We investigate the generation of a multibody Dicke state in a coupled cavity system subject to environmental noise. Based on quantum feedback control, cavity decay may play a constructive role in obtaining the intended state. The required interaction time need not be accurately controlled. In addition, the feedback operations are only applied to a single atom in one cavity during the whole evolution process, and it is not necessary to change the control strategy as the number of atoms increases. Thus, our proposal can exploit the core advantage of coupled cavities to implement a scalable control scheme for preparing multibody entanglement.

In this paper we explore the limits of the unidirectional pulse propagation equation (UPPE) in general nonlinear media. Our main aim is to investigate under which physical conditions two-way propagation becomes significant, and leads to a breakdown of the unidirectional approximation. Using a spectral constraint appearing in the derivation of UPPE we derive a first correction which renormalizes the forward-propagating amplitude. This correction is the main result of our paper and we investigate its effects through numerical simulations.

Quasi-phase-matching in a dual gas (Ar-H${}_2$) multijet array has recently been demonstrated to be a promising way to enhance the yield of high-order harmonics (HH). Here, we investigate the HH produced individually from these two gases under identical conditions. Our results indicate that the quasi-phase-matching results from the much lower recombination cross section of H${}_2$ as compared to that of Ar in the energy range of interest, rather than from full ionization of H${}_2$ by the driving laser as proposed previously.

We propose a witness operation for the nonclassical character of a harmonic oscillator state. The method does not require state reconstruction. For all harmonic oscillator states that are classical, a bound is established for the evolution of a qubit which is coupled to the oscillator. Any violation of the bound can be rigorously attributed to the nonclassical character of the initial oscillator state.

Quantum Fisher information, as an intrinsic quantity for quantum states, is a central concept in quantum detection and estimation. When quantum measurements are performed on quantum states, classical probability distributions arise, which in turn lead to classical Fisher information. In this paper, we exploit the classical Fisher information induced by quantum measurements and reveal a rich hierarchical structure of such measurement-induced Fisher information. We establish a general framework for the distribution and transfer of the Fisher information. In particular, we illustrate three extremal distribution types of the Fisher information: the locally owned type, the locally inaccessible type, and the fully shared type. Furthermore, we indicate the significant role played by the distribution and flow of the Fisher information in some physical problems, e.g., the non-Markovianity of open quantum processes, the environment-assisted metrology, the cloning and broadcasting, etc.

To provide reliable reference results for various components of the electron correlation energies of Zn${}^{2+}$ and Zn, which play a similar role for $3d$-electron systems as Ne and Mg do for lighter atoms, we have performed extensive calculations of the all-electron correlation energy and of its various components with several state-of-the-art ab initio techniques. Two pairs of basis-set sequences that systematically converge to the complete basis set (CBS) limit have been employed in the calculations. One pair [cc-pV$n$Z and aug-cc-pV$n$Z (correlation consistent polarized valence $n$-zeta and augmented cc-pV$n$Z with $n=$ D, T, Q, 5, $6(-k)$)] is oriented towards the description of valence electron correlation. The second pair of sequences [cc-pCCV$n$Z and aug-cc-pCCV$n$Z (core core-valence $n$-zeta, with $n$ = D, T, Q, 5, $6(-k)$)] is developed for the description of all-electron correlation effects. The correlation energies have been determined with second-order Møller-Plesset perturbation theory (MP2) and several single-reference coupled-cluster (CC) methods. The present correlation energies represent accurate post-MP2 correlation energies for closed-shell atoms including 3$d$ electrons both at the all-electron and subshell levels and should be useful benchmark results for various transitions. We have also employed the present results for assessments of the focal-point approximation (FPA), broadly used in approximations of difference correlation effects for molecular interaction problems, in applications aiming at estimating correlation effects in heavier atoms. Our results indicate that for the systems considered, the magnitudes of the MP2 correlation energies overestimate the magnitudes of the CC values for all electrons correlated as well as of their various subsets. For the all-electron correlation energies of the Zn atom, our result confirms the finding of S. P. McCarthy and A. J. Thakkar [J. Chem. Phys. 134, 044102 (2011)] obtained by means of non–ab initio approaches for all heavy closed-shell atoms from Zn to Rn. We have shown that for both Zn${}^{2+}$ and Zn this overestimation is directly caused by the presence of the $3d^{10}$ electron configuration.

Electron removal and fragmentation cross sections are calculated for He${}^{+}\left(1s\right)$-H${}_2$O collisions at impact energies from 20 keV/amu to several MeV/amu by using the nonperturbative basis generator method for ion-molecule collisions. Previous work for proton impact is extended to deal with the dressed projectile in the present case. The effects from the active projectile electron are taken into account by applying the same single-particle Hamiltonian to all electrons and by using the inclusive-probability formalism in the final-state analysis. Fragment-ion yields are evaluated from the single-, double-, and triple-electron removal cross sections, and the results are compared with the available experimental data. Very reasonable agreement is obtained for fragmentation caused by direct ionization, while some discrepancies remain in the capture and loss data.

