Bell inequalities are relevant for many problems in quantum information science, but finding them for many particles is computationally hard. Recently, a computationally feasible method called cone-projection technique has been developed to find all optimal Bell inequalities under some constraints, which may be given by some symmetry or other linear conditions. In this paper we extend this work in several directions. We use the method to generalize the I4422 inequality to three particles and a so-called guess-your-neighbor's-input inequality to four particles. Additionally, we find Bell inequalities for three particles that generalize the I3322 inequality and the Clauser-Horne-Shimony-Holt inequality at the same time. We discuss the obtained inequalities in some detail and characterize their violation in quantum mechanics.

The $LMM$ Auger spectra of krypton are measured using the photon energies $h\nu =1709$ eV, 1792 eV, 1950 eV, and 13 keV. This approach allows separating the contributions from the various core holes $L_1, L_2$, and $L_3$. Previously unobserved transitions are presented. Complementary theoretical work is performed allowing the assignment of the spectral features. The $L_{2,3}Y\text{−}MMY$ ($Y=M_{4,5},N_{1,2,3})$ Auger transitions of ${\mathrm{Kr}}^{2+}$ formed via Coster-Kronig Auger decay of the core holes $L_1$ and $L_2$ are also investigated. These spectra comprise about 4000 and 13 000 transitions, respectively, so that only general statements on the assignment, such as the configurations involved in the transitions, can be given.

Using an improved quantitative rescattering model, we calculate the correlated two-electron momentum distributions (CMDs) for nonsequential double ionization of Ar exposed to intense laser pulses with a wavelength of 790 nm at a peak intensity of $1.0\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$. We analyze the drastic variations in the CMDs that were observed by Kübel et al. [New J. Phys. 16, 033008 (2014)] in the transition from near-single-cycle to multicycle driving laser pulses. Our model reproduces their experimental data well. We also find that the transition from near-single-cycle to multicycle driving laser pulses depends strongly on the details of the pulse envelope. Special attention is paid to the mechanisms responsible for the cross-shaped structure observed experimentally with 4 fs pulses. Our analysis reveals that the cross-shaped structure in the carrier-envelope phase-averaged CMD for near-single-cycle pulses can be attributed to strong backward scattering of the recolliding electron as well as the narrow momentum distributions of the tunnel-ionized electrons compared to those for long pulses. This also explains why the cross-shaped distributions collapse to a rather structureless distribution when the pulse duration is increased to 8 fs.

We study the circular shaking of a two-dimensional optical lattice, which is essentially a $(2+1)$-dimensional space-time lattice exhibiting periodicities in both spatial and temporal dimensions. The near-resonant optical shaking considered here dynamically couples the low-lying $s$ band and the first excited $p$ bands by transferring a photon of shaking frequency. The intertwined space-time symmetries are further uncovered to elucidate the degeneracy in the spectrum solved with the generalized Bloch-Floquet theorem. Setting the chirality of circular shaking explicitly breaks time-reversal symmetry and lifts the degeneracy of $p_{\pm }=p_x\pm i{p}_y$ orbitals, leading to the local circulation of orbital magnetism, i.e., the imbalanced occupation in $p_{\pm }$ orbitals. Moreover, the dynamics of Berry connection is revealed by the time evolution of the Berry curvature and the polarization, which have physical observable effects in experiments. Interestingly, the dynamics is found characterized by a universal phase shift, governed by the time screw rotational symmetry involving a fractional translation of time. These findings suggest that the present lattice-shaking scheme provides a versatile platform for the investigation of the orbital physics and the symmetry-protected dynamics.

We simulate and analyze an experimental method of loading interacting ultracold atoms onto nontrivial quantum states such as nonlinear Bloch wave and soliton solutions in a one-dimensional bichromatic lattice. Of standard bands, inverted bands, and bands with Dirac-like points permitted by a bichromatic lattice, we consider the case of an inverted band and examine the loading process in terms of nonlinear Bloch waves formed by an aggregate of ultracold atoms described by the mean-field model. Specifically, we solved the Gross-Pitaevskii equation numerically and found an appropriate standing wave-pulse sequence for the inverted band, which sequence proved to be a suitable protocol for producing soliton solutions. In addition, we examined the effect of an external potential and dynamical instabilities for the postloading process. We also provide an appropriate data set for future experimental realization of our findings.

Dipolar Bose-Einstein condensates represent a powerful platform for the exploration of quantum many-body phenomena arising from long-range interactions. A series of recent experiments has demonstrated the formation of supersolid states of matter. Subsequent theoretical works have shown that quantum fluctuations can affect the underlying phase transition and may lead to the emergence of supersolids with various lattice structures in dipolar condensates. In this work, we explore the signatures of such different geometries in confined finite condensates. In addition to previously found triangular lattices, our analysis reveals a rich spectrum of states, from honeycomb patterns to striped supersolids. By optimizing relevant parameters, we show that transitions between distinct supersolids should be observable in current experiments.

