We employ the (dynamical) density-matrix renormalization-group technique to investigate the ground-state properties of the Bose-Hubbard model with nearest-neighbor transfer amplitudes $t$ and local two-body and three-body repulsion of strength $U$ and $W$, respectively. We determine the phase boundaries between the Mott-insulating and superfluid phases for the lowest two Mott lobes from the chemical potentials. We calculate the tips of the Mott lobes from the Tomonaga-Luttinger liquid parameter and confirm the positions of the Kosterlitz-Thouless points from the von Neumann entanglement entropy. We find that physical quantities in the second Mott lobe such as the gap and the dynamical structure factor scale almost perfectly in $t/(U+W)$, even close to the Mott transition. Strong-coupling perturbation theory shows that there is no true scaling but deviations from it are quantitatively small in the strong-coupling limit. This observation should remain true in higher dimensions and for not too large attractive three-body interactions.

In this paper, we investigate the influence of the linewidth enhancement factor and active region volume on the switching characteristics of bistable injection-locked multi-quantum-well Fabry-Perot lasers. In this analysis we start from the full scale model of the multimode rate equation system describing dynamics of injection-locked lasers. On the basis of this model, we derive a simple analytical procedure for calculation of switching time and energy with respect to the injection power, and for different values of frequency detuning between the master and the slave laser. We find that the higher values of linewidth and active region volume can improve switching characteristics of injection-locked Fabry-Perot lasers, providing either shorter switching times ($\sim$10 ps) or lower switching energies ($\sim$1 fJ).

Analog models of quantum information processing, such as adiabatic quantum computation and analog quantum simulation, require the ability to subject a system to precisely specified Hamiltonians. Unfortunately, the hardware used to implement these Hamiltonians will be imperfect and limited in its precision. Even small perturbations and imprecisions can have profound effects on the nature of the ground state. Here we consider an imperfect implementation of adiabatic quantum optimization and show that, for a widely applicable random control noise model, quantum stabilizer encodings are able to reduce the effective noise magnitude and thus improve the likelihood of a successful computation or simulation. This reduction builds upon two design principles: summation of equivalent logical operators to increase the energy scale of the encoded optimization problem, and the inclusion of a penalty term comprising the sum of the code stabilizer elements. We illustrate our findings with an Ising ladder and show that classical repetition coding drastically increases the probability that the ground state of a perturbed model is decodable to that of the unperturbed model, while using only realistic two-body interaction. Finally, we note that the repetition encoding is a special case of quantum stabilizer encodings, and show that this in principle allows us to generalize our results to many types of analog quantum information processing, albeit at the expense of many-body interactions.

Rate constants have been measured from 300 to 700 K for thermal electron attachment to F${}_2$ using two flowing afterglow–Langmuir probe apparatuses. Dissociative attachment yielding F${}^{-}$ is observed with a rate constant of 5.0 ± 1.3 × 10${}^{-9}$ cm${}^3$ s${}^{-1}$ at 300 K, rising to 9.6 ± 2.4 × 10${}^{-9}$ cm${}^3$ s${}^{-1}$ at 700 K, well below the previously accepted values of McCorkle et al. [D. L. McCorkle, L. G. Christophorou, A. A. Christodoulides, and L. Pichiarella, J. Chem. Phys. 85, 1966 (1986)]. The absolute concentration of F${}_2$ reaching the afterglow is verified by measuring the near-collisional rate constant (4.5 ± 1.5 × 10${}^{-10}$ cm${}^3$ s${}^{-1}$) for Ar${}^{+}$ $+$ F${}_2$→ArF${}^{+}$ $+$ F. Prior attempts to apply $R$-matrix calculations to the F${}_2$ $+$ $e^{-}$ system have failed to explain previously reported thermal and nonthermal attachment rate constants along with high-resolution, low-energy attachment cross sections. The present results are reproduced exceptionally well by $R$-matrix calculations employing previously calculated resonance widths without adjustment.

