We study a quasi-one-dimensional attractive Bose gas confined in an optical lattice with a superimposed harmonic potential by analyzing the one-dimensional Bose-Hubbard Hamiltonian of the system. Starting from the three-dimensional many-body quantum Hamiltonian, we derive strong inequalities involving the transverse degrees of freedom under which the one-dimensional Bose-Hubbard Hamiltonian can be safely used. To have a reliable description of the one-dimensional ground state, which we call a quantum bright soliton, we use the density-matrix-renormalization-group (DMRG) technique. By comparing DMRG results with mean-field (MF) ones, we find that beyond-mean-field effects become relevant by increasing the attraction between bosons or by decreasing the frequency of the harmonic confinement. In particular, we find that, contrary to the MF predictions based on the discrete nonlinear Schrödinger equation, average density profiles of quantum bright solitons are not shape-invariant. We also use the time-evolving-block-decimation method to investigate the dynamical properties of bright solitons when the frequency of the harmonic potential is suddenly increased. This quantum quench induces a breathing mode whose period crucially depends on the final strength of the superimposed harmonic confinement.

At present, great effort is spent on the experimental realization of gauge fields for quantum many-body systems in optical lattices. At the same time, the single-site-resolved detection of individual atoms has become a new powerful experimental tool. We discuss a protocol for the single-site-resolved measurement of the current statistics of quantum many-body systems, which makes use of a bichromatic optical superlattice and single-site detection. We illustrate the protocol by a numerical study of the current statistics for interacting bosons in one and two dimensions and discuss the role of the on-site interactions for the current pattern and the ground-state symmetry for small two-dimensional lattices with artificial magnetic fields.

We demonstrate the principle of one-sided device-independent continuous-variable (CV) quantum information. In situations of no trust, we show by enactment how the use of standard CV entanglement criteria can mislead Charlie into thinking that Alice and Bob share entanglement, when the data are actually generated classically using a local-hidden-variable theory based on the Wigner function. We distinguish between criteria that demonstrate CV entanglement, and criteria that demonstrate the CV Einstein-Podolsky-Rosen (EPR) steering paradox. We show that the latter, but not the former, are necessarily one-sided device-independent entanglement witnesses, and can be used by Charlie to signify genuine EPR entanglement, if he trusts only Alice. A monogamy result for the EPR steering paradox confirms the security of the shared amplitude values in that case.

We study the parity- and time-reversal ($\mathcal{PT}$) symmetric non-Hermitian Su-Schrieffer-Heeger (SSH) model with two conjugated imaginary potentials $\pm i\gamma$ at two end sites. The SSH model is known as one of the simplest two-band topological models which has topologically trivial and nontrivial phases. We find that the non-Hermitian terms can lead to different effects on the properties of the eigenvalues spectrum in topologically trivial and nontrivial phases. In the topologically trivial phase, the system undergos an abrupt transition from the unbroken $\mathcal{PT}$-symmetry region to the spontaneously broken $\mathcal{PT}$-symmetry region at a certain ${\gamma }_c$, and a second transition occurs at another transition point ${\gamma }_{c^{{}^{\prime }}}$ when further increasing the strength of the imaginary potential $\gamma$. But in the topologically nontrivial phase, the zero-mode edge states become unstable for arbitrary nonzero $\gamma$ and the $\mathcal{PT}$ symmetry of the system is spontaneously broken, which is characterized by the emergence of a pair of conjugated imaginary modes.

We propose a quantum-state transfer protocol in a spin chain that requires only the control of the spins at the ends of the quantum wire. The protocol is to a large extent insensitive to inhomogeneity caused by local magnetic fields and perturbation of exchange couplings. Moreover, apart from the free evolution regime, it allows one to induce an adiabatic spin transfer, which provides the possibility of performing the transfer on demand. We also show that the amount of information leaking into the central part of the chain is small throughout the whole transfer process (which protects the information sent from being eavesdropped) and can be controlled by the magnitude of the external magnetic field.

We exploit a ferromagnetic chain of interacting $d$-level ($d>2$) particles for arbitrary perfect transfer of quantum states with $(d-1)$ levels. The presence of one extra degree of freedom in the Hilbert space of particles, which is not used in encoding, allows one to achieve perfect transfer even in a uniform chain through a repeated measurement procedure with consecutive single site measurements. Apart from the first iteration, for which the time of evolution grows linearly with the size of the chain, in all other iterations, the evolution times are short and do not scale with the length. The success probability of the mechanism grows with the number of repetitions and practically after a few iterations the transfer is accomplished with a high probability.

