We address the existence of surface gap solitons at the interface between a uniform medium and a disordered optical lattice with a defocusing Kerr nonlinearity. Gap solitons resonating with Anderson modes feature unique properties of both surface waves and disordered lattices. Bifurcations of solitons with in-phase main peaks in the nearest-to-interface lattice channels are discussed. Resonant interactions broaden the surface gap solitons and result in the formation of multibranch nonlinear modes with different number of peaks. Linear stability analysis results demonstrate that solitons at the edges of disordered lattices are completely stable or suffer a weak oscillatory instability. Thus, we put forward an effective way for the realization of shape-preserving self-localized nonlinear bound states with many peaks.

We study the dynamics of an atomic two-level system decaying by spontaneous emission of light. Subject to continuous detection of the radiated field, the system tends with certainty to the ground state in the long time limit, but at initial times the excited-state population exhibits nontrivial stochastic behavior. Employing methods from Ito calculus, we characterize this behavior in case of unit efficiency detection, and we show, for example, that the emitter, as a result of in-phase homodyne measurements, may become fully excited during the decay process while heterodyne and out-of-phase homodyne measurements do not drive the atom completely into the excited state.

In contrast to an infinite degree of nonlocality, we demonstrate that vortex solitons in nonlinear media under competing self-focusing cubic and self-defocusing quintic nonlocal nonlinearities can be stabilized with a finite degree of nonlocality. Stable vortex solitons in the upper branch, bifurcated from the competing cubic-quintic nonlinearities, are found to be supported when the original double-ring refractive index change is transferred into a single-ring configuration due to the balance between diffusive nonlocality and defocusing quintic nonlinearity. The dynamics and stabilities of the vortex solitons are studied analytically and numerically.

We consider a dense one-dimensional laser-driven Rydberg lattice gas with perfect nearest-neighbor blockade. The ground state of this system can be found analytically in certain parameter regimes even when the applied fields are inhomogeneous in space. We will use this unique feature to investigate the effect of an impurity—introduced by the local variation of the laser parameters—on the correlations of the many-body ground state. Moreover, we explore the role of a staggered laser field which alternates from site to site thereby breaking the sublattice symmetry. We demonstrate that this technique, which can be applied experimentally, reveals insights into the role of long-range interactions on the critical properties of a Rydberg gas. Our work highlights possibilities for the exploration of many-body physics in Rydberg lattice gases based on locally tunable laser fields.

Dissipation caused by nonhomogeneous bosonic finite chain environments (implementable in, e.g., segmented ion traps) is investigated through an exact diagonalization approach, avoiding common approximations used to describe open systems. Different spectral densities, including band gaps, can be engineered to separately assess different factors leading to memory effects, namely, the environment's size, temperature, proximity of the cutoff frequency, the spectral density's shape (sub-Ohmic, Ohmic, super-Ohmic), and the strength of its coupling to the system. Non-Markovianity is quantified with two recently introduced measures related to information backflow and nondivisibility of the system dynamical map. By sweeping the bath spectrum via tuning of the system frequency we show strongest memory effects at band-gap edges and provide an interpretation based on energy flow between system and environment. A system weakly coupled to a stiff chain ensures a Markovian dynamics, while the size of the environment as well as the local density of modes are not substantial factors. We show an opposite effect when increasing the temperature inside or outside the spectral band gap. Further, non-Markovianity arises for larger (negative and positive) powers of algebraic spectral densities, being the Ohmic case not always the most Markovian one.

Dwell time for a two-state particle tunneling through a noisy thermal magnetic barrier has been calculated by studying the time evolution of the system. The effect of temperature has been included by averaging over the environmental magnetic modes. The time scale has been calculated in the framework of weak measurement. The dwell time initially increases with the rise of temperature and finally saturates. The increment of dwell time can be explained by the phenomena of quantum memory loss caused by efficient energy exchange with the environmental modes. The saturation region at higher temperature corresponds to the process of thermal hopping of the barrier.

We show that metastable states in the Winter model can be related to the eigenstates of a particle in a box by means of renormalization and mixing.

Dynamical decoupling is a powerful technique to suppress errors in quantum systems originating from environmental couplings or from unwanted interparticle interactions. However, it can also be used to selectively decouple specific couplings in a quantum system. We present a simple and easy-to-use general method to construct such selective decoupling schemes on qubit and qudit networks by means of (generalized) Pauli operations. As these constructed schemes can suppress Hamiltonian interactions on general qudit networks selectively, they are well suited for purposes of approximate quantum simulation. Some examples are presented, demonstrating the use of our method and the resulting decoupling schemes.

