We introduce an operational entanglement classification of symmetric mixed states for an arbitrary number of qubits based on stochastic local operations assisted with classical communication (SLOCC operations). We define families of SLOCC entanglement classes successively embedded into each other, we prove that they are of nonzero measure, and we construct witness operators to distinguish them. Moreover, we discuss how arbitrary symmetric mixed states can be realized in the laboratory via a one-to-one correspondence between well-defined sets of controllable parameters and the corresponding entanglement families.

Electron-impact double ionization of a helium atom in the presence of laser radiation with low frequency and intensity is studied theoretically. The kinematical regime of high impact energy and large momentum transfer, with one slow and two fast electrons in the final channel, is considered. Fully differential cross sections corresponding to the laser-assisted $(e,3e)$ and $(e,3-1e)$ processes are calculated for different models of the target state. The angular distributions of the slow ejected electron are found to be seriously modified by the laser field and, in contrast to the field-free case, are strongly dependent on the electron-electron correlations in helium. At the same time, the laser-assisted $(e,3-1e)$ results very slightly differ from those in the absence of a laser field.

The fragmentation of ${\mathrm{CD}}^{+}$ in intense ultrashort laser pulses was investigated using a coincidence three-dimensional momentum imaging technique improved by employing both transverse and longitudinal electric fields. This allowed clear separation of all fragmentation channels and the determination of the kinetic energy release down to nearly zero, for a molecule with significant mass asymmetry. The most probable dissociation pathways for the two lowest dissociation limits, $\text{C}{}^{+}+\text{D}$ and $\text{C}+{\text{D}}^{+}$, were identified for both 22-fs, 798-nm and 50-fs, 392-nm pulses. Curiously, the charge asymmetric dissociation of ${\mathrm{CD}}^{2+}$ was not observed for 392-nm photons, even though it was clearly visible for the fundamental 798 nm at the same peak intensity.

The Cooper minimum has recently been observed in the high-order-harmonic spectrum issued from the interaction of a short and intense laser pulse with krypton atoms [A. D. Shiner et al., J. Phys. B 45, 074010 (2012)]. Here we compare this observation to a semiclassical description using the single-active electron approximation. Particular attention is paid to the description of the interaction of the active valence electron with the ionic core in the framework of a mean-field approach. The computed harmonic spectrum presents a minimum at about 83 eV, which does not show up so clearly in the measurements probably because of second-order diffraction of the grating used to disperse the harmonic spectrum.

For a simple illustrative model Hamiltonian for xenon in a low-frequency linearly polarized laser field we obtain a remarkable agreement between the zero-order energy as well as the amplitude and phase of the zero-order Floquet states and the exact eigenvalues and eigenfunctions of the Floquet operator. Here we use as a zero-order Hamiltonian the adiabatic Hamiltonian where time is used as an instantaneous parameter. Moreover, for a variety of low laser frequencies, $\omega$, the deviation of the zero-order solutions from the exact quasienergy (QE) Floquet solutions approaches zero at the time the oscillating laser field is maximal. This remarkable result gives a further justification to the validity of the first step in the simple man model. It should be stressed that the numerical calculations of the exact QE Floquet solutions become extremely difficult when $\omega$ approaches zero and many Floquet channels are nested together and are coupled by the laser field. This is the main motivation for the development of perturbation theory for QE Floquet solutions when the laser frequency is small, to avoid the need to represent the Floquet operator by a matrix when the Fourier functions are used as a basis set. A way to calculate the radius of convergence of the perturbational expansion of the Floquet solutions in $\omega$ is given.

We theoretically investigate the behavior of dark solitons in a one-dimensional spin-orbit coupled atomic Fermi gas in harmonic traps by solving self-consistently the Bogoliubov–de Gennes equations. The dark soliton—to be created by phase imprinting in future experiments—is characterized by a real order parameter, which changes sign at a point node and hosts localized Andreev bound states near the node. By considering both cases of a single soliton and multiple solitons, we find that the energy of these bound states decreases to zero when the system is tuned to enter the topological superfluid phase by increasing an external Zeeman field. As a result, two Majorana fermions emerge in the vicinity of each soliton, in addition to the well-known Majorana fermions at the trap edges associated with the nontrivial topology of the superfluid. We propose that the soliton-induced Majorana fermions can be directly observed by using spatially resolved radio-frequency spectroscopy or indirectly probed by measuring the density profile at the point node. For the latter, the deep minimum in the density profile will disappear due to the occupation of the soliton-induced zero-energy Majorana fermion modes. Our prediction could be tested in a resonantly interacting spin-orbit coupled ${}^{40}\text{K}$ Fermi gas confined in a two-dimensional optical lattice.

