We consider a bosonic Josephson junction made of $N$ ultracold and dilute atoms confined by a quasi-one-dimensional double-well potential within the two-site Bose-Hubbard model framework. The behavior of the system is investigated at zero temperature by varying the interatomic interaction from the strongly attractive regime to the repulsive one. We show that the ground state exhibits a crossover from a macroscopic Schrödinger-cat state to a separable Fock state through an atomic coherent regime. By diagonalizing the Bose-Hubbard Hamiltonian we characterize the emergence of the macroscopic cat states by calculating the Fisher information $F$, the coherence by means of the visibility $\alpha$ of the interference fringes in the momentum distribution, and the quantum correlations by using the entanglement entropy $S$. Both Fisher information and visibility are shown to be related to the ground-state energy by employing the Hellmann-Feynman theorem. This result, together with a perturbative calculation of the ground-state energy, allows simple analytical formulas for $F$ and $\alpha$ to be obtained over a range of interactions, in excellent agreement with the exact diagonalization of the Bose-Hubbard Hamiltonian. In the attractive regime the entanglement entropy attains values very close to its upper limit for a specific interaction strength lying in the region where coherence is lost and self-trapping sets in.

We investigate analytically transverse-magnetic spatial bright solitons, as exact solutions of Maxwell’s equations, propagating through nonlinear metamaterials whose linear dielectric permittivity is very close to zero and whose effective nonlinear Kerr parameters can be tailored to achieve values not available in standard materials. Exploiting the fact that, in the medium considered, linear and nonlinear polarization can be comparable at feasible and realistic optical intensities, we identify two self-trapping mechanisms able to support two-peaked and flat-top solitons, respectively. Specifically, these two mechanisms are based on the occurrence of critical points at which the effective nonlinear permittivity vanishes, the two mechanisms differing in the way the compensation between linear and nonlinear polarization is achieved through the nonstandard values of the nonlinear parameters.

We present the continuous control of the light group velocity from subluminal to superluminal propagation with an on-resonant standing-wave coupling field in the $5S_{1/2}$–$5P_{1/2}$ transition of the $\Lambda$-type system of ${}^{87}\mathrm{Rb}$ atoms. When a coupling field was changed from a traveling-wave to a standing-wave field by adjusting the power of a counterpropagating coupling field, the probe pulse propagation continuously transformed from subluminal propagation, due to electromagnetically induced transparency with the traveling-wave coupling field, to superluminal propagation, due to narrow enhanced absorption with the standing-wave coupling field. The group velocity of the probe pulse was measured to be approximately 0.004$c$ to $-$0.002$c$ as a function of the disparity between the powers of the copropagating and the counterpropagating coupling fields.

We study the properties of a parity- and time-reversal- ($\mathcal{P}\mathcal{T}$) symmetric tight-binding chain of size $N$ with position-dependent hopping amplitude. In contrast to the fragile $\mathcal{P}\mathcal{T}$-symmetric phase of a chain with constant hopping and imaginary impurity potentials, we show that, under very general conditions, our model is always in the $\mathcal{P}\mathcal{T}$-symmetric phase. We numerically obtain the energy spectrum and the density of states of such a chain, and show that they are widely tunable. By studying the size dependence of inverse participation ratios, we show that although the chain is not translationally invariant, most of its eigenstates are extended. Our results indicate that tight-binding models with non-Hermitian, $\mathcal{P}\mathcal{T}$-symmetric hopping have a robust $\mathcal{P}\mathcal{T}$-symmetric phase and rich dynamics which may be explored in coupled waveguides.

The Dicke Hamiltonian describes the simplest quantum system with atoms interacting with photons: $N$ two-level atoms inside a perfectly reflecting cavity, which allows only one electromagnetic mode. It has also been successfully employed to describe superconducting circuits that behave as artificial atoms coupled to a resonator. The system exhibits a transition to a superradiant phase at zero temperature. When the interaction strength reaches its critical value, both the number of photons and atoms in excited states in the cavity, together with their fluctuations, exhibit a sudden increase from zero. By employing symmetry-adapted coherent states, it is shown that these properties scale with the number of atoms, their reported divergences at the critical point represent the limit when this number goes to infinity, and, in this limit, they remain divergent in the superradiant phase. Analytical expressions are presented for all observables of interest, for any number of atoms. Comparisons with exact numerical solutions strongly support the results.

We discuss a mechanism of generating two separable beams of light with a high degree of entanglement in momentum using a fast and sharp optical boundary. Three regimes of light generation are identified depending on the number of resonant interactions between the optical perturbation and the electromagnetic field. The intensity of the process is discussed in terms of the relevant physical parameters: variation of refractive index and apparent velocity of the optical boundary. Our results suggest a different class of generation entangled light that is robust against thermal degradation by exciting zero point fluctuations using parametric resonant optical modulations.

