We study bright solitons in a Bose-Einstein condensate with a spin-orbit coupling that has been realized experimentally. Both stationary bright solitons and moving bright solitons are found. The stationary bright solitons are the ground states and possess well-defined spin-parity, a symmetry involving both spatial and spin degrees of freedom; these solitons are real valued but not positive definite, and the number of their nodes depends on the strength of spin-orbit coupling. For the moving bright solitons, their shapes are found to change with velocity due to the lack of Galilean invariance in the system.

Quantum-degenerate mixtures of one-electron and two-electron atoms form the starting point for studying few- and many-body physics of mass-imbalanced pairs as well as the production of paramagnetic polar molecules. We recently reported the achievement of dual-species quantum degeneracy of a mixture of lithium and ytterbium atoms. Here we present details of the key experimental steps for the all-optical preparation of these mixtures. Further, we demonstrate the use of the magnetic field gradient tool to compensate for the differential gravitational sag of the two species and control their spatial overlap.

In this paper we investigate the finite-temperature properties of a Bose-Einstein condensate (BEC)-cavity system with a strong nonlinear atom-photon interaction by means of a functional path-integral approach. It is shown that the experimentally observed phase diagram [Baumann, Guerlin, Brennecke, and Esslinger, Nature (London) 464, 1301 (2010)] can be better explained in our finite-temperature theory. More importantly, we identify a new dynamical unstable phase in this experiment. By tuning various experimental parameters, we reveal some rich temperature-driven phase diagrams and, in particular, predict a four-phase coexistence point. Finally, we find analytically that the specific heat in the superradiant phase increases exponentially at lower temperatures. Moreover, it has a large jump at the temperature-driven critical point where the superradiant-normal phase transition occurs. As a result, we argue that the specific heat can serve as a powerful tool to probe the thermodynamic properties of the BEC-cavity system.

We study the cooling performance of optical-feedback controllers for open optical and mechanical resonators in the linear quadratic Gaussian setting of stochastic control theory. We utilize analysis and numerical optimization of closed-loop models based on quantum stochastic differential equations to show that coherent control schemes, where we embed the resonator in an interferometer to achieve all-optical feedback, can outperform optimal measurement-based feedback control schemes in the quantum regime of low steady-state excitation number. These performance gains are attributed to the coherent controller's ability to simultaneously process both quadratures of an optical probe field without measurement or loss of fidelity, and may guide the design of coherent feedback schemes for more general problems of robust nonlinear and robust control.

We propose a generalization of the technique of quantum state reconstruction to obtain the space derivative of the phase of a wave function, which is central to the hydrodynamic formulation of quantum mechanics in the manner of Madelung and Bohm. In this way we can construct Bohm trajectories and make contact with a recent experiment [Kocsis et al., Science 332, 1170 (2011)] extracting these trajectories after a double slit.

Pusey, Barrett, and Rudolph (PBR) have recently proven an important new theorem in the foundations of quantum mechanics [Pusey et al., Nature Phys. 8, 475 (2012)]. Here we propose alternative experimental protocols which lead to the PBR result for a special case and a weaker PBR-like result generally. Alternative experimental protocols support the assumption of measurement independence required for the PBR theorem.

We explore the possibilities of entangling two distant material qubits with the help of an optical radiation field in the regime of strong quantum electrodynamical couplingwith almost resonant interaction. For this purpose the optimum generalized field measurements are determined which are capable of preparing a two-qubit Bell state by postselection with minimum error. It is demonstrated that in the strong-coupling regime some of the recently found limitations of the nonresonant weak-coupling regime can be circumvented successfully due to characteristic quantum electrodynamical quantum interference effects. In particular, in the absence of photon loss it is possible to postselect two-qubit Bell states with fidelities close to unity by a proper choice of the relevant interaction time. Even in the presence of photon loss this strong-coupling regime offers interesting perspectives for creating spatially well-separated Bell pairs with high fidelities, high success probabilities, and high repetition rates which are relevant for future realizations of quantum repeaters.

