The basic properties of Floquet-Bloch (FB) modes in parity-time ($\mathcal{PT}$)-symmetric optical lattices are examined in detail. Due to the parity-time symmetry of such complex periodic potentials, the corresponding FB modes are skewed (nonorthogonal) and nonreciprocal. The conjugate pairs of these FB modes are obtained by reflecting both the spatial coordinate and the Bloch momentum number itself. The orthogonality conditions are analytically derived for a single cell, for both a finite and an infinite lattice. Some of the peculiarities associated with the diffraction dynamics in $\mathcal{PT}$ lattices such as nonreciprocity, power oscillations, and phase dislocations, are also examined.

By virtue of the short lifetime of excited states, we have performed three-dimensional (3D) momentum imaging on the fragments from an electronically and vibrationally cold metastable ${\mathrm{CO}}^{2+}$ beam following irradiation by intense ultrashort laser pulses. This unique target can be described as a two-channel system, since most low-lying electronic states are not accessible by dipole transitions due to their spin state. Laser excitation between the ground $X^3\Pi$ $v=0$ state and the excited ${}^3{\Sigma }^{-}$ state leads to bond softening and above-threshold dissociation, with peaks in kinetic energy release spaced by the photon energy and interesting angular distributions that peak perpendicular to the laser field. These results are compared with our solutions of the 3D time-dependent Schrödinger equation.

We present a method for detecting the entanglement of a state using nonequilibrium processes. A comparison of relative entropies allows us to construct an entanglement witness. The relative entropy can further be related to the quantum Jarzynski equality, allowing nonequilibrium work to be used in entanglement detection. To exemplify our results, we consider two different spin chains.

We show how one can solve the problem of discriminating between qubit states. We use the quantum state discrimination duality theorem and the Bloch sphere representation of qubits, which allows for an easy geometric and analytical representation of the optimal guessing strategies.

The dipole angular distribution asymmetry parameter, $\beta$, for photoelectrons resulting from $2p$ photoionization of Ar, ${\mathrm{Ar}}^{6+}$, and ${\mathrm{Ar}}^{8+}$ and Ca, ${\mathrm{Ca}}^{2+}$, and ${\mathrm{Ca}}^{8+}$ of the Ar ($Z=18$) and Ca ($Z=20$) isonuclear sequences, respectively, have been studied using the relativistic random-phase approximation over a broad range of photon energy. In the absence of relaxation, it is known that inner-shell cross sections are essentially unchanged, as a function of photon energy, upon the removal of outer-shell electrons. The present results show that this is not true for the photoelectron angular distribution asymmetry parameters, particularly near the ionization thresholds.

We consider the stability and dynamics of multiple dark solitons in cigar-shaped Bose-Einstein condensates. Our study is motivated by the fact that multiple matter-wave dark solitons may naturally form in such settings as per our recent work [Phys. Rev. Lett. 101, 130401 (2008)]. First, we study the dark soliton interactions and show that the dynamics of well-separated solitons (i.e., ones that undergo a collision with relatively low velocities) can be analyzed by means of particle-like equations of motion. The latter take into regard the repulsion between solitons (via an effective repulsive potential) and the confinement and dimensionality of the system (via an effective parabolic trap for each soliton). Next, based on the fact that stationary, well-separated dark multisoliton states emerge as a nonlinear continuation of the appropriate excited eigenstates of the quantum harmonic oscillator, we use a Bogoliubov-de Gennes analysis to systematically study the stability of such structures. We find that for a sufficiently large number of atoms, multiple soliton states are dynamically stable, while for a small number of atoms, we predict a dynamical instability emerging from resonance effects between the eigenfrequencies of the soliton modes and the intrinsic excitation frequencies of the condensate. Finally, we present experimental realizations of multisoliton states including a three-soliton state consisting of two solitons oscillating around a stationary one and compare the relevant results to the predictions of the theoretical mean-field model.

The dynamical evolution of squeezing correlations in an ultracold Bose-Einstein condensate distributed across two modes is investigated theoretically in the framework of the Bose-Hubbard model. It is shown that the eigenstates of the Hamiltonian do not exploit the full region allowed by Heisenberg’s uncertainty relation for number and phase fluctuations. The development of nonclassical correlations and relative number squeezing is studied in the transition from the Josephson to the Fock regime. Comparing the full quantum evolution with classical statistical simulations allows us to identify quantum aspects of the squeezing formation. In the quantum regime, the measurement of squeezing allows us to distinguish even and odd total particle numbers.

