The study of information scrambling in many-body systems has sharpened our understanding of quantum chaos, complexity, and gravity. Here, we extend the framework for exploring information scrambling to infinite-dimensional continuous variable (CV) systems. Unlike their discrete variable cousins, continuous variable systems exhibit two complementary domains of information scrambling: (i) scrambling in the phase space of a single mode and (ii) scrambling across multiple modes of a many-body system. Moreover, for each of these domains, we identify two distinct types of scrambling; genuine scrambling, where an initial operator localized in phase space spreads out, and quasiscrambling, where a local ensemble of operators distorts but the overall phase space volume remains fixed. To characterize these behaviors, we introduce a CV out-of-time-order correlation (OTOC) function based upon displacement operators and offer a number of results regarding the CV analog for unitary designs. Finally, we investigate operator spreading and entanglement growth in random local Gaussian circuits; to explain the observed behavior, we propose a simple hydrodynamical model that relates the butterfly velocity, the growth exponent, and the diffusion constant. Experimental realizations of continuous variable scrambling as well as its characterization using CV OTOCs will be discussed.

Dispersion forces such as van der Waals forces between two microscopic particles, the Casimir-Polder forces between a particle and a macroscopic object, or the Casimir force between two dielectric objects are well studied in vacuum. However, in realistic situations the interacting objects are often embedded in an environmental medium. Such a solvent influences the induced dipole interaction. With the framework of macroscopic quantum electrodynamics, these interactions are mediated via an exchange of virtual photons. Via this method the impact of a homogeneous solvent medium can be expressed as local-field corrections leading to excess polarizabilities which have previously been derived for hard boundary conditions. In order to develop a more realistic description, we investigate a one-dimensional analog system illustrating the influence of a continuous dielectric profile.

We present ultrahigh-resolution data on fully differential cross sections for single ionization of helium induced by 1 MeV proton impact. In the present work we explore a different regime of kinematic conditions in terms of momentum transfer and electron energies than previously published data. These data are compared with different theoretical calculations. Reasonable agreement between the first Born approximation and experiment is obtained in the kinematic regime close to the Bethe ridge. Far from this region the calculated binary peak is shifted with respect to experiment. In order to resolve this problem, we analyze several theoretical mechanisms beyond the customary first Born approximation theory. These mechanisms include the 3C model (three Coulomb functions), effective charges, off-shell pair $T$ matrices instead of pair potentials, and semiclassical postcollision interaction. We find that a combination of the 3C model with a semiclassical postcollision interaction effect may explain the observed discrepancy.

Initial-state symmetry has been underappreciated in strong-field spectroscopies, where laser fields dominate the dynamics. We demonstrate numerically that the transverse photoelectron phase structure arising from this symmetry is robust in strong-field rescattering and manifests in strong-field photoelectron spectra. Interpretation of rescattering experiments need to take these symmetry effects into account. In turn, transverse photoelectron phase structures may enable attosecond super-resolution imaging with structured electron beams.

The amplification of ultrashort extreme-ultraviolet (XUV) pulses in argon in high-order harmonic generation processes is studied by using the time-dependent Schrödinger equation in the spin-free one-active-electron and single-atom approximation. We consider a neutral argon atom initially in the valence 3p state and a sufficiently intense two-cycle driving infrared (IR) pulse for the atom to be mainly ionized after the first laser cycle. The correlated dynamics and transitions from the valence 3p to a virtual subvalence 3s state and in the ionized regions are examined by synchronizing a 1.5-fs XUV pulse to the IR pulse. The calculated single-atom gain spectrum (26–45 eV) agrees with recent experimental measurements. We discuss different channels that can be present in the gain process as a function of pulse parameters and through an analysis of the dynamics of the populations in terms of field-free eigenstates. When the XUV pulse is considered at the end of the driving IR field the amplification is due to contributions of stimulated recombination from excited Rydberg and low energy continuum states to the 3s and 3p states of argon. In regions where the IR field is intense, high energy and angular momentum states are populated and the medium can interact with the pulses through bound and continuum states involving parametric transitions, which is further confirmed by studying classical electron trajectories. We discuss how these parametric interactions might be suitable for amplification of photon energies far from the ionization threshold as observed in the experiments.