The surface code is a promising candidate for fault-tolerant quantum computation, achieving a high threshold error rate with nearest-neighbor gates in two spatial dimensions. Here, through a series of numerical simulations, we investigate how the precise value of the threshold depends on the noise model, measurement circuits, and decoding algorithm. We observe thresholds between 0.502(1)% and 1.140(1)% per gate, values which are generally lower than previous estimates.

The role of electron saddle swaps in collisions of bare Li with metastable hydrogen and alkali-metal atoms is investigated by means of the classical trajectory Monte Carlo method. In particular, we show that oscillations as a function of collision energy in the photon spectra resulting from charge exchange are directly related to the number of potential-saddle crossings that a receding electron can achieve during a given reaction. The range of impact energies spanned is 0.01–50 keV/amu, an area of interest for diagnostic purposes in tokamak nuclear fusion power reactors.

We demonstrate theoretically that laser-induced coherent quantum interference control of asymptotic states of dissociating molecules is possible even in the (one-photon) weak-field limit starting from a single vibrational eigenstate. Thus, phase dependence in the interaction with a fixed energy phase-modulated pulse can persist for some time after the pulse is over. This is illustrated for the nonadiabatic process: $\mathrm{I}+{\mathrm{Br}}^{*}\leftarrow \mathrm{IBr}\to \mathrm{I}+\mathrm{Br}$, where the relative yield of excited ${\mathrm{Br}}^{*}$ can be changed by pure phase modulation. It is shown that the phase is able to influence wave-packet spreading in the continuum as well as the average internuclear distance in each channel.

Accurate theoretical data on many time-dependent processes in atomic and molecular physics and in chemistry require the direct numerical ab initio solution of the time-dependent Schrödinger equation, thereby motivating the development of very efficient time propagators. These usually involve the solution of very large systems of first-order differential equations that are characterized by a high degree of stiffness. In this contribution, we analyze and compare the performance of the explicit one-step algorithms of Fatunla and Arnoldi. Both algorithms have exactly the same stability function, therefore sharing the same stability properties that turn out to be optimum. Their respective accuracy, however, differs significantly and depends on the physical situation involved. In order to test this accuracy, we use a predictor-corrector scheme in which the predictor is either Fatunla's or Arnoldi's algorithm and the corrector, a fully implicit four-stage Radau IIA method of order 7. In this contribution, we consider two physical processes. The first one is the ionization of an atomic system by a short and intense electromagnetic pulse; the atomic systems include a one-dimensional Gaussian model potential as well as atomic hydrogen and helium, both in full dimensionality. The second process is the decoherence of two-electron quantum states when a time-independent perturbation is applied to a planar two-electron quantum dot where both electrons are confined in an anharmonic potential. Even though the Hamiltonian of this system is time independent the corresponding differential equation shows a striking stiffness which makes the time integration extremely difficult. In the case of the one-dimensional Gaussian potential we discuss in detail the possibility of monitoring the time step for both explicit algorithms. In the other physical situations that are much more demanding in term of computations, we show that the accuracy of both algorithms depends strongly on the degree of stiffness of the problem.

An ensemble density matrix model that includes one- and two-body losses is derived for a trapped-atom clock. A trapped-atom clock is mainly affected by one- and two-body losses, generally giving nonexponential decays of populations; nevertheless, three-body recombination is also quantitatively analyzed to demonstrate the boundaries of its practical relevance. The importance of one-body losses is highlighted without which population trapping behavior would be observed. The model is written with decay constants expressed through experimental parameters. It can complement, e.g., the ISRE (identical spin rotation effect) model to improve its predictions: ISRE dramatically increases the ensemble coherence time, hence it enables one to observe the influence of two-body losses on the interferometry contrast envelope. The presented model is useful for Ramsey interferometry and is ready for immediate experimental verification in existing systems.

In a driven dense ensemble of two-level atoms the decay acts in a correlated way on several atoms simultaneously. The competition between the coherent laser excitation and the dipole-dipole interaction induced by the dissipation gives rise to a bimodal distribution of the excitation density. More interestingly, the presence of nonlocal dissipation lifts the direct connection between the photon emission rate and the density of excited atoms present in typical open atomic systems formed by, for example, Rydberg gases or trapped ions. In contrast, here the bimodality present in the excitation density distribution, which indicates the existence of a dynamical first-order transition, is not accompanied by an intermittent behavior of the photon emission. Moreover, due to the nonlocal character of the dissipation the spatial coherence of the steady state can be measured experimentally by analyzing solely global quantities—the mean values of the photon emission rate and the density of excited atoms. We show that these effects can be experimentally probed in a system of trapped Sr atoms.