We derive Casimir-Polder and van der Waals potentials of one or two atoms with diamagnetic properties in an arbitrary environment of magnetoelectric bodies. The calculations are based on macroscopic quantum electrodynamics and leading-order perturbation theory. For the examples of an atom and a perfect mirror and two atoms in free space, we show that diamagnetic dispersion potentials have the same sign as their electric counterparts but can exhibit quite different distance dependences.

We show theoretically that the dynamics of cold atoms in the lowest-energy band of a stationary optical lattice can be transformed and controlled by a second, weaker, periodic potential moving at a constant speed along the axis of the stationary lattice. The atom trajectories exhibit complex behavior, which depends sensitively on the amplitude and speed of the propagating lattice. When the speed and amplitude of the moving potential are low, the atoms are dragged through the static lattice and perform drifting orbits with frequencies an order of magnitude higher than that corresponding to the moving potential. Increasing either the speed or amplitude of the moving lattice induces Bloch-like oscillations within the energy band of the static lattice, which exhibit complex resonances at critical values of the system parameters. In some cases, a very small change in these parameters can reverse the atom's direction of motion. In order to understand these dynamics we present an analytical model, which describes the key features of the atom transport and also accurately predicts the positions of the resonant features in the atom's phase space. The abrupt controllable transitions between dynamical regimes, as well as the associated set of resonances, provide a mechanism for transporting atoms between precise locations in a lattice, as required for using cold atoms to simulate condensed matter or as a stepping stone to quantum information processing. The system also provides a direct quantum simulator of acoustic waves propagating through semiconductor nanostructures in sound analogs of the optical laser (saser).

A simple analytical model is developed to analyze and explain the complex dynamics of the multipeak modulation instability spectrum observed in dispersion oscillating optical fibers [M. Droques et al., Opt. Lett. 37, 4832 (2012)]. We provide a simple expression for the local parametric gain, which shows that each of the multiple spectral components grows thanks to a quasi-phase-matching mechanism due to the periodicity of the waveguide parameters, in good agreement with numerical simulations and experiments. This simplified model is also successfully used to tailor the multipeak modulation instability spectrum shape. These theoretical predictions are confirmed by experiments.

We theoretically study discrete photonic lattices in more than three dimensions and point out that such systems can exist in continuous three-dimensional space. We study discrete diffraction in the linear regime and demonstrate the existence of four-dimensional (4D) tesseract solitons in nonlinear 4D periodic photonic lattices. Finally, we propose a design towards a potential realization of such periodic 4D lattices in experiments.

We show that the transfer matrix for a $\mathcal{PT}$-invariant system, when recast in the appropriate variables, can be interpreted as a point in the (3+1)-dimensional de Sitter space. We introduce a natural $\mathcal{PT}$-invariant composition law for these matrices and confirm that their action appears as a Lorentz transformation. We elucidate the geometrical meaning of the $\mathcal{PT}$ symmetry breaking and suggest that the cosmological event horizon arising in the de Sitter metric can be can be unraveled with a simple optical scheme.

Recently, Gallego et al. [Phys. Rev. Lett. 107, 210403 (2011)] proved that any future information principle aiming at distinguishing between quantum and postquantum correlation must be intrinsically multipartite in nature. We establish similar results by using the device-independent success probability of Hardy's nonlocality argument for tripartite quantum systems. We construct an example of a tripartite Hardy correlation which is postquantum but satisfies not only the all-bipartite information principle but also the guess-your-neighbor's-input (GYNI) inequality.

Transferring quantum states efficiently between distant nodes of an information processing circuit is of paramount importance for scalable quantum computing. We report on an observation of a perfect state transfer protocol on a lattice, thereby demonstrating the general concept of transporting arbitrary quantum information with high fidelity. Coherent transfer over 19 sites is realized by utilizing judiciously designed optical structures consisting of evanescently coupled waveguide elements. We provide unequivocal evidence that such an approach is applicable in the quantum regime, for both bosons and fermions, as well as in the classical limit. Our results illustrate the potential of the perfect state transfer protocol as a promising route towards integrated quantum computing on a chip.

