We investigate the generation of near-threshold harmonics (NTHs) based on solving the three-dimensional time-dependent Schrödinger equation and utilizing an artificial neural network as a surrogate model to study the macroscopic propagation. Through our research, we identify two distinct pathways for NTH generation: harmoniclike transition and resonant transition. These pathways exhibit varying laser-parameter dependencies and phase-matching conditions, making it possible to spatially separate and selectively enhance NTHs by manipulating laser parameters in experimental setups. Our study provides insights into the underlying physics of the NTH macroscopic propagation and presents a methodology that can be applied to computationally intensive problems in the field of strong-field physics.

In this paper, we consider separability discrimination and decomposition problems of quantum mixed states based on the tensor optimization method. We first convert the separability determination problem of quantum mixed states to the positive Hermitian decomposition problem of Hermitian tensors. Then we study a rank-$R$ positive Hermitian approximation model of Hermitian tensors and introduce a Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm for rank-$R$ positive Hermitian approximation. We prove that the BFGS algorithm can be used to compute a decomposition of a mixed state if it is separable. Finally, we propose a BFGS algorithm for separability determination and decomposition of quantum mixed states. Numerical examples show the effectiveness of the algorithm.

To investigate the fundamental limit to far-field incoherent imaging, the prequels to this work [M. Tsang, Phys. Rev. A 99, 012305 (2019); Phys. Rev. A 104, 052411 (2021)]. have studied a quantum lower bound on the error of estimating an object moment and proved a scaling law for the bound with respect to the object size. As the scaling law was proved only in the asymptotic limit of vanishing object size, this work performs a numerical analysis of the quantum bound to verify that the law works well for nonzero object sizes in reality. We also use the numerical bounds to study the optimality of a measurement called spatial-mode demultiplexing (SPADE), showing that SPADE not only follows the scaling but is also numerically close to being optimal, at least for low-order moments.

We analyze quantum resource generation of capacitively coupled multilevel transmon circuits surrounded by bosonic baths, within the Markovian limit. Superconducting circuit elements are in practice usually part of a larger circuit, constructed with many other elements, which along with their environment is assumed to be mimicked by the baths. We study the response, to variation of the temperature of the thermal baths and the coupling strength, of resource generation for the system prepared in zero-resource initial states. We focus, in particular, on entanglement and quantum coherence as resources. We find that capacitive coupling, even if weak, can compete with Markovian decay of quantum resources and lead to significant steady-state values of the same. At short and moderate timescales, the resources exhibit nonmonotonic oscillatory behavior, reminiscent of the same in non-Markovian environs in absence of intrasystem coupling. We quantify the entanglement generation power of coupled transmon qutrits, taking into account the maximum entanglement the system can generate and the timescale over which the system can sustain a significant amount of the same. We identify the optimal initial separable states leading to maximum entanglement generating power.

There are two important, and potentially interconnecting, avenues to the realization of large-scale quantum algorithms: improvement of the hardware, and reduction of resource requirements demanded by algorithm components. In focusing on the latter, one crucial subroutine to many sought-after applications is the quantum adder. A variety of different implementations exist with idiosyncratic pros and cons. One of these, the Draper quantum Fourier adder, offers the lowest qubit count of any adder, but requires a substantial number of gates as well as extremely fine rotations. In this work we present a modification of the Draper adder which eliminates small-angle rotations to highly coarse levels, matched with some strategic corrections. This reduces hardware requirements without sacrificing the qubit saving. We show that the inherited loss of fidelity is directly given by the rate of carry and borrow bits in the computation. We derive formulas to predict this, complemented by complete gate-level matrix product state simulations of the circuit. Moreover, we analytically describe the effects of possible stochastic control error. We present an in-depth analysis of this approach in the context of Shor's algorithm, focusing on the factoring of RSA-2048. Surprisingly, we find that each of the $7\times {10}^7$ quantum Fourier transforms may be truncated down to $\pi /64$, with additive rotations left only slightly finer. This result is much more efficient than previously realized. We quantify savings in terms of both logical resources and raw magic states, demonstrating that phase adders can be competitive with Toffoli-based constructions.