Analog quantum simulation—the technique of using one experimentally well-controlled physical system to mimic the behavior of another—has quickly emerged as one of the most promising near-term strategies for studying strongly correlated quantum many-body systems. In particular, systems of interacting photons, realizable in solid-state cavity and circuit QED frameworks, for example, hold tremendous promise for the study of nonequilibrium many-body phenomena, in part due to the capability to locally create and destroy photons. These systems are typically modeled using a Jaynes-Cummings-Hubbard (JCH) Hamiltonian, named due to similarities with the Bose-Hubbard Hamiltonian. While comparisons between the two are often made in literature, the JCH Hamiltonian comprises both bosonic and psuedospin operators, leading to physical deviations from the Bose-Hubbard model for particular parameter regimes. Here, we present a nonperturbative procedure for transforming the Jaynes-Cummings Hamiltonian into a dressed operator representation that, in its most general form, admits an infinite sum of bosonic $k$-body terms where $k$ is bound only by the number of excitations in the system. We closely examine this result in both the dispersive and resonant coupling regimes, finding rapid convergence of this sum in the former and contributions from $k\gg 1$ in the latter. Through extension to the simple case of a two-site JCH system, we demonstrate that this approach facilitates close inspection of the analogy between the JCH and Bose-Hubbard models and its breakdown for resonant light-matter coupling. Finally, we use this framework to survey the many-body character of a two-site JCH for general system parameters, identifying four unique quantum phases and the parameter regimes in which they are realized, thus highlighting phenomena realizable with finite JCH-based quantum simulators beyond the Bose-Hubbard model. More broadly, this paper is intended to serve as a clear mathematical exposition of bosonic many-body interactions underlying Jaynes-Cummings-type systems, often postulated either through analogy to Kerr-like nonlinear susceptibilities or by matching coefficients to obtain the appropriate eigenvalue spectrum.

Recently, there has been intense research in proposing and developing various methods for constructing high-order exceptional points (EPs) in dissipative systems. These EPs can possess a number of intriguing properties related to, e.g., chiral transport and enhanced sensitivity. Previous proposals to realize non-Hermitian Hamiltonians (NHHs) with high-order EPs have been mainly based on either direct construction of spatial networks of coupled modes or utilization of synthetic dimensions, e.g., mapping of spatial lattices to time or photon-number space. Both methods rely on the construction of effective NHHs describing classical or postselected quantum fields, which neglect the effects of quantum jumps and which, thus, suffer from a scalability problem in the quantum regime, when the probability of quantum jumps increases with the number of excitations and dissipation rate. Here, by considering the full quantum dynamics of a quadratic Liouvillian superoperator, we introduce a simple and effective method for engineering NHHs with high-order quantum EPs, derived from evolution matrices of system operator moments. That is, by quantizing higher-order moments of system operators, e.g., of a quadratic two-mode system, the resulting evolution matrices can be interpreted as alternative NHHs describing, e.g., a spatial lattice of coupled resonators, where spatial sites are represented by high-order field moments in the synthetic space of field moments. Notably, such a mapping allows correct reproduction of the results of the Liouvillian dynamics, including quantum jumps. As an example, we consider a $U\left(1\right)$-symmetric quadratic Liouvillian describing a bimodal cavity with incoherent mode coupling, which can also possess $\mathrm{anti}\text{−}\mathcal{P}\mathcal{T}$ symmetry, whose field moment dynamics can be mapped to an NHH governing a spatial network of coupled resonators with high-order EPs.

Quantum error correction (QEC) is one of the central concepts in quantum information science and also has wide applications in fundamental physics. The capacity theorems provide solid foundations of QEC. We here provide a general and highly applicable form of capacity theorem for both classical and quantum information, i.e., hybrid information, with the assistance of a limited resource of entanglement in a one-shot scenario, which covers broader situations than the existing ones. Harnessing the wide applicability of the theorem, we show that a demonstration of QEC by short random quantum circuits is feasible and that QEC is intrinsic in quantum chaotic systems. Our results bridge the progress in quantum information theory, near-future quantum technology, and fundamental physics.

