We propose a general method by which experiments on ultracold gases can be used to determine the topological properties of the energy bands of optical lattices, as represented by the map of the Berry curvature across the Brillouin zone. The Berry curvature modifies the semiclassical dynamics and hence the trajectory of a wave packet undergoing Bloch oscillations. However, in two dimensions these trajectories may be complicated Lissajous-like figures, making it difficult to extract the effects of Berry curvature in general. We propose how this can be done using a “time-reversal” protocol. This compares the velocity of a wave packet under positive and negative external force, and allows a clean measurement of the Berry curvature over the Brillouin zone. We discuss how this protocol may be implemented and explore the semiclassical dynamics for three specific systems: the asymmetric hexagonal lattice and two “optical flux” lattices in which the Chern number is nonzero. Finally, we discuss general experimental considerations for observing Berry curvature effects in ultracold gases.

We extend a recently introduced separable interaction for the unitary trapped Fermi gas to all values of the scattering length. We derive closed expressions for the interaction matrix elements and the two-particle eigenvectors. At unitarity we analytically demonstrate the convergence of this interaction to the zero-range two-body pseudopotential for $s$-wave scattering. We apply this effective interaction to the three- and four-particle systems along the BEC-BCS crossover and find that their low-lying energies exhibit convergence in the regularization parameter that is much faster than for the conventional renormalized contact interaction. We find similar convergence properties of the three-particle free energy at unitarity.

The relative partial ionization cross sections for the fragment ions produced in direct and dissociative ionization of a N${}_2$O molecule are measured for impact of 10–25-keV electrons by using an electron-ion-coincidence technique with a linear time-of-flight spectrometer. The six ionic fragments of N${}_2$O (N${}_2$O${}^{+}$, NO${}^{+}$, N${}_2$${}^{+}$, O${}^{+}$, N${}^{+}$, and N${}^{2+}$ $+$ O${}^{2+}$) are observed and identified. The impact energy dependence of the partial ionization cross sections for these ions is expressed relative to the cross section of N${}_2$O${}^{+}$ and is found to be nearly invariant. The relative ionic fractions for the produced ions of N${}_2$O are also obtained and compared with the earlier reported data available at lower energies of electron impact. It is found that the relative ionic fractions for singly charged fragments are almost energy independent. However, for the doubly charged fragment ions (N${}^{2+}$ $+$ O${}^{2+}$), the present data are found to be higher by almost a factor of four compared to the relative ionic fraction reported earlier at a very low impact energy.

We apply a recently developed ab initio numerical framework to investigate the angular distributions of the emitted electrons in the immediate proximity of the threshold for the two-photon double ionization of helium. Provided one of the electrons is emitted perpendicular to the laser polarization direction, it is found that the angular distribution of the other electron is characterized by three lobes. The results are similar to those recently reported for the corresponding process in the hydrogen negative ion [R. Nepstad and M. Førre, Phys. Rev. A 84, 021402(R) (2011)], and provide further evidence of highly correlated electron dynamics in the vicinity of the double ionization threshold.

We propose an iterative algorithm to simulate the dynamics generated by any $n$-qubit Hamiltonian. The simulation entails decomposing the unitary time evolution operator $U$ (unitary) into a product of different time-step unitaries. The algorithm product-decomposes $U$ in a chosen operator basis by identifying a certain symmetry of $U$ that is intimately related to the number of gates in the decomposition. We illustrate the algorithm by first obtaining a polynomial decomposition in the Pauli basis of the $n$-qubit quantum state transfer unitary by Di Franco et al. [Phys. Rev. Lett. 101, 230502 (2008)] that transports quantum information from one end of a spin chain to the other, and then implement it in nuclear magnetic resonance to demonstrate that the decomposition is experimentally viable. We further experimentally test the resilience of the state transfer to static errors in the coupling parameters of the simulated Hamiltonian. This is done by decomposing and simulating the corresponding imperfect unitaries.

Majorana representation of quantum states by a constellation of $n$ “stars” (points on the sphere) can be used to describe any pure state of a simple system of dimension $n+1$ or a permutation symmetric pure state of a composite system consisting of $n$ qubits. We analyze the variance of the distribution of the stars, which can serve as a measure of the degree of noncoherence for simple systems or an entanglement measure for composed systems. Dynamics of the Majorana points induced by a unitary dynamics of a pure state is investigated.

A theoretical model for driving a two-qubit system to a stable long-lived entanglement is discussed. The entire system is represented by two atoms, initially in ground states and disentangled, each one coupled to a separate cavity with the cavities connected by a fiber. The cavities and fiber exchange energy with their individual thermal environments. Under these conditions, we apply the theory of microscopic master equation developed for the dynamics of the open quantum system. Deriving the density operator of the two-qubit system we found that stable long-lived quantum correlations are generated in the presence of thermal excitation of the environments. To the best of our knowledge, there is no a similar effect observed in a quantum open system described by a generalized microscopic master equation in the approximation of the cavity quantum electrodynamics.

We formulate a quantum formalism for the statistical mechanical models of discretized field theories on lattices and then show that the discrete version of ${\phi }^4$ theory on 2D square lattice is complete in the sense that the partition function of any other discretized scalar field theory on an arbitrary lattice with arbitrary interactions can be realized as a special case of the partition function of this model. To achieve this, we extend the recently proposed quantum formalism for the Ising model [M. Van den Nest, W. Dur, and H. J. Briegel, Phys. Rev. Lett. 98, 117207 (2007)] and its completeness property [M. Van den Nest, W. Dur, and H. J. Briegel, Phys. Rev. Lett. 100, 110501 (2008)] to the continuous variable case.