A doubly excited autodissociating resonant state in positronium hydride has been discovered, which is situated in a Rydberg series converging to the ${\mathrm{H}}^{-}\left(2s^2\right)+e^{+}$ threshold. Previous research has noted a scarcity of such highly excited resonant states, particularly those with a doubly excited nature. The exploration of these states was made possible by employing a projection operator method supported by the stochastic variational method. Accurate calculations of the resonant positions and widths were performed using the complex coordinate rotation method with explicitly correlated Gaussians as basis functions. Our analysis has revealed the intrinsic structural characteristics of these highly excited states. The probability density distribution demonstrates that most resonant states of positronium hydride tend to favor either a ${\mathrm{H}}^{-}+e^{+}$ or ${\mathrm{Ps}}^{-}+{\mathrm{H}}^{+}$ configuration. However, two doubly excited resonant states exhibit a unique characteristic involving both the ${\mathrm{H}}^{-}+e^{+}$ and ${\mathrm{Ps}}^{-}+{\mathrm{H}}^{+}$ configurations. By integrating the probability density distribution with a quantum defect formula, highly excited resonances can be accurately assigned to either the ${\mathrm{H}}^{-}\left(2s^2\right)+e^{+}$ or ${\mathrm{Ps}}^{-}\left(1s^2\right)+{\mathrm{H}}^{+}$ Rydberg series, thereby reducing discrepancies compared to earlier classifications.

We report a combined experimental and theoretical study on the fragmentation dynamics following the ultrafast intermolecular Coulombic decay (ICD) in ${\left({\mathrm{H}}_2\mathrm{O}\right)}_6$ water clusters upon electron impact ionization. By coincident fragment ions and electron momentum spectroscopy, we show that ICD can be initiated by inner-valence ionization of a water molecule. Our ab initio molecular dynamics simulations show that ICD is followed by proton transfer leading to the formation of the ${\left({\mathrm{H}}_2\mathrm{O}\right)}_3·{\mathrm{H}}^{+}\cdots \mathrm{OH}·{\left({\mathrm{H}}_2\mathrm{O}\right)}_2^{+}$ ion-radical complex. We propose a possible dissociative mechanism in which the system further dissociates into a pair of radical ions (${\mathrm{H}}_3{\mathrm{O}}^{+}/{\mathrm{H}}_5{\mathrm{O}}_2^{+}$) and neutral species of water and hydrogen peroxide (${\mathrm{H}}_2{\mathrm{O}}_2$). The calculated kinetic energy spectrum of a ${\mathrm{H}}_3{\mathrm{O}}^{+}/{\mathrm{H}}_5{\mathrm{O}}_2^{+}$ ion pair is in good agreement with experiment. Moreover, the present study of ICD in water provides an underlying production mechanism for the reactive oxygen species of ${\mathrm{H}}_2{\mathrm{O}}_2$ which is not considered previously in the radiolysis processes of water.

A calculation is performed of the parity-violating polarizations in the external electric field, which are associated with the electron electric dipole moment ($e\mathrm{EDM}$) and magnetic quadrupole moment (MQM) of the ${}^{175}\mathrm{Lu}$ nucleus, as well as the determination of the rovibrational structure for the ${}^{175}\mathrm{Lu}{\mathrm{OH}}^{+}$ cation. Beyond the bending of the molecule, the slight effect of the stretching of the distance between Lu and OH is taken into account. This study is required for the preparation of the experiment and for the extraction of the $e\mathrm{EDM}$ and MQM values of ${}^{175}\mathrm{Lu}$ from future measurements.

A circularly polarized laser pulse can induce persistent intramolecular currents by either exciting or ionizing molecules. These two cases are identified as electron currents and hole currents, respectively, and up to now they have been studied only separately. We report ab initio time-dependent density-functional theory (TDDFT) simulations of currents in a molecule, which reveal for the first time that both electron and hole currents can be present simultaneously. By adjusting the intensity of the laser pulse, the balance between the two types of current can be controlled and the overall sign of the current can be switched. We provide a physical explanation for the effect in terms of molecular orbitals, which is consistent with the TDDFT simulations.

