We present the lifetime measurement of the ${\left(4d_{3/2}^{-1}5s\right)}_{J=2}$ state in Pd-like ${\mathrm{I}}^{7+}$, which predominantly decays to the $(4d^{10}{)}_{J=0}$ ground state by an electric-quadrupole transition modified by strong spin-orbit mixing. We measure this microsecond-order lifetime in an electron-beam ion trap using pulsed laser excitation from a metastable state which is continuously populated by electron collisions. The measured lifetime provides a new benchmark for relativistic atomic structure calculations with $d$-state electrons.

The experimental determination of x-ray-production cross sections by electron impact on thick samples is faced in this work, especially focusing on the $L$ subshells of Ag. The integrodifferential method used by An et al. is compared with a recently implemented approach involving the ionization distribution function. The first method has shown good results under suitable conditions, namely, when multiple scattering, bremsstrahlung enhancement, and other secondary effects are negligible. Monte Carlo simulations were performed in order to analyze the influence of these conditions and therefore to extend the validity range of the method by adding a correction factor. The second approach uses the ionization distribution function $\varphi \left(\rho z\right)$ to predict the intensity of the emitted photons; this magnitude is assessed by the poema software, previously developed, and it is used to determine correction factors to the cross sections included in the software database. Both approaches were tested by fitting several $L$-shell spectra measured in a wide interval of incident electron energies, ranging from 4.0 to 25 keV, with an electron microprobe equipped with a wavelength-dispersive spectrometer. The x-ray-production cross sections obtained for each $L$ subshell and the total $L$ x-ray-production cross section were compared with theoretical predictions based on the distorted-wave approach theory and with experimental determinations when available.

We show that the recently observed class of long-range ion-Rydberg molecules can be divided into two families of states, which are characterized by their unique electronic structures resulting from the ion-induced admixture of quantum defect-split Rydberg $nP$ states with different low-field-seeking high-$l$ states. We predict that in both cases, these diatomic molecular states can bind additional ground-state atoms lying within the orbit of the Rydberg electron, thereby forming charged ultralong-range Rydberg molecules (ULRMs) with binding energies similar to that of conventional nonpolar ULRMs. To demonstrate this, we consider a Rydberg atom interacting with a single ground-state atom and an ion. The additional atom breaks the system's cylindrical symmetry, which leads to mixing between states that would otherwise be decoupled. The electronic structure is obtained using exact diagonalization over a finite basis and the vibrational structure is determined using the multiconfiguration time-dependent Hartree method. Due to the lobelike structure of the electronic density, bound trimers with both linear and nonlinear geometrical configurations of the three nuclei are possible. The predicted trimer binding energies and excitation series are distinct enough from those of the ion-Rydberg dimer to be observed using current experimental techniques.

In a recent work [V. A. Antonov, K. C. Han, T. R. Akhmedzhanov, M. Scully, and O. Kocharovskaya, Phys. Rev. Lett. 123, 243903 (2019)] a method of amplifying a train of attosecond pulses, produced via high-order harmonic generation of an infrared (IR) laser field, in an active medium of a plasma-based x-ray laser dressed by a replica of the IR field of the fundamental frequency was proposed. The specific case of independent amplification of each incident harmonic was considered, corresponding to a dense plasma of multiply charged ions (such as ${\mathrm{C}}^{5+}$ ions) which is strongly dispersive for the IR field. In the present paper, we consider a general case when the laser field modulation leads not only to the direct amplification of high harmonics (HHs), but also to the scattering of the harmonics into each other. The mutual coherent scattering process plays an important role in a relatively low-density plasma with a lower ion charge, corresponding to a weakly dispersive plasma at the frequency of the IR field. Constructive interference between the amplified HHs and the coherently scattered field may result in a significant enhancement of the total output field. We call this effect the mutual amplification of high-order harmonics. Considering the plasma of hydrogenlike ${\mathrm{Li}}^{2+}$ ions with an inverted transition wavelength of 13.5 nm as an example, we analytically and numerically show that synchronization of a coherently scattered field with the radiation of amplified HHs makes it possible to increase the intensity of attosecond pulses by several times compared to the case of an independent amplification of HHs.