The angular correlation functions (ACFs) of a pair of Lyman-$\alpha$ photons in photodissociation of ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ are measured with linearly polarized incident light at a 33.66-eV incident photon energy in a wider angular range at a narrower angular step with smaller distortion than before [Y. Nakanishi et al., Phys. Rev. A 90, 043405 (2014)] so that we identify the atom-pair state emitting the pair of Lyman-$\alpha$ photons and find out whether the atom pair is entangled or not. Searching for reasonable $2p$ atom-pair states that reproduce the experimental ACFs to solve the issue, we show that hydrogen molecules are photoexcited to the $Q_2{}^1{\mathrm{\Pi }}_u\left(1\right)$ state in the Franck-Condon region and then the $Q_2{}^1{\mathrm{\Pi }}_u\left(1\right)$ state comes to superpose with the $Q_2{}^3{\mathrm{\Sigma }}_u^{+}\left(2\right)$ state as the internuclear distance increases to infinity. The superposition is brought about by the spin-orbit coupling, which is effective around infinite internuclear distance because the potential-energy curves of those states are close to each other, but is negligibly small around the Franck-Condon region because they are apart from each other. The $2p$ atom pairs turn out to be in the $1_u$ superposition state, which is entangled. We therefore conclude that an entangled pair of hydrogen atoms is spontaneously produced through the photodissociation of a hydrogen molecule, and the entanglement originates from the $1_u$ symmetry properties, which are invariant during the dissociation from the Franck-Condon region towards infinite internuclear distance.

We consider evolution of one-dimensional nonlinear-Schrödinger (NLS) two-soliton complexes (breathers) with narrow repulsive or attractive potentials (barrier or well, respectively). By means of systematic simulations, we demonstrate that the breather may either split into constituent fundamental solitons (fragments) moving in opposite directions or bounce as a whole from the barrier. A critical initial position of the breather, which separates these scenarios, is predicted by an analytical approximation. The narrow potential well tends to trap the fragment with the larger amplitude, while the other one escapes. The interaction of the breather with a nonlinear potential barrier is also considered. The ratio of amplitudes of the emerging free solitons may be different from the $3:1$ value suggested by the exact NLS solution, especially in the case of the nonlinear potential barrier. Postsplitting velocities of escaping solitons may be predicted by an approximation based on the energy balance.

Models based on non-Hermitian Hamiltonians can exhibit a range of surprising and potentially useful phenomena. Physical realizations typically involve couplings to sources of incoherent gain and loss; this is problematic in quantum settings because of the unavoidable fluctuations associated with this dissipation. Here, we present several routes for obtaining unconditional non-Hermitian dynamics in nondissipative quantum systems. We exploit the fact that quadratic bosonic Hamiltonians that do not conserve particle number give rise to non-Hermitian dynamical matrices. We discuss the nature of these mappings from non-Hermitian to Hermitian Hamiltonians, and explore applications to quantum sensing, entanglement dynamics, and topological band theory. The systems we discuss could be realized in a variety of photonic and phononic platforms using the ubiquitous resource of parametric driving.

Motivated by recent experiments on ${}^6\mathrm{Li}\text{−}{}^{133}\mathrm{Cs}$ atomic mixtures with high mass imbalance, we study the Efimov correlation in an atomic system of two heavy bosons (${}^{133}\mathrm{Cs}$) immersed in a bath of light fermions (${}^6\mathrm{Li}$). Using the Born-Oppenheimer approximation, we identify two different regimes, depending on the Fermi momentum of light fermions ($k_F$) and the boson-fermion scattering length $a_s(<0)$, where the presence of an underlying Fermi sea plays distinct roles in the Efimov-type binding of bosons. Namely, in the regime $k_F\left|a_s\right|\lesssim 1$ ($k_F\left|a_s\right|\gtrsim 1$), the Fermi sea induces an attractive (repulsive) effective interaction between bosons and thus favors (disfavors) the formation of a bound state, which can be seen as an Efimov trimer dressed by a fermion cloud. Interestingly, this implies nonmonotonic behavior of these bound states as increasing the fermion density (or $k_F$). Moreover, we establish a generalized universal scaling law for the emergence and variation of such dressed Efimov bound states when incorporating a new scale ($k_F$) brought on by the Fermi sea. These results can be directly tested in Li-Cs cold-atom experiments by measuring the modified bound-state spectrum and the shifted Efimov resonance, which manifest an emergent nontrivial Efimov correlation in a fermionic many-body environment.

