Interacting quantum Hamiltonians are fundamental to quantum computing. Data-based tomography of time-independent quantum Hamiltonians has been achieved, but an open challenge is to ascertain the structures of time-dependent quantum Hamiltonians using time series measurements taken locally from a small subset of the spins. Physically, the dynamical evolution of a spin system under time-dependent driving or perturbation is described by the Heisenberg equation of motion. Motivated by this basic fact, we articulate a physics-enhanced machine-learning framework whose core is Heisenberg neural networks. In particular, we develop a deep learning algorithm according to some physics-motivated loss function based on the Heisenberg equation, which “forces” the neural network to follow the quantum evolution of the spin variables. We demonstrate that, from local measurements, not only can the local Hamiltonian be recovered, but the Hamiltonian reflecting the interacting structure of the whole system can also be faithfully reconstructed. We test our Heisenberg neural machine on spin systems of a variety of structures. In the extreme case in which measurements are taken from only one spin, the achieved tomography fidelity values can reach about $90\%$. The developed machine-learning framework is applicable to any time-dependent systems whose quantum dynamical evolution is governed by the Heisenberg equation of motion.

In continuous-variable quantum information processing, quantum error correction of Gaussian errors requires simultaneous estimation of both quadrature components of displacements in phase space. However, quadrature operators $x$ and $p$ are noncommutative conjugate observables, whose simultaneous measurement is prohibited by the uncertainty principle. Gottesman-Kitaev-Preskill (GKP) error correction deals with this problem using complex non-Gaussian states called GKP states. On the other hand, simultaneous estimation of displacement using experimentally feasible non-Gaussian states has not been well studied. In this paper, we consider a multiparameter estimation problem of displacements assuming an isotropic Gaussian prior distribution and allowing postselection of measurement outcomes. We derive a lower bound for the estimation error when only Gaussian operations are used and show that even simple non-Gaussian states such as single-photon states can beat this bound. Based on Ghosh's bound, we also obtain a lower bound for the estimation error when the maximum photon number of the input state is given. Our results reveal the role of non-Gaussianity in the estimation of displacements and pave the way toward the error correction of Gaussian errors using experimentally feasible non-Gaussian states.

Molecules containing superheavy atoms can be artificially created to serve as sensitive probes to study symmetry-violating phenomena. Here, we provide detailed theoretical studies of quantities relevant to the electron electric dipole moment (eEDM) and nucleus-electron scalar-pseudoscalar interactions in diatomic molecules containing superheavy lawrencium nuclei. The sensitivity to parity and time (or, equivalently, CP) reversal violating properties is studied for different neutral and ionic molecules. The effective electric fields in these systems are found to be about 3–4 times larger than other known molecules on which eEDM experiments are being performed. Similarly, these superheavy molecules exhibit an enhancement of more than 3 times for $CP$-violating scalar-pseudoscalar nucleus-electron interactions. Our preliminary analysis using the Woods-Saxon nuclear model also demonstrates that these results are sensitive to the diffuse surface interactions inside the Lr nucleus. We also briefly comment on some experimental aspects by discussing the production of these systems.

We study excitation transport in a two-dimensional system of randomly assembled spins with power-law hopping in two dimensions. This model can be realized in cold atom quantum simulators with Rydberg atoms. In these experiments, due to the Rydberg blockade effect, the degree of disorder in the system is effectively tunable by varying the spin density. We study dynamics and eigenstate properties of the model as a function of disorder strength and system size and discuss potential limitations for experiments. At strong disorder we predominantly observe localized eigenstates with power-law tails. In this regime the spectral and eigenstate properties can be understood in a perturbative picture of states localized on small clusters of spins. As the disorder strength is weakened eigenstates become increasingly delocalized and a set of seemingly multifractal states appears in the low-energy tail of the spectrum. A detailed study of the system-size scaling of the eigenstate properties indicates that in the infinite-size limit all states eventually become localized. We discuss the feasibility of observing localization effects experimentally in the spatial spreading of an initially localized excitation and identify limited system sizes and finite decoherence rates as major challenges. Our study paves the way towards an experimental observation of localization effects in Rydberg spin systems with tunable disorder.

