We investigate the ground state of the one-dimensional interacting anyonic system based on the exact Bethe ansatz solution for arbitrary coupling constant $(0⩽c⩽\infty )$ and statistics parameter $(0⩽\kappa ⩽\pi )$. It is shown that the density of state in quasimomentum $k$ space and the ground-state energy are determined by the renormalized coupling constant $c^{\prime }$. The effect induced by the statistics parameter $\kappa$ exhibits in the momentum distribution in two aspects: Besides the effect of renormalized coupling, the anyonic statistics results in the nonsymmetric momentum distribution when the statistics parameter $\kappa$ deviates from 0 (Bose statistics) and $\pi$ (Fermi statistics) for any coupling constant $c$. The momentum distribution evolves from a Bose distribution to a Fermi one as $\kappa$ varies from 0 to $\pi$. The asymmetric momentum distribution comes from the contribution of the imaginary part of the nondiagonal element of reduced density matrix, which is an odd function of $\kappa$. The peak at positive momentum will shift to negative momentum if $\kappa$ is negative.

We find exact solutions to the nonlinear Schrödinger equation (NLSE) in the presence of self-steepening and a self-frequency shift. These include periodic solutions and localized solutions of dark-bright type which can be chiral, the chirality being controlled by the sign of the self-steepening term. A form of self-phase-modulation that can be tuned by higher-order nonlinearities as well as by the initial conditions, distinct from the nonlinear Schrödinger equation, characterizes these solutions. In certain nontrivial parameter domains, solutions are found to satisfy the linear Schrödinger equation, indicating the possibility of linear superposition in this nonlinear system. Dark and bright solitons exist in both the anomalous and normal dispersion regimes, and a duality between the dark-bright type of solution and kinematic higher-order chirping is also seen. Localized kink solutions similar to NLSE solitons, but with very different self-phase-modulation, are identified.

A quantum state is nonclassical if its Glauber-Sudarshan $P$ function fails to be interpreted as a probability density. This quantity is often highly singular, so that its reconstruction is a demanding task. Here we present the experimental determination of a well-behaved $P$ function showing negativities for a single-photon-added thermal state. This is a direct visualization of the original definition of nonclassicality. The method can be useful under conditions for which many other signatures of nonclassicality would not persist.

We analyze the appearance of non-Markovian effects in the dynamics of a bipartite system coupled to a reservoir, which can be described within a class of non-Markovian equations given by a generalized Lindblad structure. A master equation is derived, which we term the quantum Bloch-Boltzmann equation, describing both motional and internal states of a test particle in a quantum framework. When due to the preparation of the system or to decoherence effects one of the two degrees of freedom is amenable to a classical treatment and not resolved in the final measurement, though relevant for the interaction with the reservoir, non-Markovian behaviors such as stretched exponential or power law decay of coherences can occur.

For single-qubit teleportation, it has been shown that there is a family of two-qubit mixed states whose teleportation fidelity can be enhanced by subjecting one of the qubits to an amplitude damping channel. This is an interesting result, since noise in general degrades quantum entanglement. It is believed that this enhancement is due to an improvement in the classical correlations of the two-qubit states. Here, we consider two-qubit teleportation using a family of four-qubit mixed states as a resource. In this context, we show that one can again achieve enhancement in teleportation fidelity via dissipative interactions with the local environment. For a rather general class of input states, we find that this improvement implies an enhancement in the quantum discord of some teleported states. We conjecture that an improvement in some quantum property of the four-qubit mixed states could have resulted from the local interactions. We expect that our analysis will make an important case study for future investigations on the different aspects of composite quantum systems.

A recent calculation of the one-loop radiative correction to hyperfine splitting (hfs) of $p_{1∕2}$ states that includes binding corrections to all orders is extended to $p_{3∕2}$ states. Nuclear structure plays an essentially negligible role for such states, which is highly advantageous, as difficulties in controlling the Bohr-Weisskopf effect complicate the isolation of QED contributions for both $s_{1∕2}$ and $p_{1∕2}$ states. Three cases are studied. We first treat the hydrogen isoelectronic sequence, which is completely nonperturbative in $Z\alpha$ for high $Z$. Secondly the lowest lying $p_{3∕2}$ states of the neutral alkali-metal atoms are treated, and finally lithiumlike bismuth, where extensive theoretical and experimental studies of the hfs of $2s$ and $2p_{1∕2}$ states have been made, is addressed.

We derive the effective Gross-Pitaevskii equation for a cigar-shaped dipolar Bose-Einstein condensate in one-dimensional lattices and investigate the band structures numerically. Due to the anisotropic and the long-ranged dipole-dipole interaction in addition to the known contact interaction, we elucidate the possibility of modifying the band structures by changing the alignment of the dipoles with the axial direction. With the considerations of the transverse parts and the practical physical parameters of a cigar-shaped trap, we show the possibility to stabilize an attractive condensate simply by adjusting the orientation angle of dipoles. Some interesting Bloch waves at several particle current densities are identified for possible experimental observations.

