Quantum computers (QCs) must implement quantum error correcting codes (QECCs) to protect their logical qubits from errors, and modeling the effectiveness of QECCs on QCs is an important problem for evaluating the QC architecture. The previously developed Monte Carlo (MC) error models may take days or weeks of execution to produce an accurate result due to their random sampling approach. We present an alternative deterministic error model that generates, over the course of executing the quantum program, a probability tree of the QC’s error states. By calculating the fidelity of the quantum program directly, this error model has the potential for enormous speedups over the MC model when applied to small yet useful problem sizes (containing on the order of a dozen logical qubits encoded in the [[7,1,3]] QECC plus associated ancilla). We observe a speedup on the order of $1000X$ when accuracy is required, and we evaluate the scaling properties of this new deterministic error model.

The hybrid theory of electron-hydrogen elastic scattering [Phys. Rev. A 75, 032713 (2007)] is applied to the $S$-wave scattering of electrons from ${\text{He}}^{+}$ and ${\text{Li}}^{2+}$. In this method, both short-range and long-range correlations are included in the Schrödinger equation at the same time. Phase shifts obtained in this calculation have rigorous lower bounds to the exact phase shifts and they are compared with those obtained using the Feshbach projection operator formalism [Phys. Rev. A 66, 064702 (2002)], the close-coupling approach [J. Phys. B 2, 44 (1969)], and the Harris-Nesbet method [J. Phys. B 35, 4475 (2002); J. Phys. B 36, 2291 (2003)]. The agreement among all the calculations is very good. These systems have doubly excited or Feshbach resonances embedded in the continuum. The resonance parameters for the lowest ${}^{1}S$ resonances in He and ${\text{Li}}^{+}$ are calculated and they are compared with the results obtained using the Feshbach projection operator formalism [Phys. Rev. A 11, 2018 (1975); Phys. Rev. A 15, 131 (1977)]. It is concluded that accurate resonance parameters can be obtained by the present method, which has the advantage of including corrections due to neighboring resonances and the continuum in which these resonances are embedded.

The Dicke model generalized to the case where the dependence of the coupling constant on individual atoms is taken into account is investigated. It is shown that the generalized Dicke model exhibits a quantum phase transition from the normal phase to the superradiant phase in the thermodynamic limit, as well as the standard Dicke model. The mean photon number, the atomic inversion, the lowest excitation energy, and the entanglement entropy between the field and the atoms are evaluated analytically or numerically, and the critical behavior is examined. As a result, it turns out that the critical behavior in the generalized model is essentially the same as that in the standard model. This implies universality in the Dicke model.

We propose and numerically investigate a scalable ring trap for cold atoms that surmounts problems of roughness of the potential and end effects of trap wires. A stable trapping potential is formed about an electrically isolated, conducting loop in an ac magnetic field by time averaging the superposition of the external and induced magnetic fields. We investigate the use of additional fields to eliminate Majorana spin-flip losses and to create a stable trapping geometry. The possibility of microfabrication of these ring traps offers the prospect of developing Sagnac atom interferometry in atom-chip devices.

We reveal fundamental analogies between soliton dynamics in light-induced random photonic lattices and Brownian motion of particles. In particular, we discover that the average squared soliton displacement increases linearly with distance after an initial ballistic regime of propagation. We also find that in shallow lattices the average soliton displacement grows linearly with increasing lattice depth.

Violation of modified Wigner inequality in a binary bipartite quantum system allows the discrimination between the quantum world and the classical local-realistic one, and also ensures the security of Ekert-type quantum key distribution protocol. In this paper we study both theoretically and experimentally the bounds of quantum correlation associated to the modified Wigner’s inequality finding the optimal experimental configuration for its maximal violation. We also extend this analysis to the implementation of Ekert’s protocol.

We consider the quantum cloning of continuous variable entangled states. This is achieved by introducing two symmetric entanglement cloning machines (or $e$-cloners): a local $e$-cloner and a global $e$-cloner; where we look at the preservation of entanglement in the clones under the condition that the fidelity of the clones is maximized. These cloning machines are implemented using simple linear optical elements such as beam splitters and homodyne detection along with squeeze gates. We show that the global $e$-cloner out-performs the local $e$-cloner both in terms of the fidelity of the cloned states as well as the strength of the entanglement of the clones. There is a minimum strength of entanglement (3 dB using the inseparability criterion) of the input state of the global $e$-cloner that is required to preserve the entanglement in the clones.

