We consider two ensembles of qubits dissipating into two overlapping environments, that is, with a certain number of qubits in common that dissipate into both environments. We then study the dynamics of bipartite entanglement between the two ensembles by excluding the common qubits. To get analytical solutions for an arbitrary number of qubits we consider initial states with a single excitation and show that the largest amount of entanglement can be created when excitations are initially located among side (noncommon) qubits. Moreover, the stationary entanglement exhibits a monotonic (nonmonotonic) scaling versus the number of common (side) qubits.

We study controllable generation of two-mode-entangled states in a circuit QED setup, which consists of two spatially separated superconducting transmission line resonators and a single gap-tunable superconducting qubit. Two sharp coupling sidebands are induced when the artificial atom is suitably driven by a bichromatic microwave field. The two resonators can have squeezing-type interactions with the qubit via the coupling sidebands. If the two resonators are not degenerate, we show that the two resonators can be cooled down into the two-mode squeezed vacuum via dissipation of the qubit. The generation of the two-mode squeezed state is based on a dissipative state-engineering process, which explores the energy relaxation of the qubit as a resource. Moreover, the scheme does not need both the specific preparation of the initial state and the designed special dynamical process of the system. If the resonators are degenerate, we show that entangled coherent states of the resonators can be generated by use of the unitary dynamical evolution process of the system and the state-projection measurement. Moreover, macro entangled coherent states of the resonators with huge photons can in principle be created if the resonators and the qubit have sufficiently long lifetimes. The present scheme has two remarkable features: (1) only a single qubit is used in the generation of the two-mode squeezed state; and (2) the ultrastrong coupling condition and initializing the resonators in coherent states are not required. These make the present scheme more simple and feasible in experimental implementation.

We show exactly that the squared entanglement of formation (SEF) obeys a set of hierarchical monogamy relations for an arbitrary $N$-qubit mixed state. Based on this set of monogamy relations, we are able to construct the set of hierarchical multipartite entanglement indicators for $N$-qubit states, which still work well even when the concurrence-based indicators lose efficacy. As a by-product, an intriguing analytical relation between the entanglement of formation (EOF) and squared concurrence (SC) for an arbitrary mixed state of $2\otimes d$ systems is derived, making the concurrence calculable via the corresponding EOF. Furthermore, we analyze the multipartite entanglement dynamics in composite cavity-reservoir systems with the present set of hierarchical indicators. Moreover, for multilevel systems, it is illustrated that the SEF can be monogamous even if the SC is polygamous.

Quantum error correction (QEC) is a crucial step towards long coherence times required for efficient quantum information processing. One major challenge in this direction concerns the fast real-time analysis of error syndrome measurements and the associated feedback control. Recent proposals on autonomous QEC (AQEC) have opened new perspectives to overcome this difficulty. Here, we design an AQEC scheme based on quantum reservoir engineering adapted to superconducting qubits. We focus on a three-qubit bit-flip code, where three transmon qubits are dispersively coupled to a few low-$Q$ resonator modes. By applying only continuous-wave drives of fixed but well-chosen frequencies and amplitudes, we engineer an effective interaction Hamiltonian to evacuate the entropy created by eventual bit-flip errors. We provide a full analytical and numerical study of the protocol while introducing the main limitations on the achievable error correction rates.

We present calculations of the one-loop vacuum polarization contribution (Uehling potential) for the two-center problem in the nonrelativistic quantum electrodynamics formalism. The cases of hydrogen molecular ions ($Z_1=Z_2=1$) and antiprotonic helium ($Z_1=2$, $Z_2=-1$) are considered. Numerical results for the vacuum polarization contribution at $m{\alpha }^7$ order for the fundamental transitions $(v=0,L=0)\to (v^{\prime }=1,L^{\prime }=0)$ in ${\mathrm{H}}_2{}^{+}$ and ${\mathrm{HD}}^{+}$ are presented.

We consider the low-energy scattering of two ultracold polarized dipoles with both a short-range interaction (SRI) and a weak dipole-dipole interaction (DDI), which is far away from shape resonances. In previous analytical studies, the scattering amplitude in this system was often calculated via the first-order Born approximation (FBA). Our results show that significant derivations from this approximation can arise in some cases. In these cases, the SRI can significantly modify the interdipole scattering amplitudes even if the scattering amplitudes for the SRI alone are much smaller than the dipolar length of the DDI. We further obtain approximate analytical expressions for these interdipole scattering amplitudes.