We analyze the information content of density profiles for an ultracold Bose gas of atoms and extract resolution limits for observables contained in these images. Our starting point is density correlations that we compute within the Bogoliubov approximation, taking into account quantum and thermal fluctuations beyond mean-field theory. This provides an approximate way to construct the joint counting statistics of atoms in an array of pixels covering the gas. We derive the Fisher information of an image and the associated Cramér-Rao sensitivity bound for measuring observables contained in the image. We elaborate on our recent study on position measurements of a dark soliton [Negretti et al., Phys. Rev. A 77, 043606 (2008)] where a sensitivity scaling with the atomic density as $n^{-3∕4}$ was found. We discuss here a wider class of soliton solutions and present a detailed analysis of the Bogoliubov excitations and the gapless (Goldstone) excitation modes. These fluctuations around the mean field contribute to the noise in the image, and we show how they can actually improve the ability to locate the position of the soliton.

We consider the Casimir force on a metallic slab with the thickness in the nanometer range, bounded by different dielectric media. In such systems the force is large $(\sim {10}^6\mathrm{N}∕{\mathrm{m}}^2)$ and, depending on the selected configuration, it can be squeezing or relaxing. The mode analysis, performed numerically as well as analytically under the assumption of inert bounding media, indicates that the force on a thin metallic slab is, in many situations, predominantly due to the surface polariton (SP) modes of the system (an obvious exception is the configuration with the slab sandwiched between two highly reflecting plates). Thus, the sign and the magnitude of the Casimir force are typically determined by competing contributions from the two SP modes existing in the model adopted, and are controllable by properly designing the system parameters. The same conclusion holds for a more complex description of polar dielectric media, assuming that the characteristic frequencies of polar modes in dielectrics are much smaller than the characteristic plasma frequency of a metallic slab.

Realization of controllable interaction between distant qubits is one of the major problems in scalable solid-state quantum computing. We study a superconducting transmission line resonator (TLR) as a tunable dispersive coupler for the double-dot molecules. A general interaction Hamiltonian of $n$ two-electron spin-based qubits and the TLR is presented, where the double-dot qubits are biased at the large detuning region and the TLR is always empty and virtually excited. Our analysis of the main decoherence sources indicates that various major quantum operations can be reliably implemented with current technology.

We report the observation of above-threshold dissociation of a multielectron molecular system, $\mathrm{Na}_2{}^{+}$. The process is due to continuum-continuum transitions in a field-dressed molecular continuum. Three well-resolved fragmentation channels with different kinetic energy release patterns have been detected, of which two are associated with ordinary photodissociation via “light-induced potentials” into $\mathrm{Na}\left(3s\right)+{\mathrm{Na}}^{+}$ and $\mathrm{Na}\left(3p\right)+{\mathrm{Na}}^{+}$, and one with continuum-continuum transitions and above-threshold dissociation into $\mathrm{Na}\left(3p\right)+{\mathrm{Na}}^{+}$. We show that when we dress this molecule with a field whose intensity is $\sim 3\times {10}^{12}\mathrm{W}∕{\mathrm{cm}}^2$, above-threshold dissociation prevails over other processes, such as field ionization followed by Coulomb explosion.

We consider an entangled two-particle state that is produced from two independent downconversion laser sources by the process of “entanglement swapping,” so that the particles have never met. We prove a Greenberger-Horne-Zeilinger type theorem, showing that any deterministic, local, realistic theory is inconsistent with the quantum-mechanical perfect correlations for such a state. This theorem holds for individual events, with no inequalities, for detectors of 100% efficiency.

We again consider (as in a companion paper) an entangled two-particle state that is produced from two independent downconversion sources by the process of “entanglement swapping,” so that the particles have never met. We show that there is a natural extension of the Einstein-Pololsky-Rosen discussion of “elements of reality” to include inefficient detectors. We consider inefficient deterministic, local, realistic models of quantum theory that are “robust,” which we consider to be the minimum requirement for them to be taken seriously. By robust, we mean they satisfy the following three criteria: (a) they reproduce the quantum results for perfect correlations, if all particles are detected; (b) they produce some counts for every setting of the angles (so they do not describe some experiments that can easily be performed as “impossible”); (c) all their hidden variables are relevant (they must each produce a detectable result in some experiment). For such models, we prove a Greenberger-Horne-Zeilinger type theorem for arbitrary detection efficiencies, showing that any such theory is inconsistent with the quantum-mechanical perfect correlations. This theorem holds for individual events with no inequalities. As a result, the theorem is also independent of any random sampling hypothesis, and we take it as a refutation of such realistic theories, free of the detection efficiency and random sampling “loopholes.” The hidden variable analysis depends crucially on the use of two independent laser sources for the downconversions. We also investigate the necessity of using two independent sources versus a single source for all particles. Finally, we argue that the state we use can legitimately be considered as a two-particle state, and used as such in experiments.

