We derive necessary conditions for any two-fermion reduced density matrix (2-RDM) to be representable by a pure $N$-fermion density matrix $\mathrm{\Psi }{\mathrm{\Psi }}^{*}$ where $\mathrm{\Psi }$ is the wave function. These pure $N$-representability conditions of the 2-RDM are important because they provide stringent constraints beyond those from the Pauli and the generalized Pauli constraints on the structure of many-fermion 2-RDMs and their wave functions. The pure 2-RDM conditions are derived as generalized Pauli constraints on effective one-fermion reduced density matrices (1-RDMs) generated by the removal or addition of a fermion from the wave function. Computationally, we show for four-electron molecules that the derived pure $N$-representability conditions are nontrivially active for exact ground-state 2-RDMs and that they provide significant restrictions beyond the D, Q, and G ensemble $N$-representability conditions. Constraints on higher-order $p$-RDMs where $p>2$ are derived in a similar fashion. The constraints have potentially significant applications to computing strongly correlated many-fermion states with enhanced accuracy and decreased computational complexity.

The exact factorization of an electron-nuclear wave function [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010)] allows us to define the rigorous nuclear time-dependent Schrödinger equation (TDSE) with a time-dependent potential-energy surface (TDPES) that fully accounts for the coupling to the electronic motion and drives the nuclear wave-packet dynamics. Here, we study whether the propagation of multiple classical trajectories can reproduce the quantum nuclear motion in strong-field processes when their motions are governed by the quantum Hamilton-Jacobi equation derived by applying Bohmian mechanics to this exact nuclear TDSE. We demonstrate that multiple classical trajectories propagated by the force from the gradient of the exact TDPES plus the Bohmian quantum potential can reproduce the strong-field dissociation dynamics of a one-dimensional model of the ${{\mathrm{H}}_2}^{+}$ molecule. Our results show that the force from the Bohmian quantum potential plays a non-negligible role in yielding quantum nuclear dynamics in the strong-field process studied here, where ionization and/or splitting of nuclear probability density occurs.

We investigate the behavior of several spatial grid methods and complex absorbers for strong-field and attosecond scenarios when using the time-dependent configuration-interaction singles method to solve the multi-electron time-dependent Schrödinger equation for atoms. We compare the pseudospectral grid, finite-element, and finite-element-discrete-variable-representation (DVR) methods with each other and discuss their advantages and disadvantages. Additionally, we study the performances of complex absorbing potential (CAP) and smooth exterior complex scaling (SES) to absorb the outgoing electron. We find that SES performs generally better than CAP for calculating high-harmonic generation spectra and XUV photoelectron spectra. In both of these cases, the DVR and even more the FEM grid representations show more reliable results—especially when using SES. Both absorbers show drawbacks when calculating photoelectron spectra in the strong-field regime.

We describe a theoretical method, developed in the coupled-channel formalism, to study photoionization of H atoms in a strong magnetic field of a size that is typical for magnetic white dwarfs. The coupled Schrödinger equations are solved numerically using the renormalized Numerov method proposed by Johnson [B. R. Johnson, J. Chem. Phys. 67, 4086 (1977); B. R. Johnson, J. Chem. Phys. 69, 4678 (1978)]. The distinct advantage of this method is the fact that no overflow problems are encountered in the classically forbidden region, and hence the method exhibits excellent numerical stability. Photoionization cross sections are presented for magnetized H atoms in the ground and $2p$ excited states. The calculated results are compared with those obtained by other theories. The present method is particularly useful for explaining the complex features of continuous spectra in a strong magnetic field and hence provides an efficient tool for modeling photoionization spectra observed in the atmosphere of magnetic white dwarfs.

Strong-field ionization of dense molecular gases in a short infrared laser pulse is studied by means of photoelectron spectroscopy combined with a liquid microjet technique. By increasing the gas density, we observe how the laser-assisted electron scattering on neighboring particles becomes a dominant mechanism of hot electron emission. The angle-resolved energy distributions of rescattered electrons are obtained by analyzing the density dependency of emission spectra. A semiclassical consideration of electron trajectories is shown to provide a good description of experimental spectra. The model predicts the existence of four energy plateaus. Two cutoffs at higher energies are evident in the spectra.

Atomic interferometers are often affected by magnetic field fluctuations. Using the clock transition at zero magnetic field minimizes the effect of these fluctuations. There is another transition in rubidium that minimizes the magnetic sensitivity at 3.2 G. We combine the previous two transitions to obtain minimum magnetic sensitivity at a tunable magnetic field between 2.2 and 3.2 G. The two interferometers evolve independently from each other and we control the magnetic sensitivity by changing the population in both transitions with a microwave pulse.

