We explore the mechanism of the low-order harmonic generation (LOHG) of hydrogen molecular ions in an intense laser field by solving three-dimensional time-dependent Schrödinger equation. Our simulations show that the LOHG of hydrogen molecular ions at large internuclear distances exhibits spectral and temporal fine subpeak structures. Combining with a two-state model and the Morlet transform, the dynamical origin of the LOHG is clarified. We find that the interference in cycles of the multiphoton radiation during the dipole transition between the ground state and the first excited state results in the generation of the spectral subpeak structures. Our results contribute to better understanding of the generation of low-order harmonics.

Thermalization of isolated quantum systems is a long-standing fundamental problem where different mechanisms are proposed over time. We contribute to this discussion by classifying the diverse quench-dynamical behaviors of spin-1 Bose-Einstein condensates, which includes well-defined quantum collapse and revivals, thermalization, and certain special cases. These special cases are either nonthermal equilibration with no revival but a collapse even though the system has finite degrees of freedom or no equilibration with no collapse and revival. Given that some integrable systems are already shown to demonstrate the weak form of eigenstate thermalization hypothesis (ETH), we determine the regions where ETH holds and fails in this integrable isolated quantum system. The reason behind both thermalizing and nonthermalizing behaviors in the same model under different initial conditions is linked to the discussion of “rare” nonthermal states existing in the spectrum. We also propose a method to predict the collapse and revival time scales and find how they scale with the number of particles in the condensate. We use a sudden quench to drive the system to nonequilibrium and hence the theoretical predictions given in this paper can be probed in experiments.

We present a general framework for the generation of random unitaries based on random quenches in atomic Hubbard and spin models, forming approximate unitary $n$-designs, and their application to the measurement of Rényi entropies. We generalize our protocol presented in Elben et al. [Phys. Rev. Lett. 120, 050406 (2018)] to a broad class of atomic and spin-lattice models. We further present an in-depth numerical and analytical study of experimental imperfections, including the effect of decoherence and statistical errors, and discuss connections of our approach with many-body quantum chaos.

We present a theoretical and numerical study of light propagation in graded-index (GRIN) multimode fibers where the core diameter has been periodically modulated along the propagation direction. The additional degree of freedom represented by the modulation permits us to modify the intrinsic spatiotemporal dynamics which appears in multimode fibers. More precisely, we show that modulating the core diameter at a periodicity close to the self-imaging distance allows us to induce a moiré-like pattern, whereas a longer periodicity induces an adiabatic modulation or the self-imaging pattern. This complex dynamics modifies the geometric parametric instability gain observed in homogeneous GRIN fibers by generating new spectral peaks.

We propose a formal resource-theoretic approach to quantify the degree of polarization of two- and three-dimensional random electromagnetic fields. This endows the space of spectral polarization matrices with the orders induced by majorization or convex mixing that naturally recover the best-known polarization measures.

In this work, we show that the disorder-free Kubo formula for the nonequilibrium value of an observable due to a dc electric field, represented by $E_x\widehat{x}$ in the Hamiltonian, can be interpreted as the standard time-independent theory response of the observable due to a time- and position-independent perturbation $H_{\text{MF}}$. We derive the explicit expression for $H_{\text{MF}}$ and show that it originates from the adiabatic approximation to $\langle k|E_x\widehat{x}$ in which transitions between the different eigenspinor states of a system are forbidden. The expression for $H_{\text{MF}}$ is generalized beyond the real spin degree of freedom to include other spinlike discrete degrees of freedom (e.g., valley and pseudospin). By direct comparison between Kubo formula and the time-independent perturbation theory, as well as the Sundaram-Niu wave-packet formalism, we show that $H_{\text{MF}}$ reproduces the effect of the $E$ field, i.e., $E_x\widehat{x}$, up to the first order. This replacement suggests the emergence of a spin current term that is not captured by the standard Kubo formula spin current calculation. We illustrate this via the exemplary spin current for the heavy-hole spin-$\frac{3}{2}$ Luttinger system.