The behavior of H-like ions embedded in astrophysical plasmas in the form of dense, strongly and weakly coupled plasmas is investigated. In these, the increase and decrease in temperature are impacted by a change in confinement radius $r_c$. Two independent and generalized scaling ideas have been applied to modulate the effect of the plasma-screening constant $\lambda$ and ion charge $Z$ on such systems. Several relations are derived to interconnect the original Hamiltonian and two scaled Hamiltonians. In the exponential-cosine-screened Coulomb potential (ECSCP; dense) and weakly coupled plasma (WCP) these scaling relations have provided a linear equation connecting the critical screening constant ${\lambda }^{\left(c\right)}$ and $Z$. Their ratio offers a state-dependent constant beyond which a particular state vanishes. Shannon entropy has been employed to understand the plasma effect on the ion. With an increase in $\lambda$, the accumulation of opposite charge surrounding the ion increases, leading to a reduction in the number of bound states. However, with a rise in ionic charge $Z$, this effect can be delayed. The competing effect of plasma charge density $n_e$ and temperature in WCP and ECSCP is investigated. A recently proposed simple virial-like theorem was established for these systems. Multipole ($k=1–4$) oscillator strength and polarizabilities for these are studied considering $1s,2s$ states. As a bonus, analytical closed-form expressions are derived for $f^{\left(k\right)}$ and ${\alpha }^{\left(k\right)}(k=1–4)$ involving $1s$ and $2s$ states for the free H-like ion.

We propose a tractor atom interferometer (TAI) based on three-dimensional (3D) confinement and transport of split atomic wave-function components in potential wells that follow programmed paths. The paths are programmed to split and recombine atomic wave functions at well-defined space-time points, guaranteeing closure of the interferometer. Uninterrupted 3D confinement of the interfering wave-function components in the tractor wells eliminates coherence loss due to wave-packet dispersion. Using Crank-Nicolson simulation of the time-dependent Schrödinger equation, we compute the quantum evolution of scalar and spinor wave functions in several TAI sample scenarios. The interferometric phases extracted from the wave functions allow us to quantify gravimeter sensitivity for the TAI scenarios studied. We show that spinor TAI supports matter-wave beam splitters that are more robust against nonadiabatic effects than their scalar-TAI counterparts. We confirm the validity of semiclassical path-integral phases taken along the programmed paths of the TAI. Aspects for future experimental realizations of TAI are discussed.

The computation of the internal optical force density inside a metamaterial is a controversial subject. Various stress tensors have been proposed; however, each yields a different result. Here, by adopting the Helmholtz stress tensor and effective medium theories, we calculated the force densities acting on metamaterials composed of a one-dimensional deep-subwavelength dielectric-air multilayer or a two-dimensional square lattice cylinder array. Our results agree remarkably with the benchmarking noneffective medium treatment. The key is to treat the effective parameters as operators; i.e., take different values for the wave with different $k$ vector. This work provides an approach to compute the internal optical force in metamaterials.

Electromagnetic waves in a system with a space- and time-dependent boundary experience both diffraction and Doppler-like frequency conversion. In order to analyze such situations, conventional methods call for either the eigenmodes or the dyadic Green's function in space- and time-dependent media. Here, we propose a dynamical differential method which does not require either of them. Our method utilizes a dynamical coordinate transformation in order to simplify the calculation of the optical response of the space- and time-dependent system. We reveal that the diffraction symmetry is broken in the presence of traveling-wave-type spatiotemporal modulation.

We show that it is possible to obtain perfect higher-order squeezing via strong nonlinearities in the microwave-modified electromagnetically induced transparency (EIT). In a typical $\mathrm{\Lambda }$ three-level system coupled to a control field and a microwave field, the strong nonlinearity is existent under the full-resonant conditions and can be effectively controlled by the relative intensity of the optical and microwave fields. Via dressed-state and Bogoliubov mode transformation, we explore that the internal nonlinearity is closely related to the squeezing parameter and dissipative rate for two cavity modes. As a result, it is found that the two-mode higher-order squeezing is nearly close to $100\%$ under ideal conditions, which is verified by our numerical and analytical results. In addition, we reveal that the higher-order squeezing in the present scheme is robust against the dephasing rate between two lower levels. This may find potential applications in high-precision measurement and provide a convenient way for experimental implementation.

It has been shown classically that combining two chaotic random walks can yield an ordered (periodic) walk. Our aim in this paper is to find a quantum analog for this rather counterintuitive result. We study the chaotic and periodic nature of cyclic quantum walks and focus on a unique situation wherein a periodic quantum walk on 3-cycle graph is generated via a deterministic combination of two chaotic quantum walks on the same graph. We extend our results to even numbered cyclic graphs, specifically a 4-cycle graph too. Our results will be relevant in quantum cryptography and quantum chaos control.