Experimental stirring of a toroidally trapped Bose-Einstein condensate at high temperature generates a disordered array of quantum vortices that decays via thermal dissipation to form a macroscopic persistent current [T. W. Neely et al., Phys. Rev. Lett. 111, 235301 (2013)]. We perform three-dimensional numerical simulations of the experimental sequence within the stochastic projected Gross-Pitaevskii equation using ab initio determined reservoir parameters. We find that both damping and noise are essential for describing the dynamics of the high-temperature Bose field. The theory gives a quantitative account of the formation of a persistent current, with no fitted parameters.

We present an investigation of generation, dynamics, and stability of dark solitons in anisotropic Fermi gases for a range of particle numbers and trap aspect ratios within the framework of the order-parameter equation. We calculate the periods of dark solitons oscillating in a trap and find good agreement with the results based on the Bogoliubov–de Gennes equations. By studying the stability of initially off-center dark solitons under various tight transverse confinements in the unitarity limit, we not only give the criterion of dynamical stability, but also find that the soliton and a hybrid of solitons and vortex rings can be characterized by different oscillation periods. The stability criterion is not fulfilled by the parameters of the recent experiment of Yefsah et al. [Nature (London) 499, 426 (2013)]. Therefore, instead of a very slow oscillation as observed experimentally, we find that the created dark soliton undergoes a transverse snake instability with a collapse into vortex rings, which propagate in solitonlike manner with a nearly 2 times larger period.

We derive a technique of robust and efficient adiabatic passage for a driven nonlinear quantum system, describing the transfer to a molecular Bose-Einstein condensate from an atomic one by external fields. The pulse ingredients are obtained by tracking the dynamics derived from a Hamiltonian formulation, in the adiabatic limit. This leads to a nonsymmetric and nonmonotonic chirp. The efficiency of the method is demonstrated in terms of classical phase space, more specifically with the underlying fixed points and separatrices. We also prove the crucial property that this nonlinear system does not have any solution leading exactly to a complete transfer. It can only be reached asymptotically for an infinite pulse area.

We theoretically investigate the emission properties of a single-mode cavity coupled to a mesoscopic number of incoherently pumped quantum emitters. We propose an operational measure for the medium cooperativity, valid both in the bad- and in the good-cavity regimes. We show that the opposite regimes of subradiance and super-radiance correspond to negative and positive cooperativity, respectively. The lasing regime is shown to be characterized by non-negative cooperativity. In the bad-cavity regime we show that the cooperativity defines the transitions from subradiance to super-radiance. In the good-cavity regime it helps to define the lasing threshold, also providing distinguishable signatures indicating the lasing regime. Increasing the quality factor of the cavity mode induces a crossover from the solely super-radiant to the lasing regime. Furthermore, we verify that lasing is manifested in a wide range of positive cooperative behavior, showing that stimulated emission and super-radiance can coexist. The robustness of the cooperativity is studied with respect to experimental imperfections, such as inhomogeneous broadening and pure dephasing.

Quantum information can be protected from decoherence and other errors, but only if these errors are sufficiently rare. For quantum computation to become a scalable technology, practical schemes for quantum error correction that can tolerate realistically high error rates will be necessary. In some physical systems, errors may exhibit a characteristic structure that can be carefully exploited to improve the efficacy of error correction. Here we describe a scheme for topological quantum error correction to protect quantum information from a dephasing-biased error model, where we combine a repetition code with a topological cluster state. We find that the scheme tolerates error rates of up to 1.37%–1.83% per gate, requiring only short-range interactions in a two-dimensional array.

By means of nonadiabatic quantum molecular dynamics it is shown that the amount of energy deposited into ${\mathrm{C}}_{60}$ by a short laser field strongly depends on the molecular orientation with respect to the laser polarization direction. In consequence, subsequent electron-vibration coupling leads to different nuclear relaxation mechanisms with mainly three pathways: (1) excitation of giant $A_g\left(1\right)$ modes (“breathing”), (2) formation of deformed cagelike complexes (“isomers”), and (3) fragmentation predominantly into two large pieces (“fission”). The results are in accord with and nicely explain already existing experimental data. Future experiments are proposed to confirm the detailed predictions.