Soliton molecules, composed of closely spaced pulses with strong internal interactions, have been in-depth studied in fiber lasers due to their fascinating evolution dynamics and potential applications in high-speed optical communications. Here we demonstrate a type of oscillating soliton molecules in a mode-locked fiber laser constituted by single-mode and polarization-maintaining fibers. Ascribing to the unequal coupling between two orthogonal-polarized vector modes, the constituent pulses of soliton molecules possess different intensities and further result in a dual-roundtrip and large-period oscillation. Numerical simulations reproduce the critical experimental phenomena and show that two vector modes display diverse departing behavior in polarization-maintaining fiber. This work sheds light on the role of strong birefringence on vector solitons, providing a flexible nonlinear system to generate and study oscillating soliton molecules.

The Lieb lattice and the kagome lattice, which are both well known for their Dirac cones and flat bands, can be continuously converted into each other by a shearing transformation. During this transformation, the flat band is destroyed, but the Dirac cones remain and become tilted, with types I, II, and III occurring for different parameters. In this work, we first study these tilted Dirac cones using a tight-binding model, revealing how they can be engineered into the different types. We then demonstrate conical diffraction in a photonic lattice realization of the Lieb-kagome lattice using split-step beam propagation simulations, obtaining evidence of the presence of Dirac cones tilted in different directions. Finally, we performed experiments with photonic lattices laser written in fused silica $\left({\mathrm{SiO}}_2\right)$ to validate the results of the simulations. These studies advance the understanding of the Lieb-kagome lattice and tilted Dirac cones in general and provide a basis for further research into this interesting tunable lattice system.

Operator size growth describes the scrambling of operators in quantum dynamics and stands out as an essential physical concept for characterizing quantum chaos. Important as it is, a scheme for the direct measuring of operator size on a quantum computer is still absent. Here, we propose a quantum algorithm for the direct measuring of the operator size and its distribution based on Bell measurement. The algorithm is verified with spin chains and, meanwhile, the effects of Trotterization error and quantum noise are analyzed. It is revealed that saturation of operator size growth can be due to quantum chaos itself or be a consequence of quantum noise. Nevertheless, it is found that the error mitigation will effectively reduce the influence of noise, so as to restore the distinguishability of oscillation and saturation behaviors of operator scrambling. Our work provides a feasible protocol for investigating quantum chaos on noisy quantum computers by measuring operator size growth.

Kirkwood-Dirac (KD) quasiprobability is a quantum analog of phase space probability of classical statistical mechanics, allowing negative or/and nonreal values. It gives an informationally complete representation of a quantum state. Recent works have revealed the important roles played by the KD quasiprobability in the broad fields of quantum science and quantum technology. In the present work, we use the KD quasiprobability to access the quantum coherence in a quantum state. We show that the $l_1$ norm of the imaginary part of the KD quasiprobability over an incoherent reference basis and a second basis, maximized over all possible choices of the latter, can be used to quantify quantum coherence, satisfying certain desirable properties. It is upper bounded by the quantum uncertainty, i.e., the quantum standard deviation, of the incoherent basis in the state. It gives a lower bound to the $l_1$ norm quantum coherence, and for a single qubit, they are identical. We discuss the measurement of the KD coherence based on the measurement of the KD quasiprobability and an optimization procedure in hybrid quantum-classical schemes, and suggest statistical interpretations. We also discuss its relevance in the physics of linear response regime.

One of the big challenges in exoplanet science is to determine the atmospheric makeup of extrasolar planets and to find biosignatures that hint at the existence of biochemical processes on another world. The biomarkers we are trying to detect are gases in the exoplanet atmosphere such as oxygen or methane, which have deep absorption features in the visible and near-infrared spectrum. Here we establish the ultimate quantum limit for determining the presence or absence of a spectral absorption line, for a dim source in the presence of a much brighter stellar source. We characterize the associated error exponent in both the frameworks of symmetric and asymmetric hypothesis testing. We found that a structured measurement based on spatial demultiplexing allows us to decouple the light coming from the planet and achieve the ultimate quantum limits. If the planet has intensity $\epsilon \ll 1$ relative to the star, we show that this approach significantly outperforms direct spectroscopy yielding an improvement of the error exponent by a factor $1/\epsilon$. We find the optimal measurement, which is a combination of interferometric techniques and spectrum analysis.