The search problem is to find a state satisfying certain properties out of a given set. Grover’s algorithm drives a quantum computer from a prepared initial state to the target state and solves the problem quadratically faster than a classical computer. The algorithm uses selective transformations to distinguish the initial state and target state from other states. It does not succeed unless the selective transformations are very close to phase inversions. Here we show a way to go beyond this limitation. An important application lies in quantum error correction, where the errors can cause the selective transformations to deviate from phase inversions. The algorithms presented here are robust to errors as long as the errors are reproducible and reversible. This particular class of systematic errors arises often from imperfections in the apparatus setup. Hence our algorithms offer a significant flexibility in the physical implementation of quantum search.

We study the conditions under which a subsystem code is correctable in the presence of noise that results from continuous dynamics. We consider the case of Markovian dynamics as well as the general case of Hamiltonian dynamics of the system and the environment, and derive necessary and sufficient conditions on the Lindbladian and system-environment Hamiltonian, respectively. For the case when the encoded information is correctable during an entire time interval, the conditions we obtain can be thought of as generalizations of the previously derived conditions for decoherence-free subsystems to the case where the subsystem is time dependent. As a special case, we consider conditions for unitary correctability. In the case of Hamiltonian evolution, the conditions for unitary correctability concern only the effect of the Hamiltonian on the system, whereas the conditions for general correctability concern the entire system-environment Hamiltonian. We also derive conditions on the Hamiltonian which depend on the initial state of the environment, as well as conditions for correctability at only a particular moment of time. We discuss possible implications of our results for approximate quantum error correction.

We report on the experimental estimation of a lower bound of helium. Our experiment differs from a previous one described by Hasegawa et al. [Phys. Rev. A 71, 023407 (2005)]. The photons that correspond to the 27th harmonic of a Ti:sapphire laser have an energy of $41.8\mathrm{eV}$. The extraction of the cross section rests on a theoretical model, based on the rate equations, that fully includes the contribution from the sequential channels and the macroscopic effects. Some of the experimental parameters are very difficult to measure accurately. For those parameters, we deliberately consider values compatible with their experimental determinations and that lead systematically to an underestimation of the two-photon double ionization cross section. Our estimation of this lower bound is higher than a bunch of various theoretical results. It stays, however, too close to these latter ones to draw any definite conclusion about their validity, even though it clearly indicates that the actual value of the double ionization cross section is higher than expected.

Quantum Monte Carlo (QMC) simulations and the local density approximation (LDA) are used to map the constant particle number (canonical) trajectories of the Bose-Hubbard Hamiltonian confined in a harmonic trap onto the $(\mu ∕U,t∕U)$ phase diagram of the uniform system. Generically, these curves do not intercept the tips of the Mott insulator lobes of the uniform system. This observation necessitates a clarification of the appropriate comparison between critical couplings obtained in experiments on trapped systems with those obtained in QMC simulations. The density profiles and visibility are also obtained along these trajectories. Density profiles from QMC in the confined case are compared with LDA results.

We compute the phase diagram of the one-dimensional Bose-Hubbard model with a quasiperiodic potential by means of the density-matrix renormalization group technique. This model describes the physics of cold atoms loaded in an optical lattice in the presence of a superlattice potential whose wavelength is incommensurate with the main lattice wavelength. After discussing the conditions under which the model can be realized experimentally, the study of the density vs the chemical potential curves for a nontrapped system unveils the existence of gapped phases at incommensurate densities interpreted as incommensurate charge-density-wave phases. Furthermore, a localization transition is known to occur above a critical value of the potential depth $V_2$ in the case of free and hard-core bosons. We extend these results to soft-core bosons for which the phase diagrams at fixed densities display new features compared with the phase diagrams known for random box distribution disorder. In particular, a direct transition from the superfluid phase to the Mott-insulating phase is found at finite $V_2$. Evidence for reentrances of the superfluid phase upon increasing interactions is presented. We finally comment on different ways to probe the emergent quantum phases and most importantly, the existence of a critical value for the localization transition. The latter feature can be investigated by looking at the expansion of the cloud after releasing the trap.

Motivated by recent experiments in optics and atomic physics, we derive an averaged nonlinear partial differential equation describing the dynamics of the complex field in a nonlinear Schrödinger model in the presence of a periodic nonlinearity and a periodically varying dissipation coefficient. The incorporation of dissipation in our model is motivated by experimental considerations. We test the numerical behavior of the derived averaged equation by comparing it to the original nonautonomous model in a prototypical case scenario and observe good agreement between the two.