Thermodynamic noise places a fundamental limit on the frequency stability of dielectric optical resonators. Here, we present the characterization of thermorefractive noise in photonic-chip-based silicon-nitride (${\text{Si}}_3{\text{N}}_4$) microresonators and show that thermorefractive noise is the dominant thermal noise source in the platform. We employed balanced homodyne detection to measure the thermorefractive noise spectrum of microresonators of different diameters. The measurements are in good agreement with theoretical models and finite element method simulations. Our characterization sets quantitative bounds on the scaling and absolute magnitude of thermal noise in photonic-chip-based microresonators. An improved understanding of thermorefractive noise can prove valuable in the design considerations and performance limitations of future photonic integrated devices.

We report on the experimental observation of dark-bright and antidark-bright vector solitons supported by third-order dispersion in a weakly birefringent cavity fiber laser. Using a cavity dispersion and birefringence management technique we constructed a weakly birefringent cavity fiber laser with near-zero net cavity dispersion. Operating the fiber laser in either the net normal or net anomalous dispersion regime, we found that both dark-bright and antidark-bright vector solitons could be simultaneously formed as a result of incoherent cross-polarization phase modulation. Our experimental results confirm the existence of antidark-bright vector solitons and the coexistence of dark-bright and antidark-bright vector solitons in a real physical system.

We show that matter-wave interference fringes formed by two overlapping atomic clouds can yield information about the nonlocal Bell correlations. To this end, we consider a simple atomic interferometer, where the clouds are released from the double-well potential and the relative phase is estimated from the density fit to this interference pattern. The Bell correlations can be deduced from the sensitivity of the phase obtained in this way. We examine the relation between these two quantities for a wide range of ground states of the double-well, scanning through the attractive and the repulsive interactions. The presented analysis includes the effects of finite temperature, when excited states are thermally occupied. We also consider the impact of the spatial resolution of the single-atom detectors, the fluctuations of the energy mismatch between the wells, and the atom-number fluctuations. These results establish a link between the fundamental (nonlocality) and the application-oriented (quantum metrology) aspects of entanglement.

The fast-forward scheme of adiabatic quantum dynamics is applied to finite regular spin clusters with various geometries and the nature of driving interactions is elucidated. Fast forward is the quasiadiabatic dynamics guaranteed by regularization terms added to the reference Hamiltonian, followed by a rescaling of time with the use of a large scaling factor. With the help of the regularization terms consisting of pairwise and three-body interactions, we apply the proposed formula [I. Setiawan et al., Phys. Rev. A 96, 052106 (2017)] to regular triangle and open linear chains for $N=3$ spin systems and to triangular pyramid, square, primary star graph, and open linear chains for $N=4$ spin systems. The geometry-induced symmetry greatly decreases the rank of the coefficient matrix of the linear algebraic equation for regularization terms. Choosing a transverse Ising Hamiltonian as a reference, we find, for $N=3$ spin clusters, that the driving interaction consists of only the geometry-dependent pairwise interactions and there is no need for the three-body interaction and, for $N=4$ spin clusters, that the geometry-dependent pairwise interactions again constitute a major part of the driving interaction, whereas the universal three-body interaction free from the geometry is necessary but plays a subsidiary role. Our scheme predicts the practical driving interaction in accelerating the adiabatic quantum dynamics of structured regular spin clusters.