Competing computationally with experimental groups for the construction of scaling quantum computers, we simulate a complete quantum-gate by quantum-gate implementation of Shor's algorithm on a classical 128-core cluster computer. The resulting virtual quantum computer serves as a convenient quantum laboratory for the investigation of the effect of defects in the quantum circuitry. The class of defects studied here is the removal of all rotation gates with rotation angles $\theta <\pi /2^b$. Factoring semiprimes $N=21,33,35,39,55,57$, we find that the quantum computer still operates with acceptable performance (success probability of factoring) down to $b=2$. This is surprising since the deletion of rotation gates results in large errors in the arithmetic circuitry of the quantum computer. Extrapolating on the basis of these results we conclude that for quantum computers of practical interest more than 99% of rotation gates may be discarded with acceptable consequences in quantum computer performance. This result may be of interest to experimental physicists and quantum engineers currently embarked on designing efficient circuitry for scaling quantum computers.

Circuit cavity quantum electrodynamics (QED) is proving to be a powerful platform to implement quantum feedback control schemes due to the ability to control superconducting qubits and microwaves in a circuit. Here, we present a simple and promising quantum feedback control scheme for deterministic generation and stabilization of a three-qubit $W$ state in the superconducting circuit QED system. The control scheme is based on continuous joint Zeno measurements of multiple qubits in a dispersive regime, which enables us not only to infer the state of the qubits for further information processing but also to create and stabilize the target $W$ state through adaptive quantum feedback control. We simulate the dynamics of the proposed quantum feedback control scheme using the quantum trajectory approach with an effective stochastic maser equation obtained by a polaron-type transformation method and demonstrate that in the presence of moderate environmental decoherence, the average state fidelity higher than $0.9$ can be achieved and maintained for a considerably long time (much longer than the single-qubit decoherence time). This control scheme is also shown to be robust against measurement inefficiency and individual qubit decay rate differences. Finally, the comparison of the polaron-type transformation method to the commonly used adiabatic elimination method to eliminate the cavity mode is presented.

Recent studies have shown that topological models with interacting anyonic quasiparticles can be used as self-correcting quantum memories. Here we study the behavior of these models at thermal equilibrium. It is found that the interactions allow topological order to exist at finite temperature, not only in an extension of the ground-state phase, but also in a novel form of topologically ordered phase. Both phases are found to support self-correction in all models considered, and the transition between them corresponds to a change in the scaling of memory lifetime with system size.

We propose and study a model of a quantum memory that features self-correcting properties and a lifetime growing arbitrarily with system size at nonzero temperature. This is achieved by locally coupling a two-dimensional $L\times L$ toric code to a three-dimensional (3D) bath of bosons hopping on a cubic lattice. When the stabilizer operators of the toric code are coupled to the displacement operator of the bosons, we solve the model exactly via a polaron transformation and show that the energy penalty to create anyons grows linearly with $L$. When the stabilizer operators of the toric code are coupled to the bosonic density operator, we use perturbation theory to show that the energy penalty for anyons scales with $\ln \left(L\right)$. For a given error model, these energy penalties lead to a lifetime of the stored quantum information growing, respectively, exponentially and polynomially with $L$. Furthermore, we show how to choose an appropriate coupling scheme in order to hinder the hopping of anyons (and not only their creation) with energy barriers that are of the same order as the anyon creation gaps. We argue that a toric code coupled to a 3D Heisenberg ferromagnet realizes our model in its low-energy sector. Finally, we discuss the delicate issue of the stability of topological order in the presence of perturbations. While we do not derive a rigorous proof of topological order, we present heuristic arguments suggesting that topological order remains intact when perturbative operators acting on the toric code spins are coupled to the bosonic environment.

