We present an easy, efficient, and fast method to generate arbitrary linear combinations of light orbital angular-momentum eigenstates $\ell =\pm 2$ starting from a linearly polarized TEM${}_{00}$ laser beam. The method exploits the spin-to-orbital angular-momentum conversion capability of a liquid-crystal-based $q$ plate and a Dove prism inserted into a Sagnac polarizing interferometer. The nominal generation efficiency is $100\%$, being limited only by reflection and scattering losses in the optical components. When closed paths are followed on the polarization Poincaré sphere of the input beam, the associated Pancharatnam geometric phase is transferred unchanged to the orbital angular momentum state of the output beam.

We study theoretically an atomic Bose-Einstein condensate in a double-well trap, both quantum-mechanically and classically, under conditions such that in the classical model an unstable equilibrium dissolves into large-scale oscillations of the atoms between the potential wells. Quantum mechanics alone does not exhibit such nonlinear dynamics, but measurements of the atom numbers in the potential wells may nevertheless cause the condensate to behave essentially classically.

We study a driven two-state system interacting with a generic structured environment. We outline the derivation of the time-local microscopic non-Markovian master equation, in the limit of weak coupling between the system and the reservoir, and we derive its analytic solution for general reservoir spectra in the regime of validity of the secular approximation. We also consider the non-Markovian master equation without the secular approximation and study the effect of nonsecular terms on the system dynamics for two classes of reservoir spectra: the Ohmic and the Lorentzian reservoir. Finally, we derive the analytic conditions for complete positivity of the dynamical map, with and without the secular approximation. Interestingly, the complete positivity conditions have a transparent physical interpretation in terms of the characteristic time scales of phase diffusion and relaxation processes.

We propose a scheme for efficient cluster state quantum computation by using imperfect polarization-entangled photon-pair sources, linear optical elements, and inefficient non-photon-number-resolving detectors. The efficiency threshold for loss tolerance in our scheme requires the product of source and detector efficiencies should be $>1/2$, the best known figure. This figure applies to uncorrelated loss. We further find that the loss threshold is unaffected by correlated loss in the photon pair source. Our approach sheds new light on efficient linear optical quantum computation with imperfect experimental conditions.

We explicitly calculate the time dependence of entanglement via the convex roof extension for a system of noninteracting harmonic oscillators. These oscillators interact only indirectly with each other by way of a zero-temperature bath. The initial state of the oscillators is taken to be that of an entangled Schrödinger-cat state. This type of initial condition leads to superexponential decay of the entanglement when the initial state has the same symmetry as the interaction Hamiltonian.

We analyze the effect of bounding the occupation number of bosonic field modes on the correlations among all the different spatial-temporal regions in a setting in which we have a space time with a horizon along with an inertial observer. We show that the entanglement between $A$ (inertial observer) and $R$ (uniformly accelerated observer) depends on the bound $N$, contrary to the fermionic case. Whether or not decoherence increases with $N$ depends on the value of the acceleration $a$. Concerning the bipartition $A\mathrm{R̄}$ (Alice with an observer in Rindler’s region $\mathit{IV}$), we show that no entanglement is created whatever the value of $N$ and $a$. Furthermore, $\mathit{AR}$ entanglement is very quickly lost for finite $N$ and for $N\to \infty$. We will study in detail the mutual information conservation law found for bosons and fermions. By means of the boundary effects associated to $N$ finiteness, we will show that for bosons this law stems from classical correlations while for fermions it has a quantum origin. Finally, we will present the strong $N$ dependence of the entanglement in $R\mathrm{R̄}$ bipartition and compare the fermionic cases with their finite $N$ bosonic analogs. We will also show the anti-intuitive dependence of this entanglement on statistics since more entanglement is created for bosons than for their fermion counterparts.

We demonstrate that coupled electronic and nuclear fluxes in molecules can strongly depend on the initial state preparation. Starting the dynamics of an aligned ${\mathrm{D}}_2{}^{+}$ molecule at two different initial conditions, the inner and the outer turning points, we observe qualitatively different oscillation patterns of the nuclear fluxes developing after 30 fs. This corresponds to different orders of magnitude bridged by the time evolution of the nuclear dispersion. Moreover, there are attosecond time intervals within which the electronic fluxes do not adapt to the nuclei motion depending on the initial state. These results are inferred from two different approaches for the numerical flux simulation, which are both in good agreement.