We consider scattering of electromagnetic plane waves by a linear periodic array of dielectric spheres. For incident waves with circular polarization with frequency tuned to the bound states with orbital angular momentum in the radiation continuum, the spin angular momentum of the incident wave transfers into the orbital angular momentum. This, in turn, gives rise to giant vortical power currents rotating around the array. Incident wave with linear polarization with frequency tuned to the Bloch bound state in the continuum induces giant laminar power currents.

The entanglement between two bosons or fermions can be accessed if there exists an auxiliary degree of freedom which can be used to label and effectively distinguish the two particles. For some types of entanglement between two indistinguishable particles one can observe a duality, i.e., if the entanglement is present in a Hilbert space $\mathcal{H}$ and an auxiliary Hilbert space ${\mathcal{H}}^{\prime }$ is used to label the particles, then if we use $\mathcal{H}$ as a label, entanglement will be present in ${\mathcal{H}}^{\prime }$. For distinguishable particles this effect does not occur because of superselection rules which prevent superpositions of different types of particles. However, it is known that superselection rules can be bypassed if one uses special auxiliary states that are known as reference frames. Here we study properties of reference frames which allow for the observation of a duality in entanglement between two distinguishable particles. Finally, we discuss the consequences of this result from a resource-theoretic point of view.

We explore a distinguishability $D$ and a visibility $V$, satisfying the relation $D^2+V^2=1$, to measure a single electron's particlelike and wavelike behaviors, respectively. For several typical one-dimensional nonuniform lattice systems, we find that $D^2$ is less than, equal to, and greater than $V^2$ for delocalized, critical, and localized states, respectively. In this sense, the Anderson transition can be viewed as a transition from relatively more particlelike behavior to relatively more wavelike behavior.

We investigate the emergent open dynamics of a quantum system that undergoes rapid repeated unitary interactions with a sequence of ancillary systems. We study in detail how decoherence appears as a subleading effect when a quantum system is bombarded by a quick succession of ancillas. In the most general case, these ancillas are (a) taken from an ensemble of quantum systems of different dimensions, (b) prepared in different states, and (c) interacting with the system through different Hamiltonians. We derive an upper bound on decoherence rates in this regime, and show how a rich variety of phenomena in open dynamics (such as projection, thermalization, purification, and dephasing) can emerge out of our general model of repeated interaction. Furthermore, we show a fundamental link between the strength of the leading-order dissipation and the intrinsic “unpredictability” in the system-ancilla interaction. We also discuss how these results encompass and extend results obtained with other earlier models of repeated interaction.

When an open quantum system is driven by an external time-dependent force, the coupling of the driving to the central system is usually included, whereas the impact of the driving field on the bath is neglected. We investigate the effect of a quantum bath of linearly driven harmonic oscillators on the relaxation dynamics of a quantum two-level system which is not directly driven. In particular, we calculate the frequency-dependent response of the system when the bath is subject to Dirac and Gaussian driving pulses. We show that a time-retarded effective force on the system is induced by the driven bath which depends on the full history of the perturbation and the spectral characteristics of the underlying bath. In particular, when a structured Ohmic bath with a pronounced Lorentzian peak is considered, the dynamical response of the system to a driven bath is qualitatively different than that of the undriven bath. Specifically, additional resonances appear which can be directly associated with a Jaynes-Cummings-like effective energy spectrum.

We consider the two-dimensional alternate quantum walk on a cylinder. We concentrate on the study of the motion along the open dimension, in the spirit of looking at the closed coordinate as a small or “hidden” extra dimension. If one starts from localized initial conditions on the lattice, the dynamics of the quantum walk that is obtained after tracing out the small dimension shows the contribution of several components which can be understood from the study of the dispersion relations for this problem. In fact, these components originate from the contribution of the possible values of the quasimomentum in the closed dimension. In the continuous space-time limit, the different components manifest as a set of Dirac equations, with each quasimomentum providing the value of the corresponding mass. We briefly discuss the possible link of these ideas to the simulation of high-energy physical theories that include extra dimensions. Finally, entanglement between the coin and spatial degrees of freedom is studied, showing that the entanglement entropy clearly overcomes the value reached with only one spatial dimension.

In this paper, the following scenario is considered: there are two qubits possessed by two parties at different locations. Qubits have been prepared in one of a maximum of four, mutually-orthogonal, entangled states and the parties wish to distinguish between the states by using local operations and classical communication. Although in general it is not possible to distinguish between four arbitrary states, the parties can spend some preshared entanglement to achieve perfect discrimination between four qubit states and can also preserve the entanglement of the states after discrimination. This is shown by employing the theory of majorization and the connections between entanglement transformations and state discrimination protocols.