The self-energy corrections to the hyperfine splitting is evaluated for higher excited states in hydrogenlike ions using an expansion in the binding parameter $Z\alpha$, where $Z$ is the nuclear-charge number and $\alpha$ is the fine-structure constant. We present analytic results for $D$, $F$, and $G$ states, and for a number of highly excited Rydberg states, with principal quantum numbers in the range $13⩽n⩽16$, and orbital angular momenta $\ell =n-2$ and $\ell =n-1$. A closed-form analytic expression is derived for the contribution of high-energy photons, valid for any state with $\ell ⩾2$ and arbitrary $n$, $\ell$, and total angular momentum $j$. The low-energy contributions are written in the form of generalized Bethe logarithms and evaluated for selected states.

We report on the implementation of metallic microtubes in a system of rubidium vapor at 230 bar of argon buffer gas. The high-buffer gas pressure leads to a widely pressure broadened linewidth of several nanometers, interpolating between the sharp atomic physics spectra and the band structure of solid state systems. Tube-like metallic waveguide structures have been inserted in the high-pressure buffer gas system, allowing for guiding light in an optical dense gas over a length in the tube of up to 1 mm. The system holds promise for nonlinear optics experiments and the study of atom-light polariton condensation.

Analogous to the extension of laser cooling techniques from two-level to three-level atoms, Doppler cooling of molecules with an intermediate electronic state is considered. In particular, we use a rate-equation approach to simulate cooling of ${\mathrm{SiO}}^{+}$, in which population buildup in the intermediate state is prevented by its short lifetime. We determine that Doppler cooling of ${\mathrm{SiO}}^{+}$ can be accomplished without optically repumping from the intermediate state, at the cost of causing undesirable parity flips and rotational diffusion. Since the necessary repumping would require a large number of continuous-wave lasers, optical pulse shaping of a femtosecond laser is proposed as an attractive alternative. Other candidate three-electron-level molecules are also discussed.

In the present work we extend the concept of coherent shift for the extended Bose-Hubbard model and Fermi-Hubbard model. We present two types of local bound pairs (BPs) for the Bose system and one type for the Fermi system. It is shown exactly that the perfect coherent shift can be achieved in such models in the large binding-energy limit. We find that for a Bose on-site BP, the perfect coherent shift condition depends on the nearest-neighbor interaction strength and the momentum of the incident single-particle wave packet, while for the other two types of BPs, it is independent of the initial state in the proposed systems. Numerical simulation of the scattering process between a single particle and a BP in a finite-size system is conducted and the computational results are shown to confirm the analytical investigation.

The intention of this work is twofold: first, to present a most simple system capable of simulating the intrinsic bosonic Josephson effect with photons and, second, to study various outcomes deriving from inherent or external decoherence. A qubit induces an effective coupling between two externally pumped cavity modes. Without cavity losses and in the dispersive regime, intrinsic Josephson oscillations of photons between the two modes occurs. In this case, contrary to regular Markovian decoherence, the qubit purity shows a Gaussian decay and recurrence of its coherence. Due to intrinsic nonlinearities, both the Josephson oscillations as well as the qubit properties display a rich collapse-revival structure, where, however, the complexity of the qubit evolution is in some sense stronger. The qubit as a meter of the photon dynamics is considered, and it is shown that qubit dephasing, originating, for example, from nondemolition measurements, results in an exponential destruction of the oscillations which manifests the collectiveness of the Josephson effect. Nonselective qubit measurements, on the other hand, render a Zeno effect seen in a slowing down of the Josephson oscillations. Contrary to dephasing, cavity dissipation results in a Gaussian decay of the scaled Josephson oscillations. Finally, following Ponomarev et al. [Phys. Rev. Lett. 106, 010405 (2011)], we analyze aspects of thermalization. In particular, despite similarities with the generic model studied by Ponomarev et al., our system does not seem to thermalize.

Nonlocality is a fascinating and counterintuitive aspect of nature, revealed by the violation of a Bell inequality. The standard and easiest configuration in which Bell inequalities can be measured has been proposed by Clauser-Horne-Shimony-Holt (CHSH). However, alternative nonlocality tests can also be carried out. In particular, Bell inequalities requiring multiple measurement settings can provide deeper fundamental insights about quantum nonlocality, as well as offering advantages in the presence of noise and detection inefficiency. In this paper we show how these nonlocality tests can be performed using a commercially available source of entangled photon pairs. We report the violation of a series of these nonlocality tests ($I_{3322}$, $I_{4422}$, and chained inequalities). With the violation of the chained inequality with 4 settings per side we put an upper limit at 0.49 on the local content of the states prepared by the source (instead of 0.63 attainable with CHSH). We also quantify the amount of true randomness that has been created during our experiment (assuming fair sampling of the detected events).