An integral representation for scattering phase shifts is obtained based on a modified version of Milne's phase-amplitude approach [W. E. Milne, Phys. Rev. 35, 863 (1930)]. We replace Milne's nonlinear differential equation for the amplitude function $y$ with an equivalent linear equation for the envelope $\rho =y^2$, which renders the integral representations highly amenable to numerical implementations. The phase shift is obtained directly from Milne's phase function, which in turn is expressed in terms of the envelope function. We illustrate the advantages of the representation with two scattering potentials. The integral representation presented in this work is fully general and it can be used for any type of scattering potential, including the Coulomb potential.

The complex behavior of a molecular wave packet initiated by an extreme ultraviolet (XUV) pulse is investigated with noncollinear wave mixing spectroscopy. A broadband XUV pulse spanning 12–16 eV launches a wave packet in ${\mathrm{H}}_2$ comprising a coherent superposition of multiple electronic and vibrational levels. The molecular wave packet evolves freely until a delayed few-cycle optical laser pulse arrives to induce nonlinear signals in the XUV via four-wave mixing (FWM). The angularly resolved FWM signals encode rich energy exchange processes between the optical laser field and the XUV-excited molecule. The noncollinear geometry enables spatial separation of ladder and V- or Λ-type transitions induced by the optical field. Ladder transitions, in which the energy exchange with the optical field is around 3 eV, appear off axis from the incident XUV beam. Each vibrationally revolved FWM line probes a different part of the wave packet in energy, serving as a promising tool for energetic tomography of molecular wave packets. V- or Λ-type transitions, in which the energy exchange is well under 1 eV, result in on-axis nonlinear signals. The first-order versus third-order interference of the on-axis signal serves as a mapping tool of the energy flow pathways. Intra- and interelectronic potential energy curve transitions are decisively identified. The current study opens possibilities for accessing complete dynamic information in XUV-excited complex systems.

The electron shakeoff of ${}^{19}\mathrm{F}$ and ${}^{35}\mathrm{Cl}$ atoms resulting from the ${\beta }^{+}$ decay of ${}^{19}\mathrm{Ne}^{+}$ and ${}^{35}\mathrm{Ar}^{+}$ ions has been investigated using a Paul trap coupled to a time of flight recoil-ion spectrometer. The charge-state distributions of the recoiling daughter nuclei were compared to theoretical calculations based on the sudden approximation and accounting for subsequent Auger processes. The excellent agreement obtained for ${}^{35}\mathrm{Cl}$ is not reproduced in ${}^{19}\mathrm{F}$. The shortcoming is attributed to the inaccuracy of the independent particle model employed to calculate the primary shakeoff probabilities in systems with rather low atomic numbers. This calls for more elaborate calculations, including explicitly the electron-electron correlations.

We demonstrate the laser cooling of ${}^{85}\mathrm{Rb}$ atoms in a two-dimensional optical lattice. We follow the two-step degenerate Raman sideband cooling scheme [Kerman et al., Phys. Rev. Lett. 84, 439 (2000)], where a fast cooling of atoms to an auxiliary state is followed by a slow cooling to a dark state. This method has the advantage of independent control of the heating rate and cooling rate from the optical pumping beam. We operate the lattice at a Lamb-Dicke parameter $\eta =0.45$ and show the cooling of spin-polarized ${}^{85}\mathrm{Rb}$ atoms to the recoil temperature in both dimensions within 2.4 ms with the aid of adiabatic cooling.

Interference experiments have been paramount in our understanding of quantum mechanics and are frequently the basis of testing the superposition principle in the framework of quantum theory. In recent years, several studies have challenged the nature of wave-function interference from the perspective of Born's rule—namely, the manifestation of so-called high-order interference terms in a superposition generated by diffraction of the wave functions. Here we present an experimental test of multipath interference in the diffraction of metastable helium atoms, with large-number counting statistics, comparable to photon-based experiments. We use a variation of the original triple-slit experiment and accurate single-event counting techniques to provide a new experimental bound of $2.9\times {10}^{-5}$ on the statistical deviation from the commonly approximated null third-order interference term in Born's rule for matter waves. Our value is on the order of the maximal contribution predicted for multipath trajectories by Feynman path integrals.