We use Richardson-Gaudin exact equations to derive the ground-state energy of $N$ composite bosons (cobosons) interacting via a potential which acts between fermion pairs having zero center-of-mass momentum, that is, a potential similar to the reduced BCS potential used in conventional superconductivity. Through a density expansion, we show that while for two-dimensional (2D) systems, the $N$-coboson correlation energy undergoes a surprising cancellation which leaves the interaction part with an $N(N-1)$ dependence only, such a cancellation does not exist in 1D, 3D, or 4D systems (which correspond to 2D parabolic traps) nor when the cobosons interact via a similar short-range potential but between pairs having an arbitrary center-of-mass momentum. This shows that the previously found cancellation which exists for the Cooper-pair correlation energy results not only from the very peculiar form of the reduced BCS potential, but also from a quite mysterious dimensionality effect, the density of states for Cooper pairs feeling the BCS potential being essentially constant, as for 2D systems.

Motivated by experiments performed by Landig et al. [Nature (London) 532, 476 (2016)], we consider a two-dimensional Bose gas in an optical lattice, trapped inside a single mode superradiant Fabry-Perot cavity. The cavity mediates infinite-range checkerboard interactions between the atoms, which produces competition between Mott insulator, charge-density wave, superfluid, and supersolid phases. We calculate the phase diagram of this Bose gas in a homogeneous system and in the presence of a harmonic trap.

We propose a gravitational-wave detection method based on heterodyne laser links and light-pulse atom interferometry that enables high sensitivity gravitational-wave detection in the 0.1-mHz to 1-Hz frequency band using a single, long ($>{10}^8$ m), detector baseline. The detection baseline in previous atom-based proposals was constrained by the need for a reference laser to remain collimated over the optical propagation path between two satellites. Here we circumvent this requirement by employing a strong local oscillator laser near each atom ensemble that is phase referenced or phase locked to the reference laser beam. Longer baselines offer a number of potential advantages, including enhanced sensitivity, simplified atom optics, and reduced atomic source flux requirements.

The effect of dipolar orientation with respect to the condensate plane on the mean-field dynamics of dipolar Bose-Einstein condensates in a pancake-shaped confinement is discussed. The stability of a quasi-two-dimensional condensate, with respect to the tilting angle, is found to be different from a two-dimensional layer of dipoles, indicating the relevance of the transverse extension while characterizing two-dimensional dipolar systems. An anisotropic excitation spectrum exhibiting a highly tunable, rotonlike minimum can arise entirely from the dipole-dipole interactions, by tilting the dipoles. At the magic angle and in the absence of contact interactions, the long-wavelength excitations are not phononlike and always unstable. The post-roton-instability dynamics, in contrast to phonon instability, in a uniform condensate, is featured by a transient, defect-free, stripe pattern, which eventually undergoes local collapses, and driving the condensate back into the stable regime can make them sustained for longer. Hopping between stripes has been observed before it melts into a uniform state in the presence of dissipation. Finally, we discuss a class of solutions, in which a quasi-two-dimensional condensate is self-trapped in one direction, as well as a regime of interaction parameters, including attractive short-range interactions, at which a two-dimensional anisotropic soliton can be stabilized, and we show that a chromium condensate with a relatively small number of atoms is well suited for this.

We develop a model based on a multiple scattering theory to describe the diffusion of polarized light in disordered media exhibiting short-range structural correlations. Starting from exact expressions of the average field and the field spatial correlation function, we derive a radiative transfer equation for the polarization-resolved specific intensity that is valid for weak disorder and we solve it analytically in the diffusion limit. A decomposition of the specific intensity in terms of polarization eigenmodes reveals how structural correlations, represented via the standard anisotropic scattering parameter $g$, affect the diffusion of polarized light. More specifically, we find that propagation through each polarization eigenchannel is described by its own transport mean free path that depends on $g$ in a specific and nontrivial way.

We numerically investigate the scaling behavior of midinfrared filaments at extremely high input energies. It is shown that, given sufficient power, kilometer-scale, low-loss atmospheric filamentation is attainable by prechirping the pulse. Fully resolved four-dimensional ($xyzt$) simulations show that, while in a spatially imperfect beam the modulation instability can lead to multiple hot-spot formation, the individual filaments are still stabilized by the recently proposed mechanism that relies on the temporal walk-off of short-wavelength radiation.

We consider periodic single-photon sources with combined multiplexing in which the outputs of several time-multiplexed sources are spatially multiplexed. We give a full statistical description of such systems in order to optimize them with respect to maximal single-photon probability. We carry out the optimization for a particular scenario which can be realized in bulk optics and its expected performance is extremely good at the present state of the art. We find that combined multiplexing outperforms purely spatially or time-multiplexed sources for certain parameters only, and we characterize these cases. Combined multiplexing can have the advantages of possibly using less nonlinear sources, achieving higher repetition rates, and the potential applicability for continuous pumping. We estimate an achievable single-photon probability between 85% and 89%.