Relativistic $\mathcal{PT}$-symmetric fermionic interacting systems are studied in $1+1$ and $3+1$ dimensions. The noninteracting Dirac equation is separately $\mathcal{P}$ and $\mathcal{T}$ invariant. The objective here is to include non-Hermitian $\mathcal{PT}$-symmetric interaction terms that give rise to real spectra. Such interacting systems could be physically realistic and could describe new physics. The simplest such non-Hermitian Lagrangian density is $\mathcal{L}={\mathcal{L}}_0+{\mathcal{L}}_{\mathrm{int}}=\overline{\psi }(i\partial /-m)\psi -g\overline{\psi }{\gamma }^5\psi$. The associated relativistic Dirac equation is $\mathcal{PT}$ invariant in $1+1$ dimensions and the associated Hamiltonian commutes with $\mathcal{PT}$. However, the dispersion relation $p^2=m^2-g^2$ shows that the $\mathcal{PT}$ symmetry is broken (the eigenvalues become complex) in the chiral limit $m\to 0$. For field-theoretic interactions of the form ${\mathcal{L}}_{\mathrm{int}}=-g{\left(\overline{\psi }{\gamma }^5\psi \right)}^N$ with $N=2,3$, which we can only solve approximately, we also find that if the associated (approximate) Dirac equation is $\mathcal{PT}$ invariant, the dispersion relation always gives rise to complex energies in the chiral limit $m\to 0$. Other models are studied in which $x$-dependent $\mathcal{PT}$-symmetric potentials such as $i{x}^3, -x^4, i\kappa /x$, Hulthén, or periodic potentials are coupled to the fermionic field $\psi$ using vector or scalar coupling schemes or combinations of both. For each of these models the classical trajectories in the complex-$x$ plane are examined. Some combinations of these potentials can be solved numerically, and it is shown explicitly that a real spectrum can be obtained. In $3+1$ dimensions, while the simplest system $\mathcal{L}={\mathcal{L}}_0+{\mathcal{L}}_{\mathrm{int}}=\overline{\psi }(i\partial /-m)\psi -g\overline{\psi }{\gamma }^5\psi$ resembles the $1+1$-dimensional case, the Dirac equation is not $\mathcal{PT}$ invariant because ${\mathcal{T}}^2=-\mathbb{1}$. This explains the appearance of complex eigenvalues as $m\to 0$. Other Lorentz-invariant two-point and four-point interactions are considered that give non-Hermitian $\mathcal{PT}$-symmetric terms in the Dirac equation. Only the axial vector and tensor Lagrangian interactions ${\mathcal{L}}_{\mathrm{int}}=-i\overline{\psi }{\tilde{B}}_{\mu }{\gamma }^5{\gamma }^{\mu }\psi$ and ${\mathcal{L}}_{\mathrm{int}}=-i\overline{\psi }{T}_{\mu \nu }{\sigma }^{\mu \nu }\psi$ fulfill both requirements of $\mathcal{PT}$ invariance of the associated Dirac equation and non-Hermiticity. The dispersion relations show that both interactions lead to complex spectra in the chiral limit $m\to 0$. The effect on the spectrum of the additional constraint of self-adjointness of the Hamiltonian with respect to the $\mathcal{PT}$ inner product is investigated.

Microwave magnetometry is essential to a variety of modern electronic techniques, most notably integrated circuits. The nitrogen-vacancy center in diamond has shown the ability of nanoscale resolution for the microwave magnetic field measurement and imaging. However, the characterization of the wideband magnetic field remains a challenge. Here we experimentally demonstrated a wideband microwave magnetometry with an off-resonance protocol based on the Bloch-Siegert shift effect. The off-resonance microwave magnetic field shifts the energy level of the nitrogen-vacancy center. It results in a phase accumulation during the evolution of the superposition state of the quantum sensor. According to this effect, by optimizing the evolution time, we experimentally verified the bandwidth widening of an order of magnitude compared with the Rabi oscillation, i.e., on-resonance method with an acceptable decrease of the sensitivity. In addition, we extracted the microwave frequency with a two-qubit system, which consists of a nitrogen-vacancy center and a nearby ${}^{13}\mathrm{C}$ nucleus. This approach enables the building of a wideband and potentially nanoscale microwave magnetometry to allow various potential applications, such as electronic circuits development.