We investigate quantum entanglement in an analog black hole realized in the flow of a Bose-Einstein condensate. The system is described by a three-mode Gaussian state and we construct the corresponding covariance matrix at zero and finite temperature. We study associated bipartite and tripartite entanglement measures and discuss their experimental observation. We identify a simple optical setup equivalent to the analog Bose-Einstein black hole which suggests a different way of determining the Hawking temperature and gray-body factor of the system.

We develop from first principles a theoretical model for infrared pulse propagation in graphene-covered hybrid waveguides. We model electron dynamics in graphene by Bloch equations, enabling the derivation of the nonlinear conductivity and of a rate equation accounting for free-carrier generation. Radiation propagation is modeled through a generalized nonlinear Schrödinger equation for the field envelope coupled with the rate equation accounting for the generation of free carriers in graphene. Our numerical simulations clearly indicate that unperturbed Kerr solitons accelerate due to the carrier-induced index change and experience a strong self-induced spectral blueshift. Our numerical results are fully explained by semianalytical predictions based on soliton perturbation theory.

We derive an analytical approximate solution of the time-dependent state vector in terms of material Bell states and coherent states of the field for a generalized two-atom Tavis-Cummings model with nonlinear intensity-dependent matter-field interaction. Using this solution, we obtain simple expressions for the atomic concurrence and purity in order to study the entanglement in the system at specific interaction times. We show how to implement entangling atomic operations through measurement of the field. We illustrate how these operations can lead to a complete Bell measurement. Furthermore, when considering two orthogonal states of the field as levels of a third qubit, it is possible to implement a unitary three-qubit gate capable of generating authentic tripartite entangled states such as the Greenberger-Horne-Zeilinger state and the $W$ state. As an example of the generic model, we present an ion-trap setting employing the quantized mode of the center-of-mass motion instead of the photonic field, showing that the implementation of realistic entangling operations from intrinsic nonlinear matter-field interactions is indeed possible.

We consider an approach in which the usual wave function ${\psi }_j\left(x_j\right)$ in the quadrature representation of mode $j$ of the electromagnetic field is further quantized to produce a field operator ${\widehat{\psi }}_j\left(x_j\right).$ Since the electromagnetic field is already second quantized, this corresponds to an additional or third quantization. The third-quantization approach can be used to perform certain quantum optics calculations in the Heisenberg picture that could only be performed in the Schrödinger picture when using the conventional second-quantized theory. This approach also allows an interesting generalization of quantum optics and quantum electrodynamics that is analogous to symmetry breaking in elementary particle theory. The predictions of the generalized theory could be tested using a proposed photon scattering experiment.

The Bhatia-Davis theorem provides a useful upper bound for the variance in mathematics, and in quantum mechanics, the variance of a Hamiltonian is naturally connected to the quantum speed limit due to the Mandelstam-Tamm bound. Inspired by this connection, we construct a formula, referred to as the Bhatia-Davis formula, for the characterization of the quantum speed limit in the Bloch representation. We first prove that the Bhatia-Davis formula is an upper bound for a recently proposed operational definition of the quantum speed limit, which means it can be used to reveal the closeness between the timescale of certain chosen states to the systematic minimum timescale. In the case of the largest target angle, the Bhatia-Davis formula is proved to be a valid lower bound for the evolution time to reach the target when the energy structure is symmetric. Regarding few-level systems, it is also proved to be a valid lower bound for any state in two-level systems with any target, and for most mixed states with large target angles in equally spaced three-level systems.

