The quantum marginal problem asks whether a set of given density matrices are consistent, i.e., whether they can be the reduced density matrices of a global quantum state. Not many nontrivial analytic necessary (or sufficient) conditions are known for the problem in general. We propose a method to detect consistency of overlapping quantum marginals by considering the separability of some derived states. Our method works well for the $k$-symmetric extension problem in general and for the general overlapping marginal problems in some cases. Our work is, in some sense, the converse to the well-known $k$-symmetric extension criterion for separability.

In Y. Aharonov et al. [Phys. Rev. Lett. 60, 1351 (1988)], it was shown that, in some weak measurements with postselection schemes, it is possible to obtain inferred mean values outside the range of the eigenvalues of the measured observable. In our work, we are going to show that this effect can be associated with the presence of an asymptotically vanishing but nonzero amount of system-detector quantum correlations. These correlations are also related to the presence of a finite (nonzero) amount of coherence of the initial states in the basis of the measured observable.

Mutual neutralization in the collisions of ${\mathrm{H}}^{+}$ and ${\mathrm{H}}^{-}$ is studied both theoretically and experimentally. The quantum-mechanical ab initio model includes covalent states associated with the $\mathrm{H}\left(1\right)+\mathrm{H}\left(n\le 3\right)$ limits and the collision energy ranges from 1 meV to 100 eV. The reaction is theoretically studied for collisions between different isotopes of the hydrogen ions. From the partial wave scattering amplitude, the differential and total cross sections are computed. The differential cross section is analyzed in terms of forward- and backward-scattering events, showing a dominance of backward scattering which can be understood by examining the phase of the scattering amplitudes for the gerade and ungerade set of states. The isotope dependence of the total cross section is compared with the one obtained using a semiclassical multistate Landau-Zener model. The final state distribution analysis emphasizes the dominance of the $n=3$ channel for collisions below 10 eV, while at higher collision energies, the $n=2$ channel starts to become important. For collisions of ions forming a molecular system with a larger reduced mass, the $n=2$ channel starts to dominate at lower energies. Using a merged ion-beam apparatus, the branching ratios for mutual neutralization in ${\mathrm{H}}^{+}$ and ${\mathrm{H}}^{-}$ collisions in the energy range from 11 to 185 eV are measured with position- and time-sensitive particle detectors. The measured and calculated branching ratios satisfactorily agree with respect to state contributions.

The projectile beam coherence effects occurring in ion-atom collisions are analyzed on the basis of the recent theory of Karlovets et al. [Phys. Rev. A 92, 052703 (2015)] developed for the elastic scattering of wave packets of particles off a potential field. This theory is generalized to estimate the loss of coherence for inelastically scattered projectiles in ionizing collisions. The results obtained by the suggested model are compared with experimental data for the ionization of hydrogen atoms and molecules by 75-keV proton impact. Significantly improved agreement is observed between the theory and experiment.

We show that it is possible to model accurately optical phenomena in intense laser fields by taking into account the intensity distribution over the laser beam. We present an extension of an earlier theoretical model that divides an intense laser beam into concentric regions, each with a Rabi frequency that corresponds to the intensity in that region, and solve a set of coupled optical Bloch equations for the density matrix in each region. Experimentally obtained magneto-optical resonance curves for the $F_g=2⟶F_e=1$ transition of the $D_1$ line of ${}^{87}\mathrm{Rb}$ agree very well with the theoretical model up to a laser intensity of around 200 mW/${\mathrm{cm}}^2$ for a transition whose saturation intensity is around 4.5 mW/${\mathrm{cm}}^2$. We examine the spatial dependence of the fluorescence intensity in an intense laser beam experimentally and theoretically. We present and discuss the results of an experiment in which a broad, intense pump laser excites the $F_g=4⟶F_e=4$ transition of the $D_2$ line of cesium while a narrow probe beam scans the atoms within the pump beam and excites the $D_1$ line of cesium, whose fluorescence is recorded as a function of probe beam position. Experimentally obtained spatial profiles of the fluorescence intensity agree qualitatively with the predictions of the model.

We present a theoretical study of the ${{\text{H}}_2}^{+}$ molecular ion wave-packet dynamics in plasmon-enhanced laser fields. These fields may be produced, for instance, when metallic nanostructures are illuminated by a laser pulse of moderated intensity. Their main property is that they vary in space on a nanometric scale. We demonstrate that the spatial inhomogeneous character of the plasmonic fields leads to an enhancement of electron localization (EL), an instrumental phenomenon to control molecular fragmentation. We suggest that the charge imbalance induced by the surface-plasmon resonance near the metallic nanostructure is the origin of the increase in the EL.

Spectra of ultracold neutrons that appeared in experiments on neutron diffraction by a moving grating were measured using the time-of-flight Fourier spectrometer. Diffraction lines of five orders were observed simultaneously. The obtained data are in good agreement with the theoretical predictions based on the multiwave dynamical theory of neutron diffraction by a moving grating.