We introduce the concept of boundariness capturing the most efficient way of expressing a given element of a convex set as a probability mixture of its boundary elements. In other words, this number measures (without the need of any explicit topology) how far the given element is from the boundary. It is shown that one of the elements from the boundary can be always chosen to be an extremal element. We focus on evaluation of this quantity for quantum sets of states, channels, and observables. We show that boundariness is intimately related to (semi)norms that provide an operational interpretation of this quantity. In particular, the minimum error probability for discrimination of a pair of quantum devices is lower bounded by the boundariness of each of them. We proved that for states and observables this bound is saturated and conjectured this feature for channels. The boundariness is zero for infinite-dimensional quantum objects as in this case all the elements are boundary elements.

Ancilla postselection is a common means of achieving fault tolerance in quantum error correction. However, it can lead to additional data errors due to movement or wait operations. Alternatives to postselection may achieve lower overall failure rates due to avoiding such errors. We present numerical simulation results comparing the logical error rates for the fault-tolerant [[7,1,3]] Steane code using techniques of ancilla verification vs the newer method of ancilla decoding, as described in Phys. Rev. Lett. 98, 020501 (2007). We simulate QEC procedures in which the possibility of ancilla verification failures requires the creation and storage of additional ancillae and/or additional waiting of the data until a new ancilla can be created. We find that the decoding method, which avoids verification failures, is advantageous in terms of overall error rate in various cases, even when measurement operations are no slower than others. We analyze the effect of different classes of physical error on the relative performance of these two methods.

The ground and low-lying singly excited states of the two-dimensional He and He-like atomic ions have been studied by the full configuration interaction method focusing on the angular correlation between the two electrons involved. For small values of the nuclear charge $Z_n$, the two-electron angular-density distribution for the ground state strongly depends on the two-electron angle ${\varphi }_{-}$ reaching a peak at ${\varphi }_{-}$ = 0. This strong dependence on ${\varphi }_{-}$ strongly decreases with increasing $Z_n$ along with the decreasing electron-electron interaction. In contrast, the probability-density distribution for the singlet-triplet pair of states of the $\left(1s\right)\left(2p\right)$ configuration becomes appreciable with increasing $Z_n$, reaching peaks at ${\varphi }_{-}$ = 0 and at ${\varphi }_{-}$ = $\pm \pi /2$ for the singlet and triplet states, respectively. This indicates a preference of the two electrons to be on the same side of the nucleus for the singlet $\left(1s\right)\left(2p\right){}^{1}P$ state and on opposite sides of the nucleus for the triplet $\left(1s\right)\left(2p\right){}^{3}P$ state. The origin of these angular dependences is rationalized on the basis of the genuine and conjugate Fermi hole concepts.

We describe calculations of elastic and inelastic scattering of neutral molecules and cold ions in a magnetic field. The molecule is assumed to have a magnetic and electric dipole moment. The external magnetic field splits the ground rovibrational energy levels of the molecule. The highest energy state within the ground rovibrational manifold increases in energy as the distance to the ion decreases leading to a repelling potential. At low energy, inelastic collisions are strongly suppressed due to the large distance of closest approach. Thus, a collision between a neutral molecule and a cold ion will lead to a decrease in the molecule's kinetic energy with no change in internal energy. We present results for the specific case of OH molecules cooled by ${\mathrm{Be}}^{+}$, ${\mathrm{Mg}}^{+}$, or ${\mathrm{Ca}}^{+}$ ions. Also, we perform molecular dynamics simulations of ions and molecules in a combined Paul trap and time-averaged orbiting potential trap. Our results suggest that sympathetic cooling of neutral molecules by ions would be possible if cold ions and molecules could be simultaneously trapped.

We study the localization of a noninteracting and weakly interacting Bose-Einstein condensate (BEC) with spin-orbit coupling loaded in a quasiperiodic bichromatic optical lattice potential using the numerical solution and variational approximation of a binary mean-field Gross-Pitaevskii equation with two pseudospin components. We confirm the existence of the stationary localized states in the presence of the spin-orbit and Rabi couplings for an equal distribution of atoms in the two components. We find that the interaction between the spin-orbit and Rabi couplings favors the localization or delocalization of the BEC depending on the phase difference between the components. We also studied the oscillation dynamics of the localized states for an initial population imbalance between the two components.