In this paper, we have described electron-correlation trends in the calculations of the hyperfine $A$ and $B$ constants for a few elements belonging to the Na isoelectronic sequence. The hyperfine $A$ and $B/Q$ values of the ground state $3s$ ${}^2{S}_{1/2}$ and the excited states $3p$ ${}^2{P}_{1/2}$, $3p$ ${}^2{P}_{3/2}$, $3d$ ${}^2{D}_{3/2}$, and $3d$ ${}^2{D}_{5/2}$ of the ions from Si${}^{3+}$ to V${}^{12+}$ are presented. The influence of the Breit interaction in the unretarded approximation to these hyperfine values is reported briefly. With increasing atomic number of this sequence, the variations of the different correlation contributing terms such as core correlations, core polarizations, and pair correlations are discussed in the framework of the relativistic coupled-cluster theory. The electron-correlation effect relative to the Dirac-Fock value in the hyperfine $A$ constants of the $3d$ ${}^2{D}_{3/2,5/2}$ states follows unusual trends with increasing ionization. The relative pair-correlation effect influences the hyperfine constants of the fine-structure states of a term in an identical way at each species of this sequence. The presented relativistic coupled-cluster results are found to agree excellently with the other available results for a few ions.

We discuss the possible search for optical transitions in Sm${}^{13+}$ and Sm${}^{14+}$ using ab initio calculations of differential dynamic polarizability. We calculate dynamic polarizability for $M1$ transition between first and second excited states of Sm${}^{14+}$. Transition amplitudes and energies within the optical range for states that contribute to the polarizability of the mentioned transition are presented. Employing simple analytical formula for polarizability data in the vicinity of a resonance and assuming that several values of the polarizability for different laser frequencies will be measured one can find the accurate position of the resonance. Results of similar calculations of amplitudes and energies of states that contribute to the polarizability of the $M1$ transition between ground and first excited states of Sm${}^{13+}$ are also presented.

Dielectronic and higher-order resonant electron recombination processes including a $K$-shell excitation were systematically measured at high electron energy resolution in electron beam ion traps. After storing highly charged Ar, Fe, and Kr ions, the dependence on atomic number $Z$ of the contribution of these processes to the total recombination cross section was studied and compared with theoretical calculations. Large higher-order resonant recombination contributions were found, especially for systems with $10<Z<36$. In some cases, they even surpass the strength of the dielectronic channel, which was hitherto presumed to be always the dominant one. These findings have consequences for modeling high-temperature plasmas. Features attributed to intershell quadruelectronic recombination were also observed. The experimental data obtained for the He-like to O-like isoelectronic sequences compare well with the results of advanced relativistic distorted-wave calculations employing multiconfiguration Dirac-Fock bound-state wave functions that include threefold and fourfold excitations.

We present relativistic convergent close-coupling (RCCC) calculations of the $P_3$ circular light polarization Stokes parameter for atomic silver associated with the radiative decay of the electron-impact excited $\left(4d^{10}5p\right){}^2{P}_{3/2}$ state. The results are compared with the recent measurements of Jhumka et al. [Phys. Rev. A 87, 052714 (2013)]. We find excellent agreement between the RCCC results and experiment across the full energy range of measurements. We also find that relativistic effects have a weak influence on the calculation of $P_3$ in the energy range considered.

Recent experimental developments in the loading of ultracold KRb molecules into quasi-two-dimensional traps, combined with the ability to tune the ratio between elastic and loss (inelastic, reactive) collisions through application of an external electric field, are opening the door to achieving efficient evaporative cooling of reactive polar molecules. In this paper, we use Monte Carlo simulations and semianalytic models to study theoretically the experimental parameter regimes in which evaporative cooling is feasible under current trapping conditions. We investigate the effect of the anisotropic character of dipole-dipole collisions and reduced dimensionality on evaporative cooling. We also present an analysis of the experimentally relevant antievaporation effects that are induced by chemical reactions that take place when more than one axial vibrational state is populated.