We develop a general theory of spin-dependent Bragg spectroscopy for spinor Bose-Einstein condensates. This spectroscopy involves using a density and spin-coupled optical probe to excite the system. We show that within the linear-response regime the momentum or energy transferred by the probe is determined by a set of density and spin-density dynamic structure factors. We derive a set of $f$-sum rules that provides rigorous constraints for the first energy moments of these structure factors. As an application we compute the dynamic structure factors for cases within all four distinct phases of a spin-1 condensate using Bogoliubov theory. Our results demonstrate that spin-dependent Bragg spectroscopy can be used to selectively investigate the various phonon and magnon excitation branches and will be a useful tool for advancing our understanding of spinor condensates.

We show that the ground state of a spin-1 atomic condensate with antiferromagnetic interactions constitutes a useful resource for quantum metrology upon approaching the Heisenberg limit. Unlike a ferromagnetic condensate state where individual atomic spins are aligned in the same direction, the antiferromagnetic ground-state condensate is a condensate of spin-singlet atom pairs. The inherent correlation between paired atoms allows for parameter estimation at precisions beyond the standard quantum limit (SQL) for uncorrelated atoms. The degree of improvement over the SQL is measured by the scaled quantum Fisher information (QFI), whose dependence on the ratio of linear Zeeman shift $p$ to spin-dependent atomic interaction $c$ is studied. At a typical value of $p=0.4c$, which corresponds to a magnetic field of $28.6\mu \mathrm{G}$ for $c=50\mathrm{h}$ Hz (for ${}^{23}\mathrm{Na}$ atom condensate in the $F=1$ state at a typical density of $\sim {10}^{14}{\mathrm{cm}}^{-3}$), the scaled QFI can reach $\sim 0.48N$, which approaches the limit of $0.5N$ for the twin-Fock state ${|N/2\rangle }_{+}{|N/2\rangle }_{-}$. Our work encourages experimental efforts to reach the ground state of an antiferromagnetic condensate at a extremely low magnetic field.

We numerically demonstrate that femtosecond ring-Airy wave packets are able to overcome the reference intensity clamping of $4\times {10}^{13}$ W/${\mathrm{cm}}^2$ for filaments generated with Gaussian beams at low numerical apertures and form an intense sharp intensity peak on axis. Numerical simulations, with unidirectional propagation models for the pulse envelope and the carrier resolved electric field, reveal that the driving mechanism for this unexpected intensity increase is due to the self-generated plasma. The plasma formation, in conjunction with the circular geometry of the beam, force the wave packet into a multistage collapse process which takes place faster than the saturating mechanisms can compensate. We report here a nonstandard mechanism that increases the intensity of a collapsing wave packet, due to the joint contributions of the cubic phase of the Airy beam and the formation of a partially reflecting plasma.

Recently an alternative way to quantifying the Bell nonlocality has been proposed [E. A. Fonseca and F. Parisio, Phys. Rev. A 92, 030101(R) (2015)]. In this work we further develop this concept, the volume of violation, and analytically calculate its value for the spin-singlet state with respect to the settings of the first Bell inequality. These settings correspond to three directions in space, or three arbitrary points on the unit sphere. It is shown that the triples of directions that lead to violations in local causality correspond to $1/3$ of all possible configurations. From the perspective of quantum communication, this means that two distant parties that were able to align their measurements in one direction only (the remaining direction in each site being random) have a probability of about $33.3\%$ to certify their entanglement.

In general, it is difficult to evaluate measurement errors when the initial and final conditions of the measurement make it impossible to identify the correct value of the target observable. Ozawa proposed a solution based on the operator algebra of observables which has recently been used in experiments investigating the error-disturbance trade-off of quantum measurements. Importantly, this solution makes surprisingly detailed statements about the relations between measurement outcomes and the unknown target observable. In the present paper, we investigate this relation by performing a sequence of two measurements on the polarization of a photon, so that the first measurement commutes with the target observable and the second measurement is sensitive to a complementary observable. While the initial measurement can be evaluated using classical statistics, the second measurement introduces the effects of quantum correlations between the noncommuting physical properties. By varying the resolution of the initial measurement, we can change the relative contribution of the nonclassical correlations and identify their role in the evaluation of the quantum measurement. It is shown that the most striking deviation from classical expectations is obtained at the transition between weak and strong measurements, where the competition between different statistical effects results in measurement values well outside the range of possible eigenvalues.

Many phenomena of strongly correlated materials are encapsulated in the Fermi-Hubbard model whose thermodynamic properties can be computed from its grand-canonical potential. In general, there is no closed-form expression of the grand-canonical potential for lattices of more than one spatial dimension, but solutions can be numerically approximated using cluster methods. To model long-range effects such as order parameters, a powerful method to compute the cluster's Green's function consists of finding its self-energy through a variational principle. This allows the possibility of studying various phase transitions at finite temperature in the Fermi-Hubbard model. However, a classical cluster solver quickly hits an exponential wall in the memory (or computation time) required to store the computation variables. Here it is shown theoretically that the cluster solver can be mapped to a subroutine on a quantum computer whose quantum memory usage scales linearly with the number of orbitals in the simulated cluster and the number of measurements scales quadratically. A quantum computer with a few tens of qubits could therefore simulate the thermodynamic properties of complex fermionic lattices inaccessible to classical supercomputers.