Quantum optimal control theory is applied to control electric dipole transitions in a real multilevel system. The specific system studied in the present work is comprised of a multitude of hyperfine levels in the electronic ground state of the OH molecule. Spectroscopic constants are used to obtain accurate energy eigenstates and electric dipole matrix elements. The goal is to calculate the optimal time-dependent electric field that yields a maximum of the transition probability for a specified initial and final state. A further important objective was to study the detailed quantum processes that take place during such a prescribed transition in a multilevel system. Two specific transitions are studied in detail. The computed optimal electric fields as well as the paths taken through the multitude of levels reveal quite interesting quantum phenomena.

Many applications are in need of accurate photoionization cross sections, especially in the case of complex atoms. Configuration-interaction relativistic-many-body-perturbation theory (CI-RMBPT) has been successful in predicting atomic energies, matrix elements between discrete states, and other properties, which is quite promising, but it has not been applied to photoionization problems owing to extra complications arising from continuum states. In this paper a method that will allow the conversion of discrete CI-(R)MPBT oscillator strengths (OS) to photoionization cross sections with minimal modifications of the codes is introduced and CI-RMBPT cross sections of Ne, Ar, Kr, and Xe are calculated. A consistent agreement with experiment is found. RMBPT corrections are particularly significant for Ar, Kr, and Xe and improve agreement with experimental results compared to the particle-hole CI method. The demonstrated conversion method can be applied to CI-RMBPT photoionization calculations for a large number of multivalence atoms and ions.

The main obstacle in the experimental realization of the Einstein–de Haas effect in a Bose-Einstein condensate is the need for very precise control of the extremely small (of the order of tens of $\mu \mathrm{G}$) external magnetic field. In this paper, we numerically study the response of a rubidium condensate to a magnetic field that is linearly dependent on time. We find a significant transfer of atoms from the initial maximally polarized state to the next Zeeman component at magnetic fields of the order of tens of milligauss. We propose an experiment in which such a time-dependent magnetic-field-based scheme could enable the observation of the Einstein–de Haas effect in a rubidium atom condensate.

We consider a dilute homogeneous Bose gas with both an isotropic short-range contact interaction and an anisotropic long-range dipole-dipole interaction in a weak random potential at low temperature in three dimensions. Within the realm of Bogoliubov theory, we analyze how both condensate and superfluid are depleted due to quantum and thermal fluctuations as well as disorder fluctuations.

The existence of compacton matter waves in binary mixtures of quasi-one-dimensional Bose-Einstein condensates in deep optical lattices, and in the presence of nonlinearity management, is demonstrated. For this, we derive an averaged vector discrete nonlinear Schrödinger equation (DNLSE) and show that compacton solutions of different types can exist as stable excitations. Stability properties are studied by linear analysis and by direct numerical integrations of the DNLSE system and their dependence on the inter- and intraspecies scattering lengths investigated. We show that under proper management conditions, compactons can be very robust excitations that can emerge spontaneously from generic initial conditions. A possible experimental setting for compacton observation is also discussed.

We propose a simple method to simulate and detect topological insulators with cold atoms trapped in a one-dimensional bichromatic optical lattice subjected to a time-periodic modulation. The tight-binding form of this shaken system is equivalent to the periodically driven Aubry-Andre model. We demonstrate that this model can be mapped into a two-dimensional Chern insulator model, whose energy spectrum hosts a topological phase within an experimentally accessible parameter regime. By tuning the laser phase adiabatically, such one-dimensional system constitutes a natural platform to realize topological particle pumping. We show that the Chern number characterizing the topological features of this system can be measured by detecting the density shift after one cycle of pumping.

We develop a general description of multiboson interferometry based on correlated measurements in arbitrary passive linear interferometers for multimode thermal sources with arbitrary spectral distributions. The multiorder correlation functions describing the multiboson detection probability rates can be expressed in terms of permanents of positive semidefinite matrices, depending on the interferometer evolution, the spectral distribution of the sources, and the times when the correlated measurements occur. The permanent structure of these multiorder probability rates is a manifestation of the underlying physics of multiboson interference and yields an interesting connection with the so-called boson sampling problem.