We investigate the relaxation dynamics of the integrable Lieb-Liniger model of contact-interacting bosons in one dimension following a sudden quench of the collisional interaction strength. The system is initially prepared in its noninteracting ground state and the interaction strength is then abruptly switched to a positive value, corresponding to repulsive interactions between the bosons. We calculate equal-time correlation functions of the nonequilibrium Bose field for small systems of up to five particles via symbolic evaluation of coordinate Bethe-ansatz expressions for operator matrix elements between Lieb-Liniger eigenstates. We characterize the relaxation of the system by comparing the time-evolving correlation functions following the quench to the equilibrium correlations predicted by the diagonal ensemble and relate the behavior of these correlations to that of the quantum fidelity between the many-body wave function and the initial state of the system. Our results for the asymptotic scaling of local second-order correlations with increasing interaction strength agree with the predictions of recent generalized thermodynamic Bethe-ansatz calculations. By contrast, third-order correlations obtained within our approach exhibit a markedly different power-law dependence on the interaction strength as the Tonks-Girardeau limit of infinitely strong interactions is approached.

We introduce a model of one- and two-dimensional (1D and 2D) optical media with the ${\chi }^{\left(2\right)}$ nonlinearity whose local strength is subject to cusp-shaped spatial modulation, ${\chi }^{\left(2\right)}\sim r^{-\alpha }$, with $\alpha >0$, which can be induced by spatially nonuniform poling. Using analytical and numerical methods, we demonstrate that this setting supports 1D and 2D fundamental solitons, at $\alpha <1$ and $\alpha <2$, respectively. The 1D solitons have a small instability region, while the 2D solitons have a stability region at $\alpha <0.5$ and are unstable at $\alpha >0.5$. 2D solitary vortices are found too. They are unstable, splitting into a set of fragments, which eventually merge into a single fundamental soliton pinned to the cusp. Spontaneous symmetry breaking of solitons is studied in the 1D system with a symmetric pair of the cusp-modulation peaks.

We propose a multilevel quantum heat engine with a working medium described by a generalized Rabi model which consists of a two-level system coupled to a single-mode bosonic field. The model is constructed to be a continuum limit of a quantum biological description of light-harvesting complexes so that it can amplify quantum coherence by a mechanism which is a quantum analog of classical Huygens clocks. The engine operates in a quantum Otto cycle where the working medium is coupled to classical heat baths in the isochoric processes of the four-stroke cycle, while either the coupling strength or the resonance frequency is changed in the adiabatic stages. We found that such an engine can produce work with an efficiency close to the Carnot bound when it operates at low temperatures and in the ultrastrong-coupling regime. The interplay of the effects of quantum coherence and quantum correlations on the engine performance is discussed in terms of second-order coherence, quantum mutual information, and the logarithmic negativity of entanglement. We point out that the proposed quantum Otto engine can be implemented experimentally with modern circuit quantum electrodynamic systems where flux qubits can be coupled ultrastrongly to superconducting transmission-line resonators.

We report the production of ultracold RbCs molecules in the rovibronic ground state, i.e., $X{}^1{\Sigma }^{+}(v=0,J=0)$, by short-range photoassociation to the $2{}^3{\Pi }_0$ state followed by spontaneous emission. We use narrow-band depletion spectroscopy to probe the distribution of rotational levels formed in the $X{}^1{\Sigma }^{+}(v=0)$ state. We conclude, based on selection rules, that the primary decay route to $X{}^1{\Sigma }^{+}(v=0)$ is a two-step cascade decay that leads to as much as $33\%$ branching into the $J=0$ rotational level. The experimental simplicity of our scheme opens up the possibility of easier access to the study and manipulation of ultracold heteronuclear molecules in the rovibronic ground state.

We study a practical method to measure the shot noise in real time in continuous-variable quantum key distribution systems. The amount of secret key that can be extracted from the raw statistics depends strongly on this quantity since it affects in particular the computation of the excess noise (i.e., noise in excess of the shot noise) added by an eavesdropper on the quantum channel. Some powerful quantum hacking attacks relying on faking the estimated value of the shot noise to hide an intercept and resend strategy were proposed. Here, we provide experimental evidence that our method can defeat the saturation attack and the wavelength attack.

Discrete time quantum walks (DTQWs) are nontrivial generalizations of random walks with a broad scope of applications. In particular, they can be used as computational primitives, and they are suitable tools for simulating other quantum systems. DTQWs usually spread ballistically due to their quantumness. In some cases, however, they can remain localized at their initial state (trapping). The trapping and other fundamental properties of DTQWs are determined by the choice of the coin operator. We introduce and analyze a type of walks driven by a coin class leading to strong trapping, complementing the known list of walks. This class of walks exhibits a number of exciting properties with possible applications ranging from light pulse trapping in a medium to topological effects and quantum search.

