Reliable tomography of a quantum state of atoms in room-temperature vapors offers interesting applications in quantum-information science. To step toward the applications, here, we theoretical investigate a technique of reconstruction of a collective density matrix of atoms in a state of a total angular momentum equal to unity. By studying transformation of density matrix due to magnetic-field pulses and deriving explicit relations between optical signals and specific density-matrix elements, we demonstrate full reconstruction of quantum states. Numerical simulations allow us to demonstrate that the reconstruction fidelity of pure and mixed states may exceed 0.95 and that the technique is robust against noise and uncertainties.

The boundary operator is a linear operator that acts on a collection of high-dimensional binary points (simplices) and maps them to their boundaries. This boundary map is one of the key components in numerous applications, including differential equations, machine learning, computational geometry, machine vision, and control systems. We consider the problem of representing the full boundary operator on a quantum computer. We first prove that the boundary operator has a special structure in the form of a complete sum of fermionic creation and annihilation operators. We then use the fact that these operators pairwise anticommute to produce an $O\left(n\right)$-depth circuit that exactly implements the boundary operator without any Trotterization or Taylor-series approximation errors. Having fewer errors reduces the number of shots required to obtain desired accuracies.

A general symmetric-informationally-complete (GSIC)–positive-operator-valued measure (POVM) is known to provide an optimal quantum state tomography among minimal IC POVMs with a fixed average purity. In this paper we provide a general construction of a GSIC POVM by means of a complete orthogonal basis (COB), also interpreted as a normal quasiprobability representation. A spectral property of a COB is shown to play a key role in the construction of SIC POVMs and also for the bound of the mean-square error of the state tomography. In particular, a necessary and sufficient condition to construct a SIC POVM for any $d$ is constructively given by the power of traces of a COB. We give three simple constructions of COBs from which one can systematically obtain GSIC POVMs.

We present the theoretical treatment of laser-assisted $(e,2e)$ ionizing collisions in hydrogen for fast electrons, in the framework of the first-order Born approximation at moderate laser intensities and photon energies beyond the soft-photon approximation. The interaction of the laser field with the incident, scattered, and ejected electrons is treated nonperturbatively by using Gordon-Volkov wave functions, while the atomic dressing is treated by using first-order perturbation theory. Within this semiperturbative formalism, we obtain a closed-form formula for the nonlinear triple differential cross section (TDCS), which is valid for linear as well circular polarizations. Analytical simple expressions of TDCS are derived in the weak field domain and low-photon energy limit. It was found that for nonresonant $(e,2e)$ reactions, the analytical formulas obtained for the atomic matrix element in the low-photon energy limit give a good agreement, qualitative and quantitative, with the numerical semiperturbative model calculations. We study the influence of the photon energy as well of the kinetic energy of the ejected electron on the TDCS, in the asymmetric coplanar geometry, and show that the dressing of the atomic target strongly influences the $(e,2e)$ ionization process. We discuss the exchange effects between the ejected and scattered electrons in the TDCS.

This paper considers solutions of the linear Fokker-Planck equation for the steady velocity distribution functions of electrons dilutely dispersed in an excess of either argon, xenon, or krypton. Owing to the large Ramsauer-Townsend minima in the electron-atom momentum-transfer cross sections for these atoms, the steady electron distribution, often referred to as the Davydov distribution, exhibits a bimodal distribution which varies dramatically with the strength of the external electric field. This effect provides a unique verification of the location and shape of the Ramsauer-Townsend minima in the cross sections. It is anticipated that current experimental techniques that probe the details of nonequilibrium electron distributions will verify the results reported in this paper. In addition, these nonequilibrium, non-Maxwellian distributions cannot be rationalized in terms of either the Gibbs-Boltzmann entropy nor the Tsallis nonextensive entropy.

We investigate multichannel dissociative ionization of ethanol in intense ultraviolet laser fields using a photoelectron-photoion coincidence momentum imaging technique. Product channels are clearly separated with detected photoions, and channel-specific photoelectron spectra exhibit multiple spectral components unambiguously assigned to four- and five-photon ionization to the electronic ground state and the electronically excited state. We measure kinetic energy distributions of fragment ions as a function of the energy of a correlated photoelectron to reveal how much energy is provided to the fragment recoil of fragment ions in the course of photoelectron emission and subsequent electronic excitation. Subsequent electronic excitation rather than photoelectron emission governs the internal energy of ethanol cations. The role of subsequent electronic excitation becomes more decisive as the laser intensity increases.

Anyons are particles with intermediate quantum statistics whose wave function acquires a phase $e^{i\theta }$ by particle exchange. Inspired by proposals of simulating anyons using ultracold atoms trapped in optical lattices, we study a two-site anyonic Josephson junction, i.e., anyons confined in a one-dimensional double-well potential. We show, analytically and numerically, that many properties of anyonic Josephson junctions, such as Josephson frequency, imbalanced solutions, macroscopic quantum self-trapping, coherence visibility, and condensate fraction, crucially depend on the anyonic angle $\theta$. Our theoretical predictions are a solid benchmark for near-future experimental quantum simulations of anyonic matter in double-well potentials.