Nonlocality without entanglement and its subsequent generalizations offer deep information-theoretic insights and subsequently find several useful applications. The concept of a genuinely nonlocal set of product states emerges as a natural multipartite generalization of this phenomenon. The existence of such sets eventually raises the problem concerning their entanglement-assisted discrimination. Here, we construct examples of genuinely nonlocal product states for an arbitrary number of parties. The strength of genuine nonlocality of these sets can be considered minimal as their perfect discrimination is possible with entangled resources residing in Hilbert spaces having the smallest possible dimensions. Our constructions lead to fully separable measurements that are impossible to implement even if all but one party come together. Furthermore, they also provide the opportunity to compare different multipartite states that otherwise are incomparable under single copy local manipulation.

We explore the three-particle spin model of an $S_1=\frac{1}{2}$ particle (e.g., an electron) interacting with two spin-coupled $S_{\text{2,3}}$ particles with exchange coupling and magnetic anisotropy. We show that in the case of $S_{2,3}=1$ particles, the coupled particle entanglement states can be prepared, controlled, and read by the $S_1$ particle. We also find that for particular resonance conditions of the magnetic anisotropy strength $D$ and exchange coupling strength $J$, the entanglement state-switching behavior is maximized and is robust against a range of anisotropic application of the exchange coupling.

Quantum computers based on rare-earth-ion-doped crystals show promising properties in terms of scalability and connectivity if single ions can be used as qubits. Through simulations, we investigate gate operations on such qubits. We discuss how gate and system parameters affect gate errors, the required frequency bandwidth per qubit, and the risk for instantaneous spectral diffusion (ISD). Furthermore, we examine how uncertainties in the system parameters affect the gate errors, and how precisely the system needs to be known. We find gate errors for arbitrary single-qubit gates of $2.1\times {10}^{-4}$ when ISD is not considered and $3.4\times {10}^{-4}$ when we take heed to minimize it. Additionally, we construct two-qubit gates with errors ranging from $5\times {10}^{-4}\to 3\times {10}^{-3}$ over a broad range of dipole-dipole interaction strengths.

In this paper, we report our calculations of the triple-differential cross section (TDCS) for the relativistic $(e,2e)$ process with a twisted electron beam on Cu and Ag atomic targets in coplanar asymmetric geometry mode. The theoretical formalism has been developed in the first Born approximation, in which we use the Dirac plane wave as well as the twisted electron wave for the incident electron beam to study the effect of various parameters of the twisted electron beam on the $(e,2e)$ process. We use a Dirac plane-wave function, semirelativistic Coulomb wave function, and Darwin wave function for the scattered, ejected, and K-shell electron, respectively. We compare the angular profiles of the TDCS of the twisted electron impact $(e,2e)$ process with that of the plane wave. We segregate the TDCS for charge-charge interaction and current-current interaction with their interference term and study the effect of different parameters of the twisted electron beam on them. The study is also extended to the macroscopic Cu and Ag targets to further investigate the effect of the opening angle of the twisted electron beam on TDCS. The spin asymmetry in TDCS caused by the polarized incident electron beam is also studied to elucidate the effects of the twisted electron beam on the $(e,2e)$ process.

Despite significant progress in theoretical and laboratory quantum control, engineering quantum systems remains principally challenging due to manifestation of noise and uncertainties associated with the field and Hamiltonian parameters. In this paper, we extend and generalize the asymptotic quantum control robustness analysis method, which provides more accurate estimates of quantum control objective moments than standard leading-order techniques, to diverse quantum observables, gates, and moments thereof and also introduce the Pontryagin maximum principle for quantum robust control. In addition, we present a Pareto optimization framework for achieving robust control via evolutionary open-loop (model-based) and closed-loop (model-free) approaches with the mechanisms of robustness and convergence described using asymptotic quantum control robustness analysis. In the open-loop approach, a multiobjective genetic algorithm is used to obtain Pareto solutions in terms of the expectation and variance of the transition probability under Hamiltonian parameter uncertainty. The set of numerically determined solutions can then be used as a starting population for model-free learning control in a feedback loop. The closed-loop approach utilizes a real-coded genetic algorithm with adaptive exploration and exploitation operators in order to preserve solution diversity and dynamically optimize the transition probability in the presence of field noise. Together, these methods provide a foundation for high-fidelity adaptive feedback control of quantum systems wherein open-loop control predictions are iteratively improved based on data from closed-loop experiments.