We use matched quantum entanglement witnesses to study the separable criteria of continuous variable states. The witness can be written as an identity operator minus a Gaussian operator. The optimization of the witness then is transformed to an eigenvalue problem of a Gaussian kernel integral equation. It follows a separable criterion not only for symmetric Gaussian quantum states, but also for non-Gaussian states prepared by photon adding to and/or subtracting from symmetric Gaussian states. Based on Fock space numeric calculation, we obtain an entanglement witness for more general two-mode states. A necessary criterion of separability follows for two-mode states and it is shown to be necessary and sufficient for a two-mode squeezed thermal state and the related two-mode non-Gaussian states. We also connect the witness-based criterion with Werner-Wolf criterion and refine the Werner-Wolf criterion.

We present counterdiabatic reverse annealing, a quantum annealing protocol that extends the range of application of reverse annealing to the previously inaccessible short-time domain. This is achieved by exploiting approximate counterdiabatic driving expanded in low-order nested commutators. In this work, we offer a comparative study of the performance of this technique to that of unassisted reverse annealing in terms of metrics such as the ground-state fidelity and the time to solution. We provide a quantitative measure of the energetic cost of counterdiabatic reverse annealing and show that significant improvements are possible even using local counterdiabatic potentials, paving the way toward the experimental implementation in near-term quantum devices.

Virtual distillation is an error-mitigation technique that reduces quantum-computation errors without assuming the noise type. In scenarios where the user of a quantum circuit is required to additionally employ peripherals, such as delay lines, that introduce excess noise, we find that the error-mitigation performance can be improved if the peripheral, whenever possible, is split across the entire circuit, that is, when the noise channel is uniformly distributed in layers within the circuit. We show that under the multiqubit loss and Pauli noise channels, respectively, for a given overall error rate, the average mitigation performance improves monotonically as the noisy peripheral is split (diluted) into more layers, with each layer sandwiched between subcircuits that are sufficiently deep to behave as 2-designs. For both channels, analytical and numerical evidence show that second-order distillation is generally sufficient for (near-)optimal mitigation. We propose an application of these findings in designing a quantum-computing cluster that houses realistic noisy intermediate-scale quantum circuits that may be shallow in depth, where measurement detectors are limited and delay lines are necessary to queue output qubits from multiple circuits.

In this work, we propose a completely general method to pump the gapped topological modes of a lattice of optical waveguides by controlling the propagation constant of an auxiliary waveguide and its coupling to the main lattice. In this way, we can transform a single-waveguide excitation on the auxiliary waveguide into a specific mode of the lattice. We also demonstrate the possibility of transferring supermodes between two waveguide lattices using the same method. We illustrate the results by pumping and transferring the topological modes of Su-Schrieffer-Heeger lattices. For both scenarios, we show that purities above 99% can be achieved with parameter values within experimental reach. Additionally, we demonstrate how the technique can be used to pump the bulk modes of the lattice for low number of waveguides or enable mode conversion between waveguide lattices.

Recent experiments show that periodic drives on dipolar systems lead to long-lived prethermal states. These systems are weakly coupled to the environment and reach prethermal states on a timescale much shorter than the timescale for thermalization. Such nearly closed systems have previously been analyzed using Floquet formalism, which shows the emergence of a prethermal plateau. We use a fluctuation-regulated quantum master equation (FRQME) to describe these systems. In addition to the system-environment coupling, FRQME successfully captures the dissipative effect from the various local interactions in the system. Our investigation reveals a cascaded journey of the system to a final steady state. The cascade involves a set of prethermal or arrested states characterized by a set of quasiconserved quantities. We show that these prethermal states emerge in a timescale much shorter than the relaxation timescale. We also find and report the existence of a critical limit beyond which the prethermal plateau ceases to exist.