We provide a unified description of the Gouy phase anomaly, highlighting the pivotal role of local fluctuations in transverse momentum and quantal phase changes associated with electron trajectories that touch caustics. Using arguments based on wave optics, at the interface between classical and quantum mechanics, we derive the magnitude of the quantized Gouy phase changes for scalar waves. Our analysis unifies disparate descriptions of the Gouy anomaly within a single theoretical framework. In particular, we find that the phase anomaly connects Maslov indices, quantal Berry phases, Heisenberg momentum fluctuations, and confinement-induced Lévy-Leblond phase shifts.

A single trapped ion driven away from the equilibrium position behaves like a Duffing oscillator. We demonstrate in a homebuilt surface-electrode trap (SET) the motion transduction of a trapped-ion oscillator from one dimension to another along with amplification of motional amplitudes and energies under the full control of the radio-frequency drive voltage. The phenomena, originated from different layouts and fabrication asymmetry of the SET, can be understood by complicated Duffing nonlinear equations. Our scheme provides an effective mechanism to investigate very complicated nonlinear behavior in trapped-ion setups and is expected to have extensive applications.

We study finite-temperature magnetic phases of three-component mixtures of ultracold fermions with repulsive interactions in optical lattices with simple cubic or square geometry by means of dynamical mean-field theory (DMFT). We focus on the case of one particle per site (1/3 band filling) at moderate interaction strength, where we observe a sequence of thermal phase transitions into two- and three-sublattice ordered states by means of the unrestricted real-space generalization of DMFT. From our quantitative analysis we conclude that long-range ordering in three-component mixtures should be observable at comparable temperatures as in two-component mixtures.

In a recent article [Phys. Rev. A 88, 063641 (2013)], Cizek and Kasevich claimed that quantum fragmentation occurs in the metastable state of a Bose-Einstein condensate with an attractive interaction confined in an elongated harmonic potential. This result was obtained using the two-state Gaussian variational method. However, modified methods show that no fragmentation occurs for the parameters used by Cizek and Kasevich.

We introduce an all-optical approach to producing high-flux synthetic magnetic fields for neutral atoms or molecules by designing intrinsically time-periodic optical superlattices. A single laser source, modulated to generate two frequencies, suffices to create dynamic interference patterns which have topological Floquet energy bands. We propose a simple laser setup that realizes a tight-binding model with uniform flux and well-separated Chern bands. Our method relies only on the particles' scalar polarizability and far-detuned light.

We present a closed-form solution to the eigenvalue problem of a class of master equations that describe open quantum systems with loss and dephasing but without gain. The method relies on the existence of a conserved number of excitations in the Hamiltonian part and the fact that none of the Lindblad operators describe an excitation of the system. In the absence of dephasing Lindblad operators, the eigensystem of the Liouville operator can be constructed from the eigenvalues and eigenvectors of the effective non-Hermitian Hamiltonian used in the quantum jump approach. Open versions of spin chains, the Tavis-Cummings model, and coupled Harmonic oscillators without gain can be solved using this technique.

We propose a protocol for direct quantum communication between two parties (Alice and Bob) which is achieved by controlling the phase of the signal photon. Without imperfection and noise, Alice's two detectors always click with unit probability according to Bob's different decisions. The probability of detecting a photon in the transmission channel can be controlled and can be made arbitrarily small by increasing the resources.

We present a two-state practical quantum bit commitment protocol, the security of which is based on the current technological limitations, namely the nonexistence of either stable long-term quantum memories or nondemolition measurements. For an optical realization of the protocol, we model the errors, which occur due to the noise and equipment (source, fibers, and detectors) imperfections, accumulated during emission, transmission, and measurement of photons. The optical part is modeled as a combination of a depolarizing channel (white noise), unitary evolution (e.g., systematic rotation of the polarization axis of photons), and two other basis-dependent channels, namely the phase- and bit-flip channels. We analyze quantitatively the effects of noise using two common information-theoretic measures of probability distribution distinguishability: the fidelity and the relative entropy. In particular, we discuss the optimal cheating strategy and show that it is always advantageous for a cheating agent to add some amount of white noise—the particular effect not being present in standard quantum security protocols. We also analyze the protocol's security when the use of (im)perfect nondemolition measurements and noisy or bounded quantum memories is allowed. Finally, we discuss errors occurring due to a finite detector efficiency, dark counts, and imperfect single-photon sources, and we show that the effects are the same as those of standard quantum cryptography.