We present a numerical analysis of the particle creation for a quantum field in the presence of time-dependent boundary conditions. Having in mind recent experiments involving superconducting circuits, we consider their description in terms of a scalar field in a one-dimensional cavity satisfying generalized boundary conditions that involve a time-dependent linear combination of the field and its spatial and time derivatives. We evaluate numerically the Bogoliubov transformation between $in$- and $out$-states and find that the rate of particle production strongly depends on whether the spectrum of the unperturbed cavity is equidistant or not, and also on the amplitude of the temporal oscillations of the boundary conditions. We provide analytic justifications for the different regimes found numerically.

We investigate two-pathway interferences between nonresonant one-photon and resonant two-photon ionization of atomic hydrogen. In particular, we analyze in detail the photoionization mediated by the fundamental frequency and the second harmonic of a femtosecond VUV pulse when the fundamental is tuned near an intermediate atomic state. Following our recent study [Phys. Rev. A 91, 063418 (2015)] of such effects with linearly polarized light, we analyze a similar situation with circularly polarized radiation. As a consequence of the richer structure in circularly polarized light, characterized by its right-handed or left-handed helicity, we present and discuss various important features associated with the photoelectron angular distribution.

We study harmonically trapped, unpolarized fermion systems with attractive interactions in two spatial dimensions with spin degeneracies $N_f^{}=2$ and 4 and $N/N_f^{}=1,3,5$, and 7 particles per flavor. We carry out our calculations using our recently proposed quantum Monte Carlo method on a nonuniform lattice. We report on the ground-state energy and contact for a range of couplings, as determined by the binding energy of the two-body system, and show explicitly how the physics of the $N_f$-body sector dominates as the coupling is increased.

Optical lattices with a complex-valued tunneling term have become a standard way of studying gauge-field physics with cold atoms. If the complex phase of the tunneling is made density dependent, such a system features even a self-interacting or dynamical magnetic field. In this paper we study the scenario of a few bosons in either a static or a dynamical gauge field by means of exact diagonalization. The topological structures are identified computing their Chern number. Upon decreasing the atom-atom contact interaction, the effect of the dynamical gauge field is enhanced, giving rise to a phase transition between two topologically nontrivial phases.

We propose an adiabatic method for transfer of light in a three-waveguide directional coupler in a single mode. In our scheme the propagation coefficients of the two outer waveguides are identical, but may vary simultaneously along the propagation direction. In contrast to earlier work [E. Paspalakis, Opt. Commun. 258, 30 (2006)], where the coupling coefficients are designed to act in the counterintuitive order for an input in one of the outer waveguides, here we may have initially any light input in each of the waveguides and any order of coupling coefficients. Consequently, all three adiabatic eigenstates of the system are used in the dynamics. These solutions allow us to design some interesting waveguide devices.

We investigate the bias-modulated dynamics of a strongly driven two-level system using the counterrotating-hybridized rotating-wave (CHRW) method. This CHRW method treats the driving field and the bias on equal footing by a unitary transformation with two parameters $\xi$ and $\zeta$, and is nonperturbative in driving strength, tunneling amplitude, or bias. In addition, this CHRW method is beyond the traditional rotating-wave approximation (Rabi-RWA) and yet by properly choosing the two parameters $\xi$ and $\zeta$, the transformed Hamiltonian takes the RWA form with a renormalized energy splitting and a renormalized driving strength. The reformulated CHRW method possesses the same mathematical simplicity as the Rabi-RWA approach and thus allows us to calculate analytically the dynamics and explore explicitly the effect of the bias. We show that the CHRW method gives the accurate driven dynamics for a wide range of parameters as compared to the numerically exact results. When energy scales of the driving are comparable to the intrinsic energy scale of the two-level systems, the counterrotating interactions and static bias profoundly influence the generalized Rabi frequency. In this regime, where ordinary perturbation approaches fail, the CHRW works very well and efficiently. We also demonstrate the dynamics of the system in the strong-driving and off-resonance cases for which the Rabi-RWA method breaks down but the CHRW method remains valid. We obtain analytical expressions for the generalized Rabi frequency and bias-modulated Bloch-Siegert shift as functions of the bias, tunneling, and driving field parameters. The CHRW approach is a mathematically simple and physically clear method. It can be applied to treat some complicated problems for which a numerical study is difficult to perform.

We construct the dyadic Green function of the electromagnetic field in the presence of a spatially dispersive spherical object. It contains all the information on light-scattering processes off a spatially dispersive sphere, and, in particular, its imaginary part gives the local density of states. Our construction of the Green function automatically yields a dispersion relation for surface polaritons in terms of surface impedances. From a methodological point of view, our approach is based on the extinction theorem and Huygens' principle. This allows for the straightforward application of Maxwell boundary conditions, without the need to resort to so-called additional boundary conditions. With this, we investigate the influence of spatial dispersion on the local density of states in the proximity of a nanosphere.