To reveal origins of resonance characteristics of multilayer interference structures, we developed an ab initio spatial coupled-mode theory using the approximations of general electromagnetic theory of wave propagation in stratified media. In contrast to the conventional coupled-mode theory, the coefficients of developed coupled-mode models, which describe the Fano resonance behavior of interference field enhancement, are given by analytical functions of structural and optical parameters of the resonance systems. The results of analytical modeling of low- and high-loss resonator systems supporting waveguide, Fabry-Pérot, symmetric, and antisymmetric plasmonic normal modes agree very well with electromagnetic numerical simulations. We demonstrate also that the conventional spatial phenomenological coupled-mode theory is accurate only for low-loss structures.

Higher-order exceptional points in non-Hermitian systems have recently been used as a tool to engineer high-sensitivity devices, attracting tremendous attention from multidisciplinary fields. Here, we present a simple yet effective scheme to enhance the device sensitivity by slightly deviating the gain-neutral-loss linear configuration to a triangular one, resulting in an abrupt phase transition from third-order to second-order exceptional points. Our analysis demonstrates that the exceptional points can be tailored by a judicious tuning of the coupling parameters of the system, resulting in enhanced sensitivity to a small perturbation. The tunable coupling also leads to a sharp change in the sensitivity slope, enabling the perturbation to be measured precisely as a function of coupling. This two-way detection of the perturbation opens up a rich landscape toward ultrasensitive measurements, which could be applicable to a wide range of non-Hermitian ternary platforms.

Quantum simulations of molecular systems on quantum computers often employ minimal basis sets of Gaussian orbitals. In comparison with more realistic basis sets, quantum simulations employing minimal basis sets require fewer qubits and quantum gates but yield results of lower accuracy. A natural strategy to achieve more accurate results is to increase the basis set size, which, in turn, requires increasing the number of qubits and quantum gates. Here we explore the use of intrinsic atomic orbitals in quantum simulations of molecules to improve the accuracy of energies and properties at the same computational cost required by a minimal basis. We investigate ground-state energies and one- and two-body density operators in the framework of the variational quantum eigensolver employing and comparing different Ansätze. We also demonstrate the use of this approach in the calculation of ground- and excited-state energies of small molecules by a combination of quantum algorithms using IBM quantum computers.

After the appearance of the no-cloning theorem, approximate quantum cloning machines (QCMs) has become a well-studied subject in quantum information theory. Among several measures to quantify the performance of a QCM, single-qudit fidelity and global fidelity have been most widely used. In this paper we compute the optimal global fidelity for phase-covariant cloning machines via semidefinite programming optimization, thereby completing a remaining gap in the previous results on QCMs. We also consider optimal simulations of the cloning and transpose cloning map, both by a direct optimization and by a composition of component-wise optimal QCMs. For the cloning map the composition method is suboptimal whereas for the transpose cloning map the method is asymptotically optimal.

Continuous-variable quantum key distribution (CVQKD) has been proven to be secure theoretically. However, the practical CVQKD system may still be subject to various quantum attacks due to the imperfections of devices. In this paper, we suggest a general machine learning-based defense strategy against practical quantum attacks by taking advantage of density-based spatial clustering of applications with noise (DBSCAN), which we called DBSCAN-based attack detection scheme (DADS). Specifically, we first construct a set of features that can well reflect the behaviors of different attacks, then DBSCAN is applied to obtain several clusters. This clustering result can explicitly indicate whether the CVQKD system is being eavesdropped or not. Simulation experiments show that the proposed DADS cannot only detect most of known attacks, but also has ability to identify various unknown attacks, thereby improving practical security of the CVQKD system. We also show that the overestimated secret key rate caused by ignoring practical quantum attacks can be amended by DADS so that a reasonable tighter secure bound of the practical CVQKD system can be obtained.

When a core-shell electron is ionized by coherent ultrashort x-ray pulses with varied duration, different nuclear wave packets of a cationic molecule are formed, which can be effectively studied by detecting the photoelectron-Auger electron-ion fragment as it is proposed in the present paper. We develop the theory for the photoelectron, i.e., Auger electron, ion fragment three-body coincidence spectroscopy, where dissociative Auger final states are considered. Simulations to display the HF molecule show that the coincidence spectra encode the detailed information of coherent nuclear wave-packet dynamics. Our work paves the way for using currently available coherent ultrashort x-ray pulses to investigate and manipulate molecular nuclear wave packets. Moreover, we discuss possibilities for high-resolution coincidence experimental techniques.