We derive a generalized quantum jump superoperator that can be used in the quantum trajectory description of single photon detectors, light-emitting diodes (LEDs), and lasers. Our model describes an optical single-mode cavity field coupled to a reservoir through a two-state quantum system and includes three physical parameters: the coupling of the field to the two-state system, the coupling of the two-state system to the reservoir, and the cavity loss rate. In this setup, the two-state system can act as a photodetector or as an energy-adding mechanism. In the first case, we assume that the reservoir acts as a damping mechanism for an ideal cavity and derive reduced field operators describing the photon detection events. Our model coincides with the commonly known quantum trajectory based photon counting models at the weak- and strong-coupling limits and is, furthermore, also applicable between their validity regimes. In the second case, we assume that the reservoir injects energy into a lossy cavity through the two-state system. Again we derive the reduced field operators describing photon creation events into the lossy cavity. We show that this setup can act as an LED or as a laser depending on the strength of the injection. We also investigate how the setup operates at the close proximity of the lasing threshold.

Bipartite states with vanishing quantum discord are necessarily separable and hence positive partial transpose (PPT). We show that $2\times N$ states satisfy additional property: the positivity of their partial transposition is recognized with respect to the canonical factorization of the original density operator. We call such states strong PPT (SPPT). Therefore, we provide a natural witness for a quantum discord: if a $2\times N$ state is not SPPT it must contain nonclassical correlations measured by quantum discord. It is an analog of the celebrated Peres-Horodecki criterion: if a state is not PPT it must be entangled.

In this paper, we investigate the particle entanglement in two-dimensional (2D) weakly interacting rotating Bose and Fermi gases. We find that both particle localization and vortex localization can be indicated by particle entanglement. We also use particle entanglement to show the occurrence of edge reconstruction of rotating fermions. The different properties of condensate phase and vortex liquid phase of bosons can be reflected by particle entanglement and in vortex liquid phase we construct the same trial wave function with that in [Phys. Rev. Lett. 87, 120405 (2001)] from the viewpoint of entanglement to relate the ground state with quantum Hall state. Finally, the relation between particle entanglement and interaction strength is studied.

We study the noise correlations of one-dimensional binary Bose mixtures, as a probe of their quantum phases. In previous work [Phys. Rev. A 80, 023619 (2009)], we found a rich structure of many-body phases in such mixtures, such as paired and counterflow superfluidity. Here we investigate the signature of these phases in the noise correlations of the atomic cloud after time-of-flight expansion, using both Luttinger liquid theory and the time-evolving block decimation (TEBD) method. We find that paired and counterflow superfluidity exhibit distinctive features in the noise spectra. We treat both extended and inhomogeneous systems, and our numerical work shows that the essential physics of the extended systems is present in the trapped-atom systems of current experimental interest. For paired and counterflow superfluid phases, we suggest methods for extracting Luttinger parameters from noise correlation spectroscopy.

In this paper, we present a theoretical study of a two-component Bose-Einstein condensate composed of ytterbium (Yb) isotopes in a three-dimensional anisotropic harmonic potential. The condensate consists of a mixture of ${}^{176}\mathrm{Yb}$ atoms which have a negative $s$-wave scattering length and ${}^{174}\mathrm{Yb}$ atoms having a positive $s$-wave scattering length. We study the ground-state as well as dynamic properties of this two-component condensate. Due to the attractive interactions between ${}^{176}\mathrm{Yb}$ atoms, the condensate of ${}^{176}\mathrm{Yb}$ undergoes a collapse when the particle number exceeds a critical value. The critical number and the collapse dynamics are modified due to the presence of ${}^{174}\mathrm{Yb}$ atoms. We use coupled two-component Gross-Pitaevskii equations to study the collapse dynamics. The theoretical results obtained are in reasonable agreement with the experimental results of Fukuhara et al. [Phys. Rev. A 79, 021601(R) (2009)].

We analyze the existence, stability, and mobility of gap solitons (GSs) in a periodic photonic structure built into a nonlocal self-defocusing medium. Counterintuitively, the GSs are supported even by a highly nonlocal nonlinearity, which makes the system quasilinear. Unlike local models, the variational approximation predicts the GSs in good agreement with numerical findings due to the suppression of undulating tails of the solitons.

We investigate the one-dimensional Heisenberg $\mathit{XXZ}$ model involving the Dzyaloshinskii-Moriya (DM) interaction from the viewpoint of quantum information. By using the density-matrix–renormalization-group technique, we study the Berezinskii-Kosterlitz-Thouless (BKT) phase transition using the ground-state fidelity, the fidelity susceptibility, and the entanglement entropy. We argue that the BKT phase transition can be well characterized in our model, and the critical line induced by the DM interaction can also be detected.