We test the principle of majorization J. I. Latorre and M. A. Martín-Delgado, Phys. Rev. A 66, 022305 (2002). in random circuits. Three classes of circuits were considered: (i) universal, (ii) classically simulatable, and (iii) neither universal nor classically simulatable. The studied families are: {cnot, H, T}, {cnot, H, not}, {cnot, H, S} (Clifford), matchgates, and IQP (instantaneous quantum polynomial-time). We verified that all the families of circuits satisfy on average the principle of decreasing majorization. In most cases the asymptotic state (number of gates $\to \infty$) behaves like a random vector. However, clear differences appear in the fluctuations of the Lorenz curves associated with asymptotic states. The fluctuations of the Lorenz curves discriminate between universal and nonuniversal classes of random quantum circuits, and they also detect the complexity of some nonuniversal but not classically efficiently simulatable quantum random circuits. We conclude that majorization can be used as an indicator of complexity of quantum dynamics, as an alternative to, e.g., entanglement spectrum and out-of-time-order correlators.

Aluminum monochloride (AlCl) has been proposed as an excellent candidate for laser cooling. Here we present absorption spectroscopy measurements on the $A{}^1\mathrm{\Pi }\leftarrow X^1{\mathrm{\Sigma }}^{+}$ transition in AlCl inside a cryogenic helium buffer-gas beam cell. The high-resolution absorption data enable a rigorous, quantitative comparison with our high-level ab initio calculations of the electronic and rovibronic energies, providing a comprehensive picture of the AlCl quantum structure. The combination of high-resolution spectral data and theory permits the evaluation of spectroscopic constants and associated properties, like equilibrium bond length, with an order of magnitude higher precision. Based on the measured molecular equilibrium constants of the $A{}^1\mathrm{\Pi }$ state, we estimate a Franck-Condon factor of the $A{}^1\mathrm{\Pi }\leftarrow X^1{\mathrm{\Sigma }}^{+}$ of 99.88%, which confirms that AlCl is amenable to laser cooling.

We report multiconfiguration Dirac-Hartree-Fock and relativistic configuration interaction calculations on the thallium (Tl) electron affinity, as well as on the excited energy levels arising from the ground configuration of ${\mathrm{Tl}}^{-}$. The results are compared with the available experimental values and further validated by extending the study to its homologous, lighter element, indium (In), belonging to group 13 (III.A) of the Periodic Table. The calculated electron affinities of In and Tl, 383.4 and 322.8 meV, agree with the latest measurements by within 1%. Three bound states ${}^3{P}_{0,1,2}$ are confirmed in the $5s^{2}5p^2$ configuration of ${\mathrm{In}}^{-}$, while only the ground state ${}^3{P}_0$ is bound in the $6s^{2}6p^2$ configuration of ${\mathrm{Tl}}^{-}$. The isotope shifts on the In and Tl electron affinities are also estimated. The E2 and M1 intraconfiguration radiative transition rates within $5s^{2}5p^2 {}^3{P}_{0,1,2}$ of ${\mathrm{In}}^{-}$ are used to calculate the radiative lifetimes of the metastable ${}^3{P}_{1,2}$ levels.

Dynamical instability is an inherent feature of bosonic systems described by the Bogoliubov–de Gennes (BdG) Hamiltonian. Since it causes the BdG system to collapse, it is generally thought that it should be avoided. Recently there has been much effort to harness this instability for the benefit of creating a topological amplifier with stable bulk bands but unstable edge modes which can be populated at an exponentially fast rate. We present a theorem for determining the stability of states with energies sufficiently away from zero, in terms of an unconventional commutator between the number-conserving part and number-nonconserving part of the BdG Hamiltonian. We apply the theorem to a generalization of a model from Galilo et al. [Phys. Rev. Lett. 115, 245302 (2015)] for creating a topological amplifier in an interacting spin-1 atom system in a honeycomb lattice through a quench process. We use this model to illustrate how the vanishing of the unconventional commutator selects the symmetries for a system so that its bulk states are stable against (weak) pairing interactions. We find that as long as time-reversal symmetry is preserved, our system can act like a topological amplifier, even in the presence of an onsite staggered potential which breaks the inversion symmetry.

Higher-order topological superfluids have gapped bulk and symmetry-protected Majorana zero modes with various localizations. Motivated by recent advances, we present a proposal for synthesizing multiorder topological superfluids that support various Majorana zero modes in ultracold atomic gases. For this purpose, we use the two-dimensional optical superlattice that introduces a spatial modulation to the spin-orbit coupling in one direction, providing an extra degree of freedom for the emergent higher-order topological state. We find the topologically trivial superfluids, first-order and second-order topological superfluids, as well as different topological phase transitions among them with respect to the experimentally tunable parameters. Besides the conventional transition characterized by the Chern number associated with the bulk gap closing and reopening, we find the system can support the topological superfluids with Majorana corner modes, but the topological phase transition undergoes no gap-closing of bulk bands. Instead, the transition is refined by the quadrupole moment and signaled out by the gap-closing of edge states. The proposal is based on the $s$-wave interaction and is valid using existing experimental techniques, which unifies multiorder topological phase transitions in a simple but realistic system.