Bound entangled (BE) states are strange in nature: a nonzero amount of free entanglement is required to create them but no free entanglement can be distilled from them under local operations and classical communication (LOCC). Even though the usefulness of such states has been shown in several information processing tasks, there exists no simple method to characterize them for an arbitrary composite quantum system. Here we present a $(d-3)/2$-parameter family of BE states each with positive partial transpose (PPT). This family of PPT-BE states is introduced by constructing an unextendible product basis (UPB) in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$ with $d$ odd and $d\ge 5$. The range of each such PPT-BE state is contained in a $2(d-1)$-dimensional entangled subspace, whereas the associated UPB subspace is of dimension ${(d-1)}^2+1$. We further show that each of these PPT-BE states can be written as a convex combination of $(d-1)/2$ rank-4 PPT-BE states. Moreover, we prove that these rank-4 PPT-BE states are extreme points of the convex compact set $\mathcal{P}$ of all PPT states in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$, namely, the Peres set. An interesting geometric implication of our result is that the convex hull of these rank-4 PPT-BE extreme points—the $(d-3)/2$ simplex—is sitting on the boundary between the set $\mathcal{P}$ and the set of non-PPT states. We also discuss consequences of our construction in the context of quantum state discrimination by LOCC.

We put forward the idea of lattice quantum magnetometry, i.e., quantum sensing of magnetic fields by a charged (spinless) particle placed on a finite two-dimensional lattice. In particular, we focus on the detection of a locally static transverse magnetic field, either homogeneous or inhomogeneous, by performing ground-state measurements. The system turns out to be of interest as a quantum magnetometer, since it provides non-negligible quantum Fisher information (QFI) in a large range of configurations. Moreover, the QFI shows some relevant peaks, determined by the spectral properties of the Hamiltonian, suggesting that certain values of the magnetic fields may be estimated better than others, depending on the value of other tunable parameters. We also assess the performance of coarse-grained position measurement, showing that it may be employed to realize nearly optimal estimation strategies.

Large-scale relativistic calculations are performed for the transition energy and line strength of the $1s^{2}2s2p{}^{1}P_1-1s^{2}2s^2{}^{1}S_0$ transition in Be-like carbon. Based on the multiconfiguration Dirac-Hartree-Fock (MCDHF) approach, different correlation models are developed to account for all major electron-electron correlation contributions. These correlation models are tested with various sets of the initial and the final-state wave functions. The uncertainty of the predicted line strength due to missing correlation effects is estimated from the differences between the results obtained with those models. The finite nuclear mass effect is accurately calculated taking into account the energy, wave functions, as well as operator contributions. As a result, a reliable theoretical benchmark of the $E1$ line strength is provided to support high-precision lifetime measurement of the $1s^{2}2s2p{}^{1}P_1$ state in Be-like carbon.

An experimental setup has been implemented to obtain absolute total electron detachment cross sections and relative ionization cross sections in the energy range 50–7000 eV in gas-phase collisions between anionic beams and neutral molecular targets. The primary anionic beam (${{\mathrm{O}}_2}^{-}$) is produced through a pulsed hollow cathode discharge-induced plasma, deflected and focused towards the collision region where the molecular target is maintained at a well-known pressure. Electron detachment cross sections are measured from the attenuation of the ${{\mathrm{O}}_2}^{-}$ beam after interaction with ${\mathrm{N}}_2$ molecules confined in a gas cell. Negative and positive fragment ions produced during the collisions are extracted and mass analyzed by time-of-flight mass spectrometry. Relative ionization cross sections are derived from the ratio of the measured positive ion fragment intensities (${{\mathrm{N}}_2}^{+}$, ${\mathrm{N}}^{+}$) to the primary ${{\mathrm{O}}_2}^{-}$ beam intensity.