In practice, the interaction between quantum system and environment will lead to the decoherence of entanglement. By quantifying the entanglement through the correlation tensor, we systematically investigate the entanglement robustness of two-qubit states under the four types of noisy channels and corresponding correlated channels. We use an analytical method to find all of the most robust and fragile states under the noisy channels. The puzzling phenomenon that the most robust and fragile states have the same entanglement under noisy channels has been investigated. Moreover, we compare the entanglement robustness of a three-qubit Greenberger-Horne-Zeilinger state with a $W$ state. Our method shows the behavior of entanglement under the noisy channels and characterizes the entanglement robustness of the multiqubit system analytically.

In the quantum regime, the third law of thermodynamics implies the unattainability of pure states. As shown recently, such unattainability implies that a unitary interaction between the measured system and a measuring apparatus can never implement an ideal projective measurement. In this paper, we introduce an operational formulation of the third law for the most general class of physical transformations, the violation of which is both necessary and sufficient for the preparation of pure states. Subsequently, we investigate how such a law constrains measurements of general observables, or positive operator-valued measures. We identify several desirable properties of measurements which are simultaneously enjoyed by ideal projective measurements—and are hence all ruled out by the third law in such a case—and determine if the third law allows for these properties to obtain for general measurements of general observables and, if so, under what conditions. It is shown that while the third law rules out some of these properties for all observables, others may be enjoyed by observables that are sufficiently “unsharp.”

Quantum particles performing Bloch oscillations in a spatially periodic potential can be used as a very accurate detector of constant forces. We find that similar oscillations that can appear in the Floquet phase space of a quantum particle subjected to periodic temporal driving, even in the absence of a periodic lattice potential, can likewise be exploited as detectors. Compared with their spatial Bloch analog, however, the Floquet-Bloch oscillations provide significant added flexibility and open the way to a broad range of precision metrology applications. We illustrate this property with the examples of a tachometer and a magnetometer.

Modeling nonlinear activation functions on quantum computers is vital for quantum neurons employed in fully quantum neural networks, however, remains a challenging task. We introduce an amplitude-based implementation for approximating nonlinearity in the form of the unit step function on a quantum computer. Our approach expands upon repeat-until-success protocols, suggesting a modification that requires a single measurement only. We describe two distinct circuit types which receive their input either directly from a classical computer or as a quantum state when embedded in a more advanced quantum algorithm. All quantum circuits are theoretically evaluated using numerical simulation and executed on Noisy Intermediate-Scale Quantum hardware. We demonstrate that reliable data with high precision can be obtained from our quantum circuits involving up to eight qubits and up to 25 CX-gate applications, enabled by state-of-the-art hardware-optimization techniques and measurement error mitigation.

Coulomb-bound systems in reduced dimensions are sensitive probes of increased confinement. For example, the ground-state binding energy of hydrogen atoms increases by a factor of 4 when passing from three to two dimensions. Recently, quasi–two-dimensional hydrogen has been realized experimentally in the form of low-dimensional excitons. Their sensitivity to external electric and magnetic perturbations is reduced by the confinement. To quantify the reduction, we consider in the present work two-dimensional hydrogen in crossed electric and magnetic fields. We compare analytical, numerical, and variational results for the binding energy and dipole polarizability in arbitrary magnetic fields. Our analytical expressions for both weak and strong magnetic fields are supplemented by accurate variational and hypergeometric resummation results, thereby covering arbitrary magnetic fields.

Bright sources of polarization-entangled photon pairs are essential components for quantum information technologies. In many methods proposed so far, it is necessary to introduce a resonator that combines active optical components, such as an electric optical modulator to enhance the stimulated emission of polarization-entangled photons. In these methods, however; it is technically difficult to perform the time-series operation to output the stimulated entangled photons in the resonator by synchronizing laser pulses. In this paper, we propose a scheme to scale up the stimulated emission of polarization-entangled photon pairs using a resonator with only passive optical components. We show the theoretical aspects of the scheme and perform a proof-of-principle experimental demonstration of the scheme in a double-pass configuration.