We experimentally investigate the variations of exchange-symmetry properties of the four Bell states in an exchange-symmetric pure dephasing process with a two-photon system generated from spontaneous parametric down-conversion (SPDC). Experiment results show that under such an exchange-symmetric local-noise Hamiltonian, the exchange-symmetry property remains unchanged for two of the three symmetric Bell states, i.e., the states $|\Phi \rangle {}^{\pm }=\frac{1}{\sqrt{2}}(|00\rangle \pm |11\rangle )$. For the antisymmetric Bell state $|\Psi \rangle {}^{-}=\frac{1}{\sqrt{2}}(|01\rangle -|10\rangle )$, the exchange-symmetry property increases and achieves a maximum value of 0.5 at the asymptotic limit. However, for the third exchange-symmetric Bell state $|\Psi \rangle {}^{+}=\frac{1}{\sqrt{2}}(|01\rangle +|10\rangle )$, the exchange-symmetry property breaks, surviving with a probability of 0.5 at the asymptotic limit, which provides some evidence supporting such decoherence-induced spontaneous-symmetry-breaking phenomena.

We address the experimental determination of entanglement for systems made of a pair of polarization qubits. We exploit quantum estimation theory to derive optimal estimators, which are then implemented to achieve ultimate bound to precision. In particular, we present a set of experiments aimed at measuring the amount of entanglement for states belonging to different families of pure and mixed two-qubit two-photon states. Our scheme is based on visibility measurements of quantum correlations and achieves the ultimate precision allowed by quantum mechanics in the limit of Poissonian distribution of coincidence counts. Although optimal estimation of entanglement does not require the full tomography of the states we have also performed state reconstruction using two different sets of tomographic projectors and explicitly shown that they provide a less precise determination of entanglement. The use of optimal estimators also allows us to compare and statistically assess the different noise models used to describe decoherence effects occurring in the generation of entanglement.

We study the creation of electron-positron pairs from the vacuum induced by two spatially displaced static electric fields. The strength and spatial width of each localized field is less than required for pair creation. If, however, the separation between the fields is less than the quantum-mechanical tunneling length associated with the corresponding quantum scattering system, the system produces a steady flux of electron-positron pairs. We compute the time dependence of the pair-creation probability by solving the Dirac equation numerically for various external field sequences. For the special case of two very narrow fields we provide an analytical expression for the pair-creation rate in the long-time limit.

Superradiant Rayleigh scattering in a Bose gas released from an optical lattice is analyzed with incident light pumping at the Bragg angle for resonant light diffraction. We show that competition between superradiance scattering into the Bragg mode and into end-fire modes clearly leads to suppression of the latter at even relatively low lattice depths. A quantum light-matter interaction model is proposed for qualitatively explaining this result.

We present variational calculations using a Gaussian trial function to calculate the ground state of the Gross-Pitaevskii equation (GPE) and to describe the dynamics of the quasi-two-dimensional solitons in dipolar Bose-Einstein condensates (BECs). Furthermore, we extend the ansatz to a linear superposition of Gaussians, improving the results for the ground state to exact agreement with numerical grid calculations using imaginary time and the split-operator method. We are able to give boundaries for the scattering length at which stable solitons may be observed in an experiment. By dynamic calculations with coupled Gaussians, we are able to describe the rather complex behavior of the thermally excited solitons. The discovery of dynamically stabilized solitons indicates the existence of such BECs at experimentally accessible temperatures.

We perform a variational Gutzwiller calculation to study the ground state of the repulsive SU(3) Hubbard model on the Bethe lattice with infinite coordination number. We construct a ground-state phase diagram focusing on phases with a two-sublattice structure and find five relevant phases: (1) a paramagnet, (2) a completely polarized ferromagnet, (3) a two-component antiferromagnet where the third component is depleted, (4) a two-component antiferromagnet with a metallic third component (an “orbital selective” Mott insulator), and (5) a density-wave state where two components occupy dominantly one sublattice and the last component the other one. First-order transitions between these phases lead to phase separation. A comparison of the SU(3) Hubbard model to the better-known SU(2) model shows that the effects of doping are completely different in the two cases.

Capillary instability and the resulting dynamics in an immiscible two-component Bose-Einstein condensate are investigated using the mean-field and Bogoliubov analyses. A long, cylindrical condensate surrounded by the other component is dynamically unstable against breakup into droplets due to the interfacial tension arising from the quantum pressure and interactions. A heteronuclear system confined in a cigar-shaped trap is proposed for realizing this phenomenon experimentally.

The problem of photonic phase transition for the system of a two-level atomic ensemble interacting with a quantized single-mode electromagnetic field in the presence of optical collisions (OCs) is considered. We have shown that for large and negative atom-field detuning a photonic field exhibits high-temperature second-order phase transition to superradiant state under thermalization condition for coupled atom-light states. Such a transition can be connected with superfluid (coherent) properties of photonlike low branch (LB) polaritons. We discuss the application of metallic cylindrical waveguide for observing predicted effects.