We theoretically investigate ground-state properties of a three-component Fermi gas with pairwise contact interactions between different components near a triatomic resonance where bound trimers are about to appear. Using variational equations for in-medium two- and three-body cluster states in three dimensions, we elucidate the competition of pair and triple formations due to the Fermi surface effects. We present the ground-state phase diagram that exhibits transition from a Cooper pair to Cooper triple state and crossover from a Cooper triple to tightly bound trimer state at negative scattering lengths. This three-body crossover is analogous to the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation crossover observed in a two-component Fermi gas. We predict that the threshold scattering length $a_{-}$ for three-body states can be shifted towards the weak-coupling side due to the emergence of Cooper triples.

The question of electromagnetic field intensification towards the values typical for strong field quantum electrodynamics is of fundamental importance. One of the most promising intensification schemes is based on the relativistic-flying mirror concept, which shows that the electromagnetic radiation reflected by the mirror will be frequency upshifted by a factor of $4{\gamma }^2$ ($\gamma$ is the Lorentz factor of the mirror). In laser-plasma interactions, such a mirror travels with relativistic velocities through plasma and typically has a parabolic form, which is advantageous for light intensification. Thus, a relativistic-flying parabolic mirror reflects the counterpropagating radiation in the form of a focused and flying electromagnetic wave with a high frequency. The relativistic-flying motion of the laser focus makes the electric and magnetic field distributions of the focus complicated, and the mathematical expressions describing the field distributions of the focus become of fundamental interest. We present analytical expressions describing the field distribution formed by an ideal flying mirror which has a perfect reflectance over the entire surface and wavelength range. The peak field strength of an incident laser pulse with a center wavelength of ${\lambda }_0$ and an effective beam radius of $w_e$ is enhanced by a factor proportional to ${\gamma }^3(w_e/{\lambda }_0)$ in the relativistic limit. Electron-positron pair production is investigated in the context of invariant fields based on the enhanced electromagnetic field. The pair production rate under the relativistic-flying laser focus is modified by the Lorentz $\gamma$-factor and the beam radius-wavelength ratio ($w_e/{\lambda }_0$). We show that the electron-positron pairs can be created by colliding two counterpropagating relativistic-flying laser focuses in vacuum, each of which is formed when a 180 TW laser pulse is reflected by a relativistic-flying parabolic mirror with $\gamma =12.2$.

Cross-polarization coupling (CPC) between coresonant orthogonally polarized modes in a single whispering-gallery microresonator can lead to induced transparency effects. Depending on the CPC strength, coupled-mode-induced transparency (CMIT) or Autler-Townes splitting (ATS) can be observed. Determining the CPC strength is crucial in locating the exceptional point, where CMIT evolves into ATS and an enhancement in sensitivity to perturbations is expected. The CPC strength can be calculated theoretically based on the transverse structure of whispering-gallery modes. Experimentally, however, CPC strength has been inferred only indirectly by fitting the experimental throughput spectrum to a steady-state model. In this work, we propose and demonstrate a direct determination of the CPC strength based on the response of the throughput to a sinusoidal amplitude modulation of the input light. Our experimental results agree with numerical fitting values and are in the same range as predicted by theoretical calculations.

The supercontinuum (SC) is generally assumed to inherit the polarization of the incident pulse in isotropic media. In this study, we experimentally investigated the polarization properties of SC spectra induced by different polarized femtosecond lasers in water. The results show that the extent of depolarization of the SC induced by a quasicircularly polarized pulse is more pronounced than that of a quasilinearly polarized pulse. In terms of the different spectral components, the long-wavelength components experienced more depolarization, and the short-wavelength components tended to be linearly polarized for both polarized input femtosecond lasers. The depolarization mechanism can be attributed to two factors, namely, the energy coupling between the two polarized components of the input femtosecond pulse, and the various degrees of nonlinear birefringence experienced by different spectral components of the SC during propagation.