For quantum fluids, the role of quantum fluctuations may be significant in several regimes such as when the dimensionality is low, the density is high, the interactions are strong, or for low particle numbers. In this paper, we propose a fundamentally different regime for enhanced quantum fluctuations without being restricted by any of the above conditions. Instead, our scheme relies on the engineering of an effective attractive interaction in a dilute, two-component Bose-Einstein condensate (BEC) consisting of thousands of atoms. In such a regime, the quantum spin fluctuations are significantly enhanced (atom bunching with respect to the noninteracting limit) since they act to reduce the interaction energy, a remarkable property given that spin fluctuations are normally suppressed (antibunching) at zero temperature. In contrast to the case of true attractive interactions, our approach is not vulnerable to BEC collapse. We numerically demonstrate that these quantum fluctuations are experimentally accessible by either spin or single-component Bragg spectroscopy, offering a useful platform on which to test beyond-mean-field theories. We also develop a variational model and use it to analytically predict the shift of the immiscibility critical point, finding good agreement with our numerics.

We propose a multimode optomechanical system to realize tunable optical nonreciprocity that has the prospect of making an optical diode for information technology. The proposed model consists of two subsystems, each of which contains two optical cavities, injected with a classical field and a quantum signal via a 50:50 beam splitter, and a mechanical oscillator, coupled to both cavities via optomechanical coupling. Meanwhile two cavities and an oscillator in a subsystem are respectively coupled to their corresponding cavities and an oscillator in the other subsystem. Our scheme yields nonreciprocal effects at different frequencies with opposite directions, but each effective linear optomechanical coupling can be controlled by an independent classical one-frequency pump. With this setup one is able to apply quantum states with large fluctuations, which extends the scope of applicable quantum states, and exploit the independence of paths. Moreover, the optimal frequencies for nonreciprocal effects can be controlled by adjusting the relevant parameters. We also exhibit the path switching of two directions, from a mechanical input to two optical output channels, via tuning the signal frequency. In experiment, the considered scheme can be tuned to reach small damping rates of the oscillators relative to those of the cavities, which is more practical and requires less power than in previous schemes.

The elastic Rayleigh scattering of twisted light and, in particular, the polarization (transfer) of the scattered photons have been analyzed within the framework of second-order perturbation theory and Dirac's relativistic equation. Special attention was paid hereby to the scattering on three different atomic targets: single atoms, a mesoscopic (small) target, and a macroscopic (large) target, which are all centered with regard to the beam axis. Detailed calculations of the polarization Stokes parameters were performed for ${\mathrm{C}}^{5+}$ ions and for twisted Bessel beams. It is shown that the polarization of scattered photons is sensitive to the size of an atomic target and to the helicity, the opening angle, and the projection of the total angular momentum of the incident Bessel beam. These computations indicate more that the Stokes parameters of the (Rayleigh) scattered twisted light may significantly differ from their behavior for an incident plane-wave radiation.

We propose a hierarchy set of minimal optical Raman lattice schemes to pave the way for experimental realization of high-dimensional spin-orbit (SO) couplings for ultracold atoms, including two-dimensional (2D) Dirac type, 2D Rashba type, and three-dimensional (3D) Weyl type. The proposed Dirac-type SO coupling exhibits precisely controllable high symmetry, for which a large topological phase region is predicted. The generation of 2D Rashba and 3D Weyl types requires that two sources of laser beams have distinct frequencies of factor 2 difference. Surprisingly, we find that ${}^{133}\mathrm{Cs}$ atoms provide an ideal candidate for the realization. A common and essential feature is of high controllability and absent of any fine-tuning in the realization, and the resulting SO coupled ultracold atoms have a long lifetime. In particular, a long-lived topological Bose gas of 2D Dirac SO coupling has been proved in the follow-up experiment. These schemes essentially improve over the current experimental accessibility and controllability, and open a realistic way to explore novel high-dimensional SO physics, particularly quantum many-body physics and quantum far-from-equilibrium dynamics with novel topology for ultracold atoms.

