberg state is more likely to be attached to ${\mathrm{He}}^{2+}$ than to ${\mathrm{H}}^{+}$. Our results indicate that in triple and frustrated triple ionization electronic correlation is weak. Moreover, we compute the sum of the kinetic energies as well as the angular patterns of the final ion fragments in triple and frustrated triple ionization. These patterns suggest that the fragmenting molecule deviates from its initial linear configuration.

Recent technological advances allowed the coherent optical manipulation of high-energy electron wave packets with attosecond precision. Here we theoretically investigate the collision of optically modulated pulsed electron beams with field-free atomic targets and reveal a quantum interference associated with different momentum components of the incident broadband electron pulse, which coherently modulates both the elastic and inelastic scattering cross sections. We show that the quantum interference has a high spatial sensitivity at the level of angstroms, offering potential applications in high-resolution ultrafast electron microscopy. Our findings are rationalized by a simple model.

Using quantum systems to efficiently solve quantum chemistry problems is one of the long-sought applications of near-future quantum technologies. In a recent work [J. Argüello-Luengo et al., Nature (London) 574, 215 (2019)], ultracold fermionic atoms have been proposed for this purpose by showing us how to simulate in an analog way the quantum chemistry Hamiltonian projected in a lattice basis set. Here, we continue exploring this path and go beyond these results in several ways. First, we numerically benchmark the working conditions of the analog simulator and find less demanding experimental setups where chemistry-like behavior in three dimensions can still be observed. We also provide a deeper understanding of the errors of the simulation appearing due to discretization and finite-size effects and provide a way to mitigate them. Finally, we benchmark the simulator characterizing the behavior of two-electron atoms (He) and molecules (${\mathrm{HeH}}^{+}$) beyond the example considered in the original work.

Photon blockade is an important quantum nonlinear phenomenon in cavity optomechanics. Here, we investigate the two-photon blockade effect by exploiting the mechanical squeezing. This squeezing can enhance the optomechanical-coupling strength into the single-photon strong-coupling regime. With strong coupling, we find the photon blockade effects can be generated and enhanced, and the region where the two-photon blockade occurs can be widened. Finally, we study the transition between photon-induced tunneling and blockade.

Spontaneous parametric down conversion (PDC), in the perturbative limit, can be considered as a probabilistic splitting of one input photon into two output photons. Conversely, sum-frequency generation (SFG) implements the reverse process of combining two input photons into one. Here we show that a single-photon projective measurement in the temporal-mode basis of the output photon of a two-photon SFG process affects a generalized measurement on the input two-photon state. We describe the positive operator-valued measure (POVM) associated with such a measurement and show that its elements are proportional to the two-photon states produced by the time-reversed PDC process. Such a detection acts as a joint measurement on two photons and is thus an important component of many quantum information processing protocols relying on photonic entanglement. Using the retrodictive approach, we analyze the properties of the two-photon POVM that are relevant for quantum protocols exploiting two-photon states and measurements.

We propose a scheme comprising an array of anisotropic optical waveguides, embedded in a gas of cold atoms, which can be tuned from a Hermitian to an odd-$\mathcal{P}\mathcal{T}$-symmetric configuration through the manipulation of control and assistant laser fields. We show that the system can be controlled by tuning intra- and intercell coupling coefficients, enabling the creation of topologically distinct phases and linear topological edge states. The waveguide array, characterized by a quadrimer primitive cell, allows for implementing transitions between Hermitian and odd-$\mathcal{P}\mathcal{T}$-symmetric configurations, broken and unbroken $\mathcal{P}\mathcal{T}$-symmetric phases, topologically trivial and nontrivial phases, as well as transitions between linear and nonlinear regimes. The introduced scheme generalizes the Rice-Mele Hamiltonian for a nonlinear non-Hermitian quadrimer array featuring odd-$\mathcal{P}\mathcal{T}$ symmetry and makes accessible unique phenomena and functionalities that emerge from the interplay of non-Hermiticity, topology, and nonlinearity. We also show that in the presence of nonlinearity the system sustains nonlinear topological edge states bifurcating from the linear topological edge states and the modes without a linear limit. Each nonlinear mode represents a doublet of odd-$\mathcal{P}\mathcal{T}$-conjugate states. In the broken $\mathcal{P}\mathcal{T}$ phase, the nonlinear edge states may be effectively stabilized when an additional absorption is introduced into the system.

A workflow for evaluation of entanglement source quality is proposed. Based on quantum state density matrices obtained from theoretical models and experimental data, we make an estimate of a potential performance of a quantum entanglement source in quantum key distribution protocols. This workflow is showcased for continuously pumped spontaneous parametric down-conversion (SPDC) source, where it highlights the trade-off between entangled pair generation rate and entanglement quality caused by multiphoton nature of the generated quantum states. We employ this characterization technique to show that secure key rate of down-converted photon pairs is limited to 0.029 bits per detection window due to intrinsic multiphoton contributions. We also report that there exists one optimum gain for continuous-wave down-conversion sources. We find a bound for secure key rate extracted from SPDC sources and make a comparison with perfectly single-pair quantum states, such as those produced by quantum dots.