Inner-shell $2p_{3/2}$ photoionization of high-$Z$ neutral atoms by linearly polarized light and subsequent $L{\alpha }_1(3d_{5/2}\to 2p_{3/2})$, $L{\alpha }_2(3d_{3/2}\to 2p_{3/2})$, and $L\ell (3s_{1/2}\to 2p_{3/2})$ radiative decays are investigated within the framework of the density-matrix theory. Special attention is paid to angular and polarization behaviors of the radiated $L{\alpha }_1$, $L{\alpha }_2$, and $L\ell$ lines. To do this, relativistic single-configuration Dirac-Hartree-Fock calculations are performed for Ba, Yb, Hg, and Rn atoms with closed subshells. It is found that the $L{\alpha }_1$ line is nearly isotropic and that the $L{\alpha }_2$ and $L\ell$ lines are weakly anisotropic, behaviors that are rather different from the results predicted with nonrelativistic dipole approximations or analytical perturbation theory [V. K. Garg et al., J. Electron Spectrosc. Relat. Phenom. 248, 147054 (2021)]. In contrast, the polarization behaviors of these characteristic lines are found to be more promising for experimental implementation. To be specific, not only are the presently obtained linear polarizations of these lines strong enough to be measurable in experiment, but their dependences on the nuclear charge of atoms and ionizing photon energy are also noteworthy to be readily observed, in particular, for the weakest $L\ell$ line among them, which could be employed for exploring electron screening effect in inner-shell photoionization and decay dynamics of atoms.

By studying the dynamic stability of Bose-Einstein-condensed binary mixtures trapped on the surface of an ideal two-dimensional spherical bubble, we show how the Rabi coupling between the species can modulate the interactions leading to parametric resonances. In this spherical geometry, the discrete unstable angular modes drive both phase separations and spatial patterns, with Faraday waves emerging and coexisting with an immiscible phase. Noticeable is the fact that, in the context of discrete kinetic energy spectrum, the only parameters to drive the emergence of Faraday waves are the $s\text{−}wave$ contact interactions and the Rabi coupling. Once analytical solutions for population dynamics are obtained, the stability of homogeneous miscible species is investigated through Bogoliubov–de Gennes and Floquet methods, with predictions being analyzed by full numerical solutions applied to the corresponding time-dependent coupled formalism.

We study the scissors modes of a harmonically trapped Bose-Einstein condensate under the influence of a synthetic magnetic field, which induces rigid rotational components in the velocity field. Our investigation reveals that the scissors mode, excited in the plane perpendicular to the synthetic magnetic field, becomes coupled to the quadrupole modes of the condensate, giving rise to typical beating effects. Moreover, the two scissors modes excited in the vertical planes are also coupled together by the synthetic magnetic field, resulting in intriguing gyroscope dynamics. Our analytical results, derived from a spinor hydrodynamic theory, are further validated through numerical simulations of the three-dimensional Gross-Pitaevskii equation. These predictions for the condensates subject to a synthetic magnetic field are experimentally accessible with current cold-atom setups and hold promise for potential applications in quantum sensing.

This paper is a joint publication with the paper by Vimal et al. [Phys. Rev. Lett. 131, 203402 (2023)]. High-order harmonic generation (HHG) is an extreme nonlinear optical phenomenon at the heart of modern ultrafast physics. When HHG is driven by two noncollinear beams, one being significantly weaker than the other, the yields of the harmonic emission channels obey a perturbative power law with respect to the drivers' intensity ratio, even though HHG has a nonperturbative efficiency in general. Here, we drive HHG with two different transverse modes and show this power law to be directly imprinted in the spatial structure of the harmonic beamlets. As the driving beam intensities are brought closer, changes in the beamlet profiles reflect a transition from a perturbative to a nonperturbative behavior, understood by generalizing the photon-pathway formalism introduced in the companion paper. This work provides a visual method to study the efficiency of nonlinear optical processes and paves the way for finer all-optical shaping of extreme ultraviolet light.

We present the interesting resonance of two kinds of geometric quantities, namely, the Aharonov-Anandan phase and the time-energy uncertainty, and reveal the relation between resonance and the hidden symmetry in the asymmetric Rabi model by numerical and analytical methods. By combining the counter-rotating hybridized rotating-wave method with time-dependent perturbation theory, we solve systematically the time evolution operator and then obtain the geometric phase of the Rabi model. In comparison with the numerically exact solutions, we find that the analytical results accurately describe the geometric quantities in a wide parameter space. We unveil the effect of the bias on the resonance of geometric quantities: (1) the positions of all harmonic resonances stemming from the shift of the Rabi frequency at the presence of the bias, and (2) the occurrence of even order harmonic resonance due to the bias. When the driving frequency is equal to the subharmonics of the bias, the odd higher-order harmonic resonances disappear. Finally, the hidden symmetry has a resemblance to that of the quantum Rabi model with bias, which indicates the quasienergy spectra are similar to the energy spectra of the latter.