The localization properties of one-dimensional degenerate Fermi gases with cavity-assisted nonlocal quasiperiodic interactions are numerically studied. Although the cavity-induced interaction is typically nonlocal, it is proved that the eigenstate thermalization hypothesis is still applicable in our system depending on the system parameters. We also find the segment of the spectrum corresponding to infinite effective temperature varies for different system parameters, which indicates the spectral range employed in the spectral statistical analysis should be varied accordingly. The features of many-body localization (MBL) are numerically identified by analyzing the spectral statistics and the entanglement entropy using exact diagonalization. These features are further confirmed by our time-evolution results. In addition, the number of cavity photons are found stable over long-time dynamics in the MBL phase. Such a feature cannot only be utilized to nondestructively diagnose the MBL phase by monitoring the number of leaking photons from the cavity but leveraged for constructing a device to produce a stable number of photons.

We analyze the dynamics of a quantum kicked rotor (QKR) driven with a binary Fibonacci sequence of two distinct drive amplitudes. While the dynamics at low drive frequencies is found to be diffusive, a long-lived preergodic regime emerges in the other limit. Furthermore, the dynamics in this preergodic regime can be associated with the onset of a dynamical quasilocalization, similar to the dynamical localization observed in a regular QKR. We establish that this peculiar behavior arises due to the presence of localized eigenstates of an approximately conserved effective Hamiltonian, which drives the evolution at Fibonacci instants. However, the effective Hamiltonian picture does not persist indefinitely, and the dynamics eventually becomes ergodic after asymptotically long times.

We study characteristic, dynamic, and saturation regimes of the out-of-time-order correlation (OTOC) in the constant-field Floquet system with and without longitudinal field. In the calculation of OTOC, we take local spins in longitudinal and transverse directions as observables which are local and nonlocal in terms of Jordan-Wigner fermions, respectively. We use the exact analytical solution of OTOC for the integrable model (without the longitudinal field term) with transverse direction spins as observables and numerical solutions for other integrable and nonintegrable cases. OTOCs in both cases depart from unity at a kick equal to the separation between the observables when the local spins are in the transverse direction, and one additional kick is required when the local spins are in the longitudinal direction. The number of kicks required to depart from unity depends on the separation between the observables and is independent of the Floquet period and system size. In the dynamic region, OTOCs show power-law growth in both models, the integrable one (without longitudinal field) and the nonintegrable one (with longitudinal field). The exponent of the power-law increases with increasing separation between the observables. Near the saturation region, OTOCs grow linearly at a very low rate.

The rotational and fine structure of open-shell molecules in a $\mathrm{\Sigma }$ electronic state gives rise to crossings between Zeeman states of different parity. These crossings become avoided in the presence of an electric field. We propose an algorithm that encodes Ising models into qubits defined by pairs of ${}^2\mathrm{\Sigma }$ molecules sharing an excitation near these avoided crossings. This can be used to realize a transverse field Ising model tunable by an external electric or magnetic field, suitable for quantum annealing applications. We perform dynamical calculations for several examples with one- and two-dimensional connectivities. Our results demonstrate that the probability of obtaining valid annealing solutions is high and can be optimized by varying the annealing times.

We consider leading $O(m/M)$ nuclear recoil corrections to the hyperfine splitting in light atomic systems. Due to the singularity of hyperfine interactions, the electromagnetic form factors of the nucleus have to be introduced as a function of the four-momentum square, which goes beyond the Hamiltonian description of the system. We present a compact formula for $O\left(Z\alpha \right)$ recoil corrections and indicate the importance, especially for light atoms, of a more realistic description of the nuclear structure effects.

Based on the Langevin equation, a stochastic formulation is implemented to describe the dynamics of a trapped ion in a bath of ultracold atoms, including an excess of micromotion. The ion dynamics is described following a hybrid analytical-numerical approach in which the ion is treated as a classical impurity in a thermal bath. As a result, the ion energy's time evolution and distribution are derived from studying the sympathetic cooling process. Furthermore, the ion dynamics under different stochastic noise terms is also considered to gain information on the bath properties' role in the system's energy transfer processes. Finally, the results obtained from this formulation are contrasted with those obtained with a more traditional Monte Carlo approach.

The photon momentum transfer in the two-photon double ionization of helium is theoretically studied based on the $abinitio$ calculations. A nonlinear dependence of the transferred momentum on the photon energy is identified at relatively small photon energies. As expected, the linear dependence is recovered with the slope approaching 1.60 when the photon energy becomes sufficiently large. With a semianalytical model including the Coulomb screen effect in the two-electron ground state, we can qualitatively reproduce the nonlinear dependence and find that it is mainly contributed by the fast electron. However, compared with the results from the $abinitio$ calculations, the quantitative discrepancies at relatively small photon energies can be accounted for only by the electron correlation in the intermediate state. The present study reveals the vital roles played by the two-electron effects for the complicated photon momentum transfer process in the few-photon and few-electron systems.