In a random laser based on a mixture of ${\mathrm{Nd}}^{3+}:{\mathrm{Ba}}_5$(${\mathrm{PO}}_4$)${}_3$ and ${\mathrm{Cr}}^{4+}:{\mathrm{Y}}_3$${\mathrm{Al}}_5$${\mathrm{O}}_{12}$ powders, we have observed trains of anomalously delayed stimulated emission pulses, which lasted for several tens of nanoseconds after the end of the pumping pulse. The phenomenon is explained by the color-center formation and reversed-saturable absorption in ${\mathrm{Cr}}^{4+}$:YAG powder.

We investigate theoretically the dissociative ionization of an ${{\mathrm{H}}_2}^{+}$ molecule using two ultrashort laser (pump-probe) pulses. The pump pulse prepares a dissociating nuclear wave packet on an ungerade surface of ${{\mathrm{H}}_2}^{+}$. Next, an ultraviolet [or extreme ultraviolet (XUV)] probe pulse ionizes this dissociating state at large ($R=20–100$ bohr) internuclear distance. We calculate the momenta distributions of protons and photoelectrons which show a (two-slit-like) interference structure. A general, simple interference formula is obtained which depends on the electron and protons momenta, as well as, on the pump-probe delay and also on the durations and polarizations of the laser pulses. This pump-probe scheme reveals a striking quantum delocalization of the electron over two protons which intuitively should be localized on just one of the protons separated by the distance $R$ much larger than the atomic Bohr orbit.

A single broadband squeezed field constitutes a quantum communication resource that is sufficient for the realization of a large number $N$ of quantum channels based on distributed Einstein-Podolsky-Rosen entangled states. Each channel can serve as a resource for, for example, independent quantum key distribution or teleportation protocols. $N$-fold channel multiplexing can be realized by accessing $2N$ squeezed modes at different Fourier frequencies. We report on the experimental implementation of the $N=1$ case through the interference of two squeezed states, extracted from a single broadband squeezed field, and demonstrate all techniques required for multiplexing ($N>1$). Quantum channel frequency multiplexing can be used to optimize the exploitation of a broadband squeezed field in a quantum information task. For instance, it is useful if the bandwidth of the squeezed field is larger than the bandwidth of the homodyne detectors. This is currently a typical situation in many experiments with squeezed and two-mode squeezed entangled light.

Recent advances in experimental techniques now permit measurement of the Casimir force with unprecedented precision. To achieve a comparable precision in the theoretical prediction of the force, it is necessary to accurately determine the electric permittivity of the materials constituting the plates along the imaginary frequency axis. The latter quantity is not directly accessible to experiments, but it can be determined via dispersion relations from experimental optical data. In the experimentally important case of conductors, however, a serious drawback of the standard dispersion relations commonly used for this purpose is their strong dependence on the chosen low-frequency extrapolation of the experimental optical data, which introduces a significant and not easily controllable uncertainty in the result. In this paper we show that a simple modification of the standard dispersion relations, involving suitable analytic window functions, resolves this difficulty, making it possible to reliably determine the electric permittivity at imaginary frequencies using solely experimental optical data in the frequency interval where they are available, without any need for uncontrolled data extrapolations.

The dissociative recombination (DR) of CH${{}_5}^{+}$ and CD${{}_5}^{+}$ has been studied at the heavy-ion storage ring CRYRING. The fragmentation dynamics of the dominant reaction channel ${\mathrm{CH}}_3+\mathrm{H}+\mathrm{H}$ has been investigated using an imaging detector. The results indicate that a two-step process via the production of a CH${}_4$ intermediate, which has sufficient energy to fragment further to ${\mathrm{CH}}_3+\mathrm{H}$, may play an important role. Discrepancies between the present and earlier results obtained from storage ring measurements with those from flowing afterglow experiments are addressed. Newly measured branching fractions in the DR of CD${{}_5}^{+}$ show an excellent agreement with branching fractions previously measured for CH${{}_5}^{+}$, and the absolute DR cross sections have been also measured over an interaction energy range between $~0$ and 0.1 eV for both isotopologs.

A two-component Bose-Einstein condensate that is confined in a one-dimensional ring potential supports solitary-wave solutions, which we evaluate analytically in the limit of a large ring. The derived solutions are shown to be unique. The corresponding dispersion relation that generalizes the case of a single-component system shows interesting features.