The principle of microscopic reversibility is a fundamental element in the formulation of fluctuation relations and Onsager reciprocal relations. As such, a clear description of whether and how this principle is adapted to the quantum-mechanical scenario might be essential for a better understanding of nonequilibrium quantum processes. Here, we propose a quantum generalization of this principle which highlights the role played by coherence in the symmetry relations involving the probability of observing a quantum transition and that of the corresponding time-reversed process. We study the implications of our findings in the framework of a qubit system interacting with a thermal reservoir and implement an optical experiment that simulates the dynamics. Our theoretical and experimental results show that the influence of coherence is more decisive at low temperatures and that the maximum departure from the classical case does not take place for maximally coherent states. Classical predictions are recovered in the appropriate limits.

Closing the fair sampling loophole in Bell-type experiments is crucial for a better understanding of the fundamentals of quantum mechanics and for realizing the security of quantum cryptography. However, an experimental demonstration of a Bell test without the fair sampling loophole is challenging. A central obstacle in photonic implementations is that the sampling efficiency, including the collection and detection efficiencies, must be above a certain threshold. We here investigate the minimum sampling efficiency for violating a multiparticle Bell inequality in an asymmetric configuration. The results show that the minimum sampling efficiency is arbitrarily close to $\frac{1}{n}$ in the $n$-particle system. Since the security of device-independent quantum key distribution (DI-QKD) protocols relies on the violation of a Bell inequality, we also investigate the application of the asymmetric Bell test in quantum cryptography. Based on the standard DI-QKD protocol, we demonstrate that the minimum sampling efficiency for extracting secure keys is reduced from $92.4\%$ to $84.4\%$. Therefore, we believe our work can serve as a recipe for experimentalists planning to implement DI-QKD.

The Gottesman-Kitaev-Preskill (GKP) code is a promising bosonic quantum error-correcting code, encoding logical qubits into a bosonic mode in such a way that many physically relevant noise types can be corrected effectively. A particularly relevant noise channel is the pure loss channel, which the GKP code is known to protect against. In particular, it is commonly pointed out that losses can be corrected by the GKP code by transforming the losses into random Gaussian displacements through a quantum-limited amplification channel. However, implementing such amplification in practice is not ideal and could easily introduce an additional overhead of noise from associated experimental imperfections. Here, we analyze the performance of teleportation-based GKP error correction against loss in the absence of an amplification channel. We show that amplification is not required to perform GKP error correction and that performing amplification actually worsens the performance for practically relevant parameter regimes.

Unitary $t$-designs have a wide variety of applications in quantum information theory, such as quantum data encryption and randomized benchmarking. However, experimental realizations of $t$-designs are subject to noise. Here we investigate the effect of noise channels on the quality of single-qubit $t$-designs. The noise channels we study are bit flips, phase flips, bit and phase flips, phase damping, amplitude damping, and depolarizing noise. We consider two noise models: The first has noise applied before the $t$-design unitary operations, while the second has noise applied after the unitary operations. We show that the single-qubit 1-design is affected only by amplitude damping, while numeric results obtained for the 2-, 3-, 4-, and 5-designs suggest that a $2t$-design is significantly more sensitive to noise than a $(2t-1)$-design and that, with the exception of amplitude damping, a $(2t+1)$-design is as sensitive to noise as a $2t$-design. Numeric results also reveal substantial variations in sensitivity to noise throughout the Bloch sphere. In particular, $t$-designs appear to be most sensitive to noise when acting on pure states and least sensitive to noise for the maximally mixed state. For depolarizing noise, we show that our two noise models are equivalent, and for the other noise channels, numeric results obtained for the model where noise is applied after the unitaries reflect the transformation of the noise channel into a depolarizing channel, an effect exploited in randomized benchmarking with 2-designs.