We propose and develop the complex-scaled multiconfigurational spin-tensor electron propagator (CMCSTEP) technique for theoretical determination of resonance parameters with electron-atom and electron-molecule systems including open-shell and highly correlated atoms and molecules. The multiconfigurational spin-tensor electron propagator (MCSTEP) method developed and implemented by Yeager and co-workers in real space gives very accurate and reliable ionization potentials and attachment energies. The CMCSTEP method uses a complex-scaled multiconfigurational self-consistent field (CMCSCF) state as an initial state along with a dilated Hamiltonian where all of the electronic coordinates are scaled by a complex factor. The CMCSCF was developed and applied successfully to resonance problems earlier. We apply the CMCSTEP method to get ${}^{2}P{\text{Be}}^{-}$ shape resonance parameters using $14s11p5d,14s14p2d$, and $14s14p5d$ basis sets with a $2s2p3d$ complete active space. The obtained values of the resonance parameters are compared to previous results. Here CMCSTEP has been developed and used for a resonance problem. It appears to be among the most accurate and reliable techniques. Vertical ionization potentials and attachment energies in real space are typically within $\pm 0.2\text{eV}$ or better of excellent experimental results and full configuration-interaction calculations with a good basis set. We expect the same sort of agreement in complex space.

We prove a Lieb-Oxford-type inequality on the indirect part of the Coulomb energy of a general many-particle quantum state, with a lower constant than the original statement but involving an additional gradient correction. The result is similar to a recent inequality of Benguria et al. [Int. J. Quantum Chem. 112, 1579 (2012)], except that the correction term is purely local, which is more usual in density functional theory. In an appendix, we discuss the connection between the indirect energy and the classical Jellium energy for constant densities. We show that they differ by an explicit shift due to the long range of the Coulomb potential.

We show that the Rydberg blockade mechanism, which is well known in the case of $s$ states, can be significantly different for $p$ and $d$ states due to the van der Waals couplings between different Rydberg Zeeman sublevels and the presence of a magnetic field. We show, in particular, the existence of magic distances corresponding to the laser excitation of a superposition of doubly excited states.

Describing time-dependent many-body systems where correlation effects play an important role remains a major theoretical challenge. In this paper we develop a time-dependent many-body theory that is based on the two-particle reduced density matrix (2-RDM). We present a closed equation of motion for the 2-RDM by developing a reconstruction functional for the three-particle reduced density matrix (3-RDM) that preserves norm, energy, and spin symmetries during time propagation. We show that approximately enforcing $N$-representability during time evolution is essential for achieving stable solutions. As a prototypical test case which features long-range Coulomb interactions we employ the one-dimensional model for lithium hydride (LiH) in strong infrared laser fields. We probe both one-particle observables such as the time-dependent dipole moment and two-particle observables such as the pair density and mean electron-electron interaction energy. Our results are in very good agreement with numerically exact solutions for the $N$-electron wave function obtained from the multiconfigurational time-dependent Hartree-Fock method.

We report a highly efficient source of narrow-band photon pairs based on parametric down-conversion in a crystalline whispering-gallery-mode resonator. Remarkably, each photon of a pair is detected in a single spatial and temporal mode, as witnessed by Glauber's autocorrelation function. We explore the phase-matching conditions in spherical geometries, and determine the requirements for single-mode operation. Understanding these conditions has allowed us to experimentally demonstrate a single-mode pair-detection efficiency of $1.13\times {10}^6$ pairs/s per mW pump power per 26.8 MHz bandwidth.

We study the steady-state behaviors of a typical optomechanical cavity coupled to cold Rydberg atoms with dipole-dipole interactions. The interacting atoms are described as one superatom of three collective states in a ladder configuration in the limit of a strong dipole blockade and a weak cavity field. We find that this hybrid system exhibits phenomena of conditional duality and nonlinear bistability in terms of mirror displacement, number of cavity photons, and Rydberg population, depending on the detuning of the cavity field, the strength of the optical driving field, and the number of cold atoms. It is of particular interest that the two branches of relevant curves may intersect to yield a nontrivial duality and bistability. Such correlated optical, mechanical, and atomic responses arise from the efficient feedback between atom-light and optomechanical interactions and have realistic applications, e.g., in realizing accurate optomechanical detection or attaining deterministic single photons.

We study optical analogs of two-dimensional (2D) Dirac solitons in square binary waveguide lattices with two different topologies in the presence of Kerr nonlinearity. These 2D solitons turn out to be quite robust. We demonstrate that with the found 2D solitons, the coupled mode equations governing light dynamics in square binary waveguide lattices can be converted into the nonlinear relativistic 2D Dirac equation with the four-component bispinor. This paves the way for using binary waveguide lattices as a classical simulator of quantum nonlinear effects arising from the 2D Dirac equation, something that is thought to be impossible to achieve in conventional (i.e., linear) quantum field theory.