We explore wave-packet dynamics in the ground $X$ ${}^1{\Sigma }_g^{+}$ and excited $B$ ${}^1{\Pi }_u$ states of cesium dimers (Cs${}_2$). In particular, we study the dependence of the wave-packet dynamics on the relative timing between femtosecond pump, Stokes, and probe pulses in a nondegenerate BOXCARS beam geometry, which are commonly used for coherent anti-Stokes Raman scattering (CARS) spectroscopy. The experimental results are elucidated by theoretical calculations, which are based on the Liouville equations for the density matrix for the molecular states. We observe oscillations in CARS signals as functions of both Stokes and probe pulse delays with respect to the pump pulse. The oscillation period relates to the wave-packet motion cycle in either the ground or excited state of Cs${}_2$ molecules, depending on the sequence of the input laser pulses in time. The performed analysis can be applied to study and/or manipulate wave-packet dynamics in a variety of molecules. It also provides an excellent test platform for theoretical models of molecular systems.

The gauge field of a uniform line of magnetic monopoles is created using a single Laguerre-Gauss laser mode and a gradient in the physical magnetic field. We study the effect of these monopoles on a Bose condensed atomic gas, whose vortex structure transforms when more than six monopoles are trapped within the cloud. Finally, we study this transition with the collective modes.

Time-resolved measurement techniques are opening a window on nonequilibrium quantum phenomena that is radically different from the traditional picture in the frequency domain. The simulation and interpretation of nonequilibrium dynamics are conspicuous challenges for theory. This paper presents an approach to quantum many-body dynamics that is based on a Hamiltonian formulation of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy of equations of motion for reduced density matrices. These equations have an underlying symplectic structure, and we write them in the form of the classical Hamilton equations for canonically conjugate variables. Applying canonical perturbation theory or the Krylov-Bogoliubov averaging method to the resulting equations yields a systematic approximation scheme. The possibility of using memory-dependent functional approximations to close the Hamilton equations at a given level of the hierarchy is discussed. The geometric structure of the equations gives rise to reduced geometric phases that are observable even for noncyclic evolutions of the many-body state. The approach is applied to a finite Hubbard chain which undergoes a quench in on-site interaction energy $U$. Canonical perturbation theory, carried out to second order, fully captures the nontrivial real-time dynamics of the model, including resonance phenomena and the coupling of fast and slow variables.

The idea to base the uncertainty relation for photons on the electromagnetic energy distribution in space enabled us to derive a sharp inequality that expresses the uncertainty relation [Phys. Rev. Lett. 108, 140401 (2012)]. An alternative version of the uncertainty relation derived in this paper is closer in spirit to the original Heisenberg relation because it employs the analog of the position operator for the photon—the center of the energy operator. The noncommutativity of the components of the center of the energy operator results in the increase of the bound $3\hslash /2$ in the standard Heisenberg uncertainty relation in three dimensions. This difference diminishes with the increase of the photon energy. In the infinite-momentum frame, the lower bound in the Heisenberg uncertainty relations for photons is the same as in nonrelativistic quantum mechanics. A similar uncertainty relation is also derived for coherent photon beams. This relation has direct experimental consequences since it gives a precise relationship between the spectral composition of the laser beam and the minimal focal volume.

Traditional quantum physics solves ground states for a given Hamiltonian, while quantum information science asks for the existence and construction of certain Hamiltonians for given ground states. In practical situations, one would be mainly interested in local Hamiltonians with certain interaction patterns, such as nearest-neighbor interactions on some types of lattices. A necessary condition for a space $V$ to be the ground-state space of some local Hamiltonian with a given interaction pattern is that the maximally mixed state supported on $V$ is uniquely determined by its reduced density matrices associated with the given pattern, based on the principle of maximum entropy. However, it is unclear whether this condition is in general also sufficient. We examine the situations for the existence of such a local Hamiltonian to have $V$ satisfying the necessary condition mentioned above as its ground-state space by linking to faces of the convex body of the local reduced states. We further discuss some methods for constructing the corresponding local Hamiltonians with given interaction patterns, mainly from physical points of view, including constructions related to perturbation methods, local frustration-free Hamiltonians, as well as thermodynamical ensembles.

We analyze the Uhlmann fidelity of a pair of $n$-mode Gaussian states of the quantum radiation field. This quantity is shown to be the product of an exponential function depending on the relative average displacement and a factor fully determined by the symplectic spectrum of the covariance matrix of a specific Gaussian state. However, it is difficult to handle our general formula unless the Gaussian states commute or at least one of them is pure. On the contrary, in the simplest cases $n=1$ and $n=2$, it leads to explicit analytic formulas. Our main result is a calculable expression of the fidelity of two arbitrary two-mode Gaussian states. This can be applied to build reliable measures of quantum correlations between modes in various branches of quantum physics.