We compare pseudopure state ensemble implementations, quantified by their initial polarization and ensemble size, of Grover’s search algorithm to probabilistic classical sequential search algorithms in terms of their success and failure probabilities. We propose a criterion for quantifying the resources used by the ensemble implementation via the aggregate number of oracle invocations across the entire ensemble and use this as a basis for comparison with classical search algorithms. We determine bounds for a critical polarization such that the ensemble algorithm succeeds with a greater probability than the probabilistic classical sequential search. Our results indicate that the critical polarization scales as $N^{-1/4}$, where $N$ is the database size and that for typical room temperature solution state NMR, the polarization is such that the ensemble implementation of Grover’s algorithm would be advantageous for $N\gtrsim {10}^{22}$.

The classical dynamics of a charged particle traveling in a laser field modeled by an elliptically polarized monochromatic electromagnetic plane wave is discussed within the time reparametrization invariant form of the nonrelativistic Hamilton-Jacobi theory. The exact parametric representation for a particle’s orbit in an arbitrary plane wave background beyond the dipole approximation and including effect of the magnetic field is derived. For an elliptically polarized monochromatic plane wave the particle’s trajectory, as an explicit function of the laboratory frame’s time, is given in terms of the Jacobian elliptic functions, whose modulus is proportional to the laser’s intensity and depends on the polarization of radiation. It is shown that the system exposes the intensity duality, correspondence between the motion in the backgrounds with various intensities. In virtue of the modular properties of the Jacobian functions, by starting with the representative “fundamental solution” and applying a certain modular transformation one can obtain the particle’s orbit in the monochromatic plane wave background with arbitrarily prescribed characteristics.

A two-mode Bose-Einstein condensate coupled by a high-frequency modulation field is found to display rich features. An effective stationary Hamiltonian approach reveals the emergence of additional degenerate eigenstates as well as additional topological structures of the spectrum. Possible applications, such as the suppression of nonlinear Landau-Zener tunneling, are discussed. An interesting phenomenon, which we call “deterministic symmetry-breaking trapping” associated with separatrix crossing, is also found in an adiabatic process.

We propose a two-qubit phase gate for ultracold atoms in a tilted double-well optical lattice. Such a lattice is capable of confining pairs of atoms in a two-dimensional array of double-well potentials where both the barrier height and the energy difference of the minima of the two wells (known as the “tilt”) can be controlled. The four lowest single-particle motional states can be used to form spatially separated qubits. We present a time-dependent scheme to manipulate the tilt to induce tunneling oscillations which produce a collisional phase gate. Numerical simulations demonstrate that this gate can be performed with high fidelity.

We report the stopping of a molecular oxygen beam, using a series of pulsed electromagnetic coils. A series of coils is fired in a timed sequence to bring the molecules to near rest, where they are detected with a quadrupole mass spectrometer. Applications to cold chemistry are discussed.

In this paper we calculate the block entanglement entropies of spin models whose ground states have perfect antiferromagnetic or ferromagnetic long-range order. In the latter case the definition of entanglement entropy is extended to properly take into account the ground state degeneracy. We find in both cases the entropy grows logarithmically with the block size. Implication of our results on states with general long-range order will be discussed.

We develop a fast algorithm to calculate the entanglement of formation of a mixed state, which is defined as the minimum average entanglement of the pure states that form the mixed state. The algorithm combines conjugat-gradient and steepest-descent algorithms and outperforms both. Using this new algorithm, we obtain the statistics of the entanglement of formation on ensembles of random density matrices of higher dimensions than possible before. The correlation between the entanglement of formation and other quantities that are easier to compute, such as participation ratio and negativity are presented. Our results suggest a higher percentage of zero-entanglement states among zero-negativity states than previously reported.