Given an arbitrary measurement over a system of interest, the outcome of a posterior measurement can be used for improving the statistical estimation of the system state after the former measurement. Here, we realize an informational-entropic study of this kind of (Bayesian) retrodicted quantum measurement formulated in the context of quantum state smoothing. We show that the (average) entropy of the system state after the retrodicted measurement (smoothed state) is bounded from below and above by the entropies of the first measurement when performed in a selective and nonselective standard predictive way, respectively. For bipartite systems the same property is also valid for each subsystem. Their mutual information, in the case of a former single projective measurement, is also bounded in a similar way. The corresponding inequalities provide a kind of retrodicted extension of Holevo bound for quantum communication channels. These results quantify how much information gain is obtained through retrodicted quantum measurements in quantum state smoothing. While an entropic reduction is always granted, in bipartite systems mutual information may be degraded. Relevant physical examples confirm these features.

Supraquantum nonlocality refers to correlations that are more nonlocal than allowed by quantum theory but still physically conceivable in postquantum theories, in the sense of respecting the basic no-faster-than-light communication principle. While supraquantum correlations are relatively well understood for finite-dimensional systems, little is known in the infinite-dimensional case. Here, we study supraquantum nonlocality for bipartite systems with two measurement settings and infinitely many outcomes per subsystem. We develop a formalism for generic no-signaling black-box measurement devices with continuous outputs in terms of probability measures, instead of probability distributions, which involves a few technical subtleties. We show the existence of a class of supraquantum Gaussian correlations, which violate the Tsirelson bound of an adequate continuous-variable Bell inequality. We then introduce the continuous-variable version of the celebrated Popescu–Rohrlich (PR) boxes, as a limiting case of the above-mentioned Gaussian ones. Finally, we characterize the geometry of the set of continuous-variable no-signaling correlations. Namely, we show that that the convex hull of the continuous-variable PR boxes is dense in the no-signaling set. We also show that these boxes are extreme in the set of no-signaling behaviors and provide evidence suggesting that they are indeed the only extreme points of the no-signaling set. Our results lay the grounds for studying generalized-probability theories in continuous-variable systems.

The device-independent approach to quantum key distribution (QKD) aims to establish a secret key between two or more parties with untrusted devices, potentially under full control of a quantum adversary. The performance of a QKD protocol can be quantified by the secret key rate, which can be lower bounded via the violation of an appropriate Bell inequality in a setup with untrusted devices. We study secret key rates in the device-independent scenario for different quantum repeater setups and compare them to their device-dependent analogon. The quantum repeater setups under consideration are the original protocol by Briegel et al. [Phys. Rev. Lett. 81, 5932 (1998)] and the hybrid quantum repeater protocol by van Loock et al. [Phys. Rev. Lett. 96, 240501 (2006)]. For a given repeater scheme and a given QKD protocol, the secret key rate depends on a variety of parameters, such as the gate quality or the detector efficiency. We systematically analyze the impact of these parameters and suggest optimized strategies.

Single ionization by electron impact of the ${\mathrm{Se}}^{3+}$ ion is investigated in the Dirac-Fock-Slater approximation. Contributions from direct ionization (DI), excitation-autoionization, and resonant-excitation double-autoionization processes are taken into account. Good agreement with the experiment is obtained at the lower energies of the incident electron when the DI process is considered in the potential of the ionizing ion. On the other hand, the potential of the ionized ion has to be used for the higher energies of the electron. It is shown that ionization-ionization and ionization-excitation-ionization processes can play the significant role in the double ionization of ${\mathrm{Se}}^{3+}$ ions.

The ab initio method based on the Faddeev-Merkuriev equations is used to calculate cross sections involving the $(\overline{p},e^{+},e^{-})$ three-body system, with an emphasis on antihydrogen formation $\left(\overline{\mathrm{H}}\right)$ via antiproton $\left(\overline{p}\right)$ scattering on positronium. This system is studied in the energy range between the $e^{-}+\overline{\mathrm{H}}(n=2)$ and the $e^{-}+\overline{\mathrm{H}}(n=3)$ thresholds, where precisely calculated cross sections can be useful for future experiments (GBAR, AEGIS, etc.) aiming to produce antihydrogen atoms. A special treatment is developed to take into account the long-range charge-dipole interaction effect on the wave function. Emphasis is placed on the impact of Feshbach resonances and Gailitis-Damburg oscillations appearing in the vicinity of the $\overline{p}+\mathrm{Ps}(n=2)$ threshold.