We study the possibility for generating a new type of spin-orbit coupling for the center-of-mass motion of cold atoms, using laser beams that resonantly couple $N$ atomic internal ground states to an extra state. After a general analysis of the scheme, we concentrate on the tetrapod setup ($N=4$) where the atomic state can be described by a three-component spinor, evolving under the action of a Rashba-Dresselhaus-type spin-orbit coupling for a spin 1 particle. We illustrate a consequence of this coupling by studying the negative refraction of atoms at a potential step and show that the amplitude of the refracted beam is significantly increased in comparison to the known case of spin $1/2$ Rashba-Dresselhaus coupling. Finally, we explore a possible implementation of this tetrapod setup, using stimulated Raman couplings between Zeeman sublevels of the ground state of alkali-metal atoms.

We calculate the density profiles of a trapped spin-imbalanced Fermi gas with attractive interactions in a one-dimensional optical lattice, using both the local-density approximation (LDA) and density-matrix renormalization-group (DMRG) simulations. Based on the exact equation of state obtained by Bethe ansatz, the LDA predicts that the gas phase separates into shells with a partially polarized core and fully paired wings, the latter occurring below a critical spin polarization. This behavior is also seen in numerically exact DMRG calculations at sufficiently large particle numbers. We show that, unlike in the continuum case, the critical polarization is a nonmonotonic function of the interaction strength and vanishes in the limit of large interactions.

We study the quantum phase transition of the 1D weakly interacting Bose gas in the presence of disorder. We characterize the phase transition as a function of disorder and interaction strengths, by inspecting the long-range behavior of the one-body density matrix as well as the drop in the superfluid fraction. We focus on the properties of the low-energy Bogoliubov excitations that drive the phase transition and find that the transition to the insulator state is marked by a diverging density of states and a localization length that diverges as a power-law with power $1$. We draw the phase diagram and we observe that the boundary between the superfluid and the insulator phase is characterized by two different algebraic relations. These can be explained analytically by considering the limiting cases of zero and infinite disorder correlation length.

Quasi-transverse-electric and -transverse-magnetic fundamental whispering gallery modes in a polymer-coated silica microtoroid are theoretically investigated and demonstrated to possess very high-quality factors. The existence of a nanometer-thickness layer not only evidently reduces the cavity mode volume but also draws the maximal electric field’s position of the mode to the outside of the silica toroid, where single quantum dots or nanocrystals are located. Both effects result in a strongly enhanced coherent interaction between a single dipole (for example, a single defect center in a diamond crystal) and the quantized cavity mode. Since the coated microtoroid is highly feasible and robust in experiments, it may offer an excellent platform to study strong-coupling cavity quantum electrodynamics, quantum information, and quantum computation.

General principles for the existence of perfect transmission resonances in photonic multilayer structures are formulated in terms of light interference described by recurrent Airy formulas. Mirror symmetry in the multilayer is shown to be a sufficient but not necessary condition for perfect transmission resonances. Asymmetric structures displaying perfect transmission in accordance with the proposed principles are demonstrated. A hybrid Fabry-Pérot photonic-crystal structure of the type $(\mathit{BA}){}^k(\mathit{AB}){}^k(\mathit{AABB}){}^m$ is proposed, combining perfect transmission and highly asymmetric electric field localization. Strength and asymmetry of localization can be controlled independently to be of use in tailoring nonreciprocal behavior of nonlinear all-optical diodes.

We report Bose-Einstein condensation of ${}^{88}\mathrm{Sr}$, which has a small, negative $s$-wave scattering length ($a_{88}=-2a_0$). We overcome the poor evaporative cooling characteristics of this isotope by sympathetic cooling with ${}^{87}\mathrm{Sr}$ atoms. ${}^{87}\mathrm{Sr}$ is effective in this role despite the fact that it is a fermion because of the large ground-state degeneracy arising from a nuclear spin of $I=9/2$, which reduces the impact of Pauli blocking of collisions. We observe a limited number of atoms in the condensate ($N_{\max }\approx {10}^4$) that is consistent with the value of $a_{88}$ and the optical dipole trap parameters.