By means of mean-field theory, we have studied the structure and excitation spectrum of a purely dipolar Bose gas in a pancake shaped trap where the confinement in the $x$-$y$ plane is provided by a highly anharmonic potential, resulting in an almost uniform confinement in the plane. We show that the stable condensates are characterized by marked radially structured density profiles. The stability diagram is calculated by independently varying the strength of the interaction and the trap geometry. By computing the Bogoliubov excitation spectrum near the instability line we show that soft “angular” rotons are responsible for the collapse of the system. The free expansion of the cloud after the trap is released is also studied by means of time-dependent calculations, showing that a prolate cigar-shaped condensate is dynamically stabilized during the expansion, which would otherwise collapse. Dipolar condensates rotating with sufficiently high angular velocity show the formation of multiply quantized giant vortices, while the condensates acquire a ring-shaped form.

We chart out the possible phases of laser-driven Rydberg atoms in the presence of a hypercubic optical lattice. We define a pseudospin degree of freedom whose up (down) components correspond to the excited (ground) states of the Rydberg atoms and use them to demonstrate the realization of a canted Ising antiferromagnetic (CIAF) Mott phase of the atoms in these systems. We also show that, on lowering the lattice depth, the quantum melting of the CIAF and density-wave Mott states (which are also realized in these systems) leads to supersolid phases of the atoms. We provide analytical expressions for the phase boundaries and collective excitations of these phases in the hard-core limit within mean-field theory and discuss possible experiments to test our theory.

The realization and detection of topological phases with ultracold atomic gases is at the frontier of current theoretical and experimental research. Here, we identify cold atoms in optical ladders subjected to synthetic magnetic fields as readily realizable bridges between one-dimensional spin-orbit (time-reversal) topological insulators and two-dimensional quantum Hall insulators. We reveal three instances of their promising potential: (i) they realize spin-orbit coupling, with the left-right leg degree of freedom playing the role of an effective spin, (ii) their energy bands and eigenstates exactly reproduce the topological chiral edge modes of two-dimensional Chern insulators, and (iii) they can be tailored to realize a topological phase transition from a trivial to a topological insulating phase. We propose realistic schemes to observe the chiral and topological properties of ladder systems with current optical lattice-based experiments. Our findings open a door to the exploration of the physics of the edges of quantum Hall insulators and to the realization of spin-orbit coupling and topological superfluid phases with ultracold atomic gases.

We study a model describing $N$ identical bosonic atoms trapped in a double-well potential together with a single-impurity atom, comparing and contrasting it throughout with the Dicke model. As the boson-impurity coupling strength is varied, there is a symmetry-breaking pitchfork bifurcation which is analogous to the quantum phase transition occurring in the Dicke model. Through stability analysis around the bifurcation point, we show that the critical value of the coupling strength has the same dependence on the parameters as the critical coupling value in the Dicke model. We also show that, like the Dicke model, the mean-field dynamics goes from being regular to chaotic above the bifurcation and macroscopic excitations of the bosons are observed. Although the boson-impurity system behaves like a poor man's version of the Dicke model, we demonstrate a self-trapping phenomenon which thus far has not been discussed in the realm of the Dicke model.

Using the $\varepsilon$-expansion technique, we compute $\eta /s$, where $\eta$ is the shear viscosity and $s$ is the entropy density of the normal phase of unitary Fermi gas in $d=4-\varepsilon$ dimensions to leading order (LO) in $\varepsilon$. We use the kinetic theory approach and solve transport equations for a medium perturbed by a shear hydrodynamic flow. The collision integrals are calculated to ${\varepsilon }^2$, which is LO. The LO result is temperature independent with $\eta /s\simeq (0.11/{\varepsilon }^2)(\hslash /k_B)$. The $d=3$ prediction for $\eta /s$ exceeds the $\hslash /4\pi k_B$ bound by a factor of about $1.4$.

We numerically study the dynamics of a spinor chromium condensate in low magnetic fields. We show that the condensate evolution has a resonant character revealing a rich structure of resonances similar to that already discussed in the case of alkali-metal-atom condensates. This indicates that dipolar resonances occur commonly in systems of cold atoms. In fact, they have already been observed experimentally. We further simulate two recent experiments with chromium condensates in which the threshold in spin relaxation and spontaneous demagnetization phenomena were observed. We demonstrate that both these effects originate in the resonant dynamics of chromium condensates.