We present a method for the accurate quantum treatment of the planar three-body Coulomb problem under electromagnetic driving. Our ab initio approach combines Floquet theory, complex dilation, and the representation of the Hamiltonian in suitably chosen coordinates, without adjustable parameters. The resulting complex-symmetric sparse banded generalized eigenvalue problem of rather high dimension is solved using advanced techniques of parallel programming. This theoretical and numerical machinery is employed to provide a complete description of the bound and of the doubly excited spectrum of the field-free two-dimensional (2D) helium atom. For the driven atom, we focus on the near resonantly driven frozen planet configuration, and give evidence for the existence of nondispersive two-electron wave packets.

By means of the variational approximation (VA) and systematic simulations, we study dynamics and stability boundaries for solitons in a two-dimensional (2D) self-attracting Bose-Einstein condensate (BEC), trapped in an optical lattice (OL) whose amplitude is subjected to periodic time modulation (the modulation frequency $\omega$ may be in the range of several kHz). Regions of stability of the solitons against the collapse and decay are identified in the space of the model’s parameters. A noteworthy result is that the stability limit may reach the largest (100%) modulation depth, and the collapse threshold may exceed its classical value in the static lattice (which corresponds to the norm of Townes soliton). The minimum norm $N_{\text{min}}$ necessary for the stability of the solitons is identified too. It features a strong dependence on $\omega$ at low frequencies, due to a resonant decay of the soliton. Predictions of the VA are reasonably close to results of the simulations. In particular, the VA helps understand salient resonant features in the shape of the stability boundaries observed with the variation of $\omega$.

We achieved a 0.5 Hz optical beat note linewidth with $\sim 0.1\text{Hz}/\text{s}$ frequency drift at 972 nm between two external cavity diode lasers independently stabilized to two vertically mounted Fabry-Pérot (FP) reference cavities with a finesse of 400 000. Vertical FP reference cavities are suspended in midplane such that the influence of vertical vibrations to the mirror separation is significantly suppressed. This makes the setup virtually immune for vertical vibrations that are more difficult to isolate than horizontal vibrations. To compensate for thermal drifts the FP spacers are made from ultralow-expansion (ULE) glass which possesses a zero linear expansion coefficient. A design using Peltier elements in vacuum allows operation at an optimal temperature where the quadratic temperature expansion of ULE could be eliminated as well. The measured linear drift of such ULE FP cavity of 63 mHz/s was due to material aging and the residual frequency fluctuations were less than $\pm 20\text{Hz}$ during 16 h of measurement. Some part of the temperature-caused drift is attributed to the thermal expansion of the mirror coatings. Thermally induced fluctuations that cause vibrations of the mirror surfaces limit the stability of our cavity. By comparing two similar laser systems we obtain an Allan instability of $2\times {10}^{-15}$ between 0.1 and 10 s averaging time, which is close to the theoretical thermal noise limit.

We present a systematic study of the transmitted field of an ultrashort pulse through Young’s double slit. We show how the spatial-temporal distribution of the field in the near and intermediate zone is affected by the input polarization state of the pulse. The analysis has been separated to study the dispersion, the diffraction and the interference effects individually. A combination of these effects provide the key to understand the temporal dependence of the field observed at various distinctive locations. A thorough understanding of the near- and intermediate-field distribution of a single- or double-slit for an ultrashort pulse can be exploited in many near-field applications, and tailored by tuning the width, thickness, and separation of the slits.

A mechanism for the selective population of $1s2s2p{}^{4}P_J$ states by electron capture in energetic collisions of ${\mathrm{F}}^{7+}\left(1s2s{}^{3}S\right)$ ions with ${\mathrm{H}}_2$ and He is elucidated. Capture calculations indicate $\left(1s2s{}^{3}S\right)nl{}^{2,4}L$ doublet and quartet levels to be approximately evenly populated for $n=2–5$. Following capture the doublets Auger decay strongly to the $1s^2$ ground state allowing for negligible feeding of other lower-lying doublets by radiative transitions. The quartets, however, find this decay channel blocked by spin conservation and instead radiatively cascade through lower lying quartets, eventually strongly populating the lowest-lying $1s2s2p{}^{4}P_J$ levels in agreement with older experimental results for collision energies above $0.7\mathrm{MeV}∕\mathrm{u}$.