We present a quantum theory of slow light beyond the weak probe pulse approximation. By reduction of the full Hamiltonian of the system to an effective Hamiltonian for a single quantum field we demonstrate that the concept of dark-state polaritons can be introduced even if the linearized approach is no longer valid. The developed approach allows us to study the evolution of nonclassical quantum states of the polariton field.

Quantum metrology allows the enhanced precision on estimating phase shifts in an optical interferometer to reach the $\propto 1/N$ scaling of precision ($N$ is the mean photon number of the light field). But when $N$ is very large, the nonlinear optical effects may be nonnegligible. Here we investigate theoretically the quantum uncertainty bounds for simultaneously detecting the linear and nonlinear phase shifts. Focusing our attentions only on the linear and the nonlinear Kerr phase shifts, we find the NOON states can not be used to measure the two phase parameters. Using the entangled coherent states, the estimation precision is limited by the $1/N^{1/2}$ ($1/N^{3/2}$) scaling for the linear (nonlinear) phase. To increase the precisions and beat the standard quantum limit, we show that the entangled Schrödinger-cat states can be used to reach the $1/N$ scaling for the linear phase and $1/N^2$ scaling for the nonlinear phase.

Quantum mechanics allows systems to be entangled with each other, which results in stronger than classical correlations. Many methods of identifying entanglement have been proposed over years, most of which are based on violating some statistical inequalities. In this work we extend the idea formed by Hardy, in which entanglement is not identified with the use of statistical inequalities, but by simultaneous satisfaction of certain conditions. We show that this variant of the Hardy paradox relying on marginal probabilities can be resolved only by true multipartite entangled states. Also, the state resolving this paradox for given local measurements is pure and unique in the case of qubit collections.

Density effects in plasmas are analyzed using a Thomas-Fermi approach for free electrons. First, scaling properties are determined for the free-electron potential and density. For hydrogen-like ions, the first two terms of an analytical expansion of this potential as a function of the plasma coupling parameter are obtained. In such ions, from these properties and numerical calculations, a simple analytical fit is proposed for the plasma potential, which holds for any electron density, temperature, and atomic number, at least assuming that Maxwell-Boltzmann statistics is applicable. This allows one to analyze perturbatively the influence of the plasma potential on energies, wave functions, transition rates, and electron-impact collision rates for single-electron ions. Second, plasmas with an arbitrary charge state are considered, using a modified version of the Flexible Atomic Code (FAC) package with a plasma potential based on a Thomas-Fermi approach. Various methods for the collision cross-section calculations are reviewed. The influence of plasma density on these cross sections is analyzed in detail. Moreover, it is demonstrated that, in a given transition, the radiative and collisional-excitation rates are differently affected by the plasma density. Some analytical expressions are proposed for hydrogen-like ions in the limit where the Born or Lotz approximation applies and are compared to the numerical results from the FAC.

Through the description of several simple atomic-scale systems for illustration, the hydrodynamical interpretation of results of solving the time-dependent Schrödinger equation is used to elucidate the fundamental processes of angular momentum and energy transfer. Connections are made between the hydrodynamical interpretation and conventional views such as interference of superpositions of states. Along with previous theoretical and experimental demonstration of the existence of the hydrodynamical signatures born in atomic-scale interactions and remaining in the asymptotic observables, these illustrations show the complementarity of the hydrodynamical and conventional pictures as well as additional insight provided by the former.

We investigate the phase diagrams of theoretical models describing bosonic atoms in a lattice in the presence of randomly localized impurities. By including multiband and nonlinear hopping effects we enrich the standard model containing only the chemical-potential disorder with the site-dependent hopping term. We compare the extension of the MI and the BG phase in both models using a combination of the local mean-field method and a Hartree-Fock-like procedure, as well as the Gutzwiller-ansatz approach. We show analytical argument for the presence of triple points in the phase diagram of the model with chemical-potential disorder. These triple points, however, cease to exist after the addition of the hopping disorder.

We report an observation of spatial solitons in a medium managed to present fifth-seventh (focusing-defocusing) refractive nonlinearities with suppressed third-order nonlinearity. Propagation of two-dimensional bright spatial solitons for ∼10 Rayleigh lengths was observed and characterized in a suspension of silver nanoparticles in acetone using the scattered light imaging method. Numerical calculations based on a nonlinear Schrödinger-type equation, including contributions up to the seventh-order susceptibility, were performed showing good agreement with the experimental results.