Comparison theorems are established for the Dirac and Klein-Gordon equations. We suppose that $V^{(1)}(r)$ and $V^{(2)}(r)$ are two real attractive central potentials in $d$ dimensions that support discrete Dirac eigenvalues $E_{k_d\nu }^{(1)}$ and $E_{k_d\nu }^{(2)}$. We prove that if $V^{(1)}(r)⩽V^{(2)}(r)$, then each of the corresponding discrete eigenvalue pairs is ordered $E_{k_d\nu }^{(1)}⩽E_{k_d\nu }^{(2)}$. This result generalizes an earlier, more restrictive theorem that required the wave functions to be node-free. For the the Klein-Gordon equation, similar reasoning also leads to a comparison theorem provided in this case that the potentials are negative and the eigenvalues are positive.

The parity-nonconservation (PNC) effect on the laser-induced $2\hspace{0.5em}{}^3{S}_1$–$2\hspace{0.5em}{}^1{S}_0$ transition in heavy heliumlike ions is considered. A simple analytical formula for the PNC correction to the cross section is derived for the case, when the opposite-parity $2\hspace{0.5em}{}^1{S}_0$ and $2\hspace{0.5em}{}^3{P}_0$ states are almost degenerate and, therefore, the PNC effect is strongly enhanced. Numerical results are presented for heliumlike gadolinium and thorium, which seem the most promising candidates for such experiments. In both Gd and Th cases the photon energy required will be anticipated with a high-energy laser built at GSI. Alternatively, it can be gained with ultraviolet lasers utilizing relativistic Doppler tuning at FAIR facilities in Darmstadt.

The techniques of principal and independent component analysis are applied to images of ultracold atoms. As an illustrative example, we present the use of these model-independent methods to rapidly determine the differential phase of a Bose-Einstein condensate interferometer from large sets of images of interference patterns. These techniques have been useful in the calibration of the experiment and in the investigation of phase randomization. The details of the algorithms are provided.

We consider spatial solitons as, for example, self-confined optical beams in spaces of constant curvature, which are a natural generalization of flat space. Due to the symmetries of these spaces we are able to define respective dynamical parameters, for example, velocity and position. For positively curved space we find stable multiple-hump solitons as a continuation from the linear modes. In the case of negatively curved space we show that no localized solution exists and a bright soliton will always decay through a nonlinear tunneling process.

A comprehensive theory of the Landau-Zener transition in quadratic nonlinear two-state systems is developed. A compact analytic formula involving elementary functions only is derived for the final transition probability. The formula provides a highly accurate approximation for the whole rage of the variation of the Landau-Zener parameter.

Six-qubit cluster states built on the simultaneous entanglement of two photons in three independent degrees of freedom, that is, polarization and a double longitudinal momentum, have been recently demonstrated. We present here the peculiar entanglement properties of the linear cluster state $|\mathrm{L͠C}{}_6\rangle$ related to the three degrees of freedom. This state has been adopted to realize various kinds of controlled not (cnot) gates, obtaining high values of the fidelity of the expected output states for all considered cases. Our results demonstrate that these states may represent a promising approach toward scalable quantum computation in a medium-term time scale. The future perspectives of a hybrid approach to one-way quantum computing based on multiple degrees of freedom and multiphoton cluster states are also discussed in the conclusion of this article.

Entanglement, as studied in quantum information science, and nonlocal quantum correlations, as studied in condensed matter physics, are fundamentally akin to each other. However, their relationship is often hard to quantify due to the lack of a general approach to study both on the same footing. In particular, while entanglement and nonlocal correlations are properties of states, both arise from symmetries of global operators that commute with the system Hamiltonian. Here, we introduce a framework for completely classifying the local and nonlocal properties of all such global operators, given the Hamiltonian and a bipartitioning of the system. This framework is limited to descriptions based on stabilizer quantum codes, but may be generalized. We illustrate the use of this framework to study entanglement and nonlocal correlations by analyzing global symmetries in topological order, distribution of entanglement, and entanglement entropy.