The harmonium model has long been regarded as an exactly solvable laboratory bench for quantum chemistry [W. Heisenberg, Z. Phys. 38, 411 (1926)]. For studying correlation energy, only the ground state of the system has received consideration heretofore. This is a spin singlet state. In this work we exhaustively study the lowest excited (spin triplet) harmonium state, with the main purpose of revisiting the relation between entanglement measures and correlation energy for this quite different species. The task is made easier by working with Wigner quasiprobabilities on phase space.

Large-scale $R$ matrix with pseudostates calculations for electron collisions with neon atoms, using a recently developed parallel version of our $B$-spline $R$-matrix code, are reported. The calculations were carried out in the $jK$-coupling scheme. They are intended to provide converged (with respect to the number of coupled states) results for electron impact excitation of individual target states with dominant configurations $2p^{5}3s$, $2p^{5}3p$, and $2p^{5}3d$ for incident electron energies from threshold to 300 eV. The close-coupling expansion includes 457 target states, with the lowest 87 states representing the bound spectrum and the remaining 370 the ionization continuum. The results reveal dramatic reductions of the predicted excitation cross sections at intermediate energies due to a strong influence of coupling to the target continuum and the higher-lying Rydberg states. Comparison with available experimental data for the excitation of the $2p^{5}3s$ and $2p^{5}3p$ states raises questions about the absolute normalization in the measurements. Considerable improvement over previous work is obtained in the agreement between experiment and theory for the angle-differential cross sections. In particular, a long-standing discrepancy regarding the angular dependence for excitation of the metastable $2p^{5}3s$ levels is resolved.

An Efimov trimer near the atom-dimer threshold can increase the atom loss rate in ultracold trapped atoms through the avalanche mechanism proposed by Zaccanti et al. A three-body recombination event creates an energetic atom and dimer, whose subsequent elastic collisions produce additional atoms with sufficient energy to escape from the trapping potential. We use Monte Carlo methods to calculate the average number of atoms lost and the average heat generated by recombination events in both a Bose-Einstein condensate and a thermal gas. We take into account the energy-dependence of the cross sections and the spatial structure of the atom cloud. While the number of atoms lost in a recombination event can be much larger than the value 3, we find that the avalanche mechanism does not produce a narrow loss feature near the atom-dimer resonance.

In earlier work [Phys. Rev. A 65, 043412 (2002)] we examined the description of atom-radiation coupling in terms of the multipolar Hamiltonian rather than the minimal coupling one, and reached the conclusion that the simple operator $D_{SF}\left(r\right)=\{\begin{array}{cc}r,& r<r_0\\ r_0,& r\ge r_0\end{array}$ constitutes a good approximation to the full electric interaction, $H_{\mathrm{el}}$. Unlike the standard length form of the electric dipole approximation (EDA), $D_{SF}\left(r\right)$ does not increase indefinitely. Instead, it stops at $r_0=3\lambda /8$, where $\lambda$ is the wavelength, and then remains constant. This theoretically founded simplification of $H_{\mathrm{el}}$ has obvious computational advantages over $H_{\mathrm{el}}$, while at the same time accounts for effects beyond the EDA. The present paper discusses the elucidation of the singularities of the free-free matrix elements using $D_{SF}\left(r\right)$ and state-specific, energy-normalized, numerical scattering functions in polyelectronic atoms, and explains how their computation can be done efficiently. Accurate knowledge of such matrix elements is critical to the quantitative solution of time-dependent or time-independent problems involving various multiphoton processes that are induced by strong fields and involve off-resonance coupling between extended wave functions representing high-$n$ Rydberg states of the discrete spectrum or asymptotically unbound states of the continuum. For completeness, the singularities of the EDA are also derived and discussed within the present approach.

Impurity motion in one-dimensional ultracold quantum liquids confined in an optical trap has attracted much interest recently. As a step towards its full understanding, we construct a generating functional from which we derive the position nonequilibrium correlation function of a quantum Brownian particle with general Gaussian nonfactorizing initial conditions. We investigate the slow dynamics of a particle confined in a harmonic potential after a position measurement; the rapid relaxation of a particle trapped in a harmonic potential after a quantum quench realized as a sudden change in the potential parameters; and the evolution of an impurity in contact with a one-dimensional bosonic quantum gas. We argue that such an impurity–Luttinger-liquid system, which has been recently realized experimentally, admits a simple modeling as quantum Brownian motion in a super-Ohmic bath.

We put forth and discuss in detail a scheme to achieve Bose-Einstein condensation of stationary-light dark-state polaritons with dipolar interaction. To this end we introduce a diamondlike coupling scheme in a vapor of Rydberg atoms under the frozen gas approximation. To determine the system's dynamics we employ normal modes and identify the dark-state polariton corresponding to one of the modes. We show that in contrast to atomic dipolar ultracold vapors, the dark-state polariton Bose-Einstein condensates proposed here can be stable for a negative dipolar interaction constant.