A major obstacle to implementing Shor's quantum number-factoring algorithm is the large size of modular-exponentiation circuits. We reduce this bottleneck by customizing reversible circuits for modular multiplication to individual runs of Shor's algorithm. Our circuit-synthesis procedure exploits spectral properties of multiplication operators and constructs optimized circuits from the traces of the execution of an appropriate greatest-common-divisor algorithm. Empirically, gate counts are reduced by four to five times, and circuit latency is reduced by larger factors.

We study the spectra of diamagnetic rubidium Rydberg atoms in strong magnetic and weak electric parallel fields, in the $n$-mixing regime. Our emphasis is on isolated pairs of near-degenerate, opposite-parity, diamagnetic states that become mixed by the weak electric field. Such level pairs allow for the generation of nondegenerate states with large, tunable permanent electric dipole moments and large optical excitation cross sections from the atomic ground state. We investigate how the dipole moments and the zero-electric-field energy defects of these level pairs can be tuned using small variations of the electric and magnetic fields. Using calculations, we explore the abundance of such level pairs over wide spectral regions for several magnetic quantum numbers. Applications of polar, diamagnetic Rydberg states in Rydberg-atom interaction experiments are briefly discussed.

Exact analytical expressions for the matrix elements of the Uehling potential in a basis of explicitly correlated exponential wave functions are presented. The obtained formulas are then used to compute with an improved accuracy the vacuum polarization correction to the binding energy of muonic and pionic molecules, both in a first-order perturbative treatment and in a nonperturbative approach. The first resonant states lying below the $n=2$ threshold are also studied, by means of the stabilization method with a real dilatation parameter.

We present ab initio calculations for the dissociative recombination rates of LiHe${}^{+}$ ions. The study involves first a realistic understanding of the electronic structure of the ion and neutral LiHe molecule and then carrying out the nuclear dynamics the system undergoes during the dissociation process. For the electronic part we employ $R$-matrix calculations to describe the situation of low-energy electrons scattered by LiHe${}^{+}$ ions. These results are further extended by additional quantum chemistry calculations of the higher Rydberg states of the neutral LiHe molecule as a compound state after the primary ionic interaction. We demonstrate that the two separate and independent results are smoothly connected via the use of Seaton's theorem. The subsequent motion of the nuclei is then incorporated via a rovibrational frame transformation based on the use of Siegert pseudostates. Finally, the resulting thermal dissociative recombination rates are shown for different initial states of the target LiHe${}^{+}$ ion in the presence of the impinging electron.

The guiding of highly charged ions through a single cylindrical nanocapillary is simulated to compare with previous experiments using capillaries in polyethylene terephthalate (PET) and polycarbonate (PC) polymers. The ions move in the three-dimensional electric field produced by the charges that ions have deposited before. Guiding conditions are achieved, using a nonlinear conductivity law to transport the deposited charges along the capillary surface. Remarkably, it is found that the migration of the deposited charges perpendicular to the capillary axis has a bigger effect on maintaining the ion guiding than the transport parallel to it. The ion trajectories are found to be focused, enhancing the ion guiding. The mean angle of the transmitted ions exhibit pronounced oscillations, in agreement with previous measurements. Experimentally observed differences in the oscillatory frequency as well as partial blocking of the ion transmission are interpreted by the calculations using a larger conductivity for PC in comparison with PET. Emphasis is given to the understanding of the self-organized formation of the charge patches.

Ultracold neutral plasmas exhibit a density-dependent resonant response to applied radio-frequency (rf) fields in the frequency range of several to hundreds of megahertz for achievable densities. We have conducted measurements where short bursts of an rf fieldwere applied to these plasmas, with pulse durations as short as two cycles. We still observed a density-dependent resonant response to these short pulses, but the time scale of the response is too short to be consistent with local heating of electrons in the plasma from collisions under a range of experimental parameters. Instead, our results are consistent with rapid energy transfer to individual electrons from electric fields resulting from an overall displacement of the electron cloud from the ions during the collective motion of the electrons. This collective motion was also observed by applying two sharp electric field pulses separated in time to the plasma. These measurements demonstrate the importance of collective motion in the energy transport in these systems.