We present a theoretical model for describing ultracold atomic collision based on the multichannel quantum-defect theory. An analytical expression for the quantum-defect matrix Y is derived for the truncated $1/R^6$ model potential, and threshold behaviors of the quantum-defect parameters are discussed. The model allows us to predict the Feshbach resonances when the singlet and triplet scattering lengths are known or to fit the scattering lengths when a couple of Feshbach resonances is located experimentally. As an illustrative example, we investigate the ${}^6$Li-${}^{40}$K scattering. The theoretical results agree quite well with experimental values.

A uniform dilute Bose gas of known density has a universal behavior as the atomic scattering length tends to infinity at unitarity while most of its properties are determined by a universal parameter $\xi$ relating the energies of the noninteracting and unitary gases. The usual mean-field equation is not valid in this limit, and beyond mean-field corrections become important. We use a dynamical model including such corrections to investigate a trapped disk-shaped dipolar Bose-Einstein condensate (BEC) and a dipolar BEC vortex for large scattering length. We study the sensitivity of our results on the parameter $\xi$ and discuss the possibility of extracting the value of this parameter from experimental observables.

Intrapulse quantum spectral correlation of photon numbers of a femtosecond optical pulse, which propagates a 5-m-long optical fiber, is presented in a matrix format for quantum noise study by numerical calculation. The calculation includes the higher-order optical effects such as intrapulse-stimulated Raman scattering and self-steepening effects, as well as self-phase modulation and group velocity dispersion. The quantum correlations between spectral components (spectral resolution of 0.7 nm) which evolve with the pulse energy are provided in a matrix format at soliton orders including the low orders, $N=0.1$ to 1.0 (a 0.1 step), to give the detailed properties of spectral correlation evolutions in the matrix format. It is shown that the photon-number correlations between spectral components near the pulse spectrum center form strong correlations of a square shape in the matrix, at a soliton order $N$ ($\le$0.4), and then are redistributed into those between spectral components near the spectrum wings such that the cross-shaped correlation pattern in the matrix begin to be visible at $N=0.5$ before their further redistribution as $N\to 1.0$. In addition, significant anticorrelations can be increasingly extended to be found between spectral components near the spectrum center as $N\to 1.0$, leading to the expectation that the degree of photon-number squeezing by spectral filtering for subsolitons can be lower than that for solitons. Intrapulse-stimulated Raman scattering that starts to become visible at around $N=0.6$ produces an asymmetric correlation structure with respect to the spectrum center in the correlation matrices while the relevant pulse self-frequency shift becomes visible at $N\ge 0.8$. The calculation presented indicates that the measurement of nonlinear effects which are not detectable distinctly at the classical level is possible at the quantum level.

The emission of light from a multiply excited atomic ensemble is examined and it is shown how symmetric (spin-wave) and nonsymmetric states of excitation radiate into spatially separate field modes. This observation has potential application to single-photon generation and spin-wave entanglement, since in the presence of atomic interactions it can result in isolated single-photon emission into a phase-matched field mode.

It is now possible to study experimentally the combined effect of disorder and interactions in cold atom physics. Motivated by these developments we investigate the dynamics around the metal-insulator transition (MIT) in a one-dimensional Fermi gas with short-range interactions in a quasiperiodic potential by the time-dependent density-matrix renormalization group technique. By tuning disorder and interactions we study the MIT from the weakly to the strongly interacting limit. The MIT is not universal as time evolution, well described by a process of anomalous diffusion, depends qualitatively on the interaction strength. By using scaling ideas we relate the parameter that controls the diffusion process with the critical exponent that describes the divergence of the localization length. In the limit of strong interactions theoretical arguments suggest that the motion at the MIT tends to ballistic and critical exponents approach mean-field predictions.

We present a quantum repeater scheme based on the recently proposed qubit amplifier [N. Gisin, S. Pironio, and N. Sangouard, Phys. Rev. Lett. 105, 070501 (2010)]. It relies on an on-demand entangled-photon-pair source which uses on-demand single-photon sources, linear optical elements, and atomic ensembles. Interestingly, the imperfections affecting the states created from this source, caused, for example, by detectors with nonunit efficiencies, are systematically purified from an entanglement swapping operation based on a two-photon detection. This allows the distribution of entanglement over very long distances with a high fidelity, that is, without vacuum components and multiphoton errors. Therefore, the resulting quantum repeater architecture does not necessitate final postselections and thus achieves high entanglement distribution rates. This also provides unique opportunities for device-independent quantum key distribution over long distances with linear optics and atomic ensembles.

A collinear beams apparatus has been used to determine photodetachment cross sections for K${}^{-}$ in the photon energy range 4.250–4.360 eV. State-selective detection, utilizing a resonance ionization scheme, was applied to measure partial cross sections for those channels which leave the residual K atoms in the excited $7{}^{2}S$, $5{}^{2}F$, and $5{}^{2}G$ states. The energy region studied encompassed the openings of the aforementioned channels, as well as the channel that leaves the K atom in the $7{}^{2}P$ state. Two previously unobserved resonances were seen in all three partial cross sections between the K($5{}^{2}G$) and K($7{}^{2}P$) thresholds. It is shown that a more reliable determination of resonance parameters can be made if the same resonances are observed in several channels. In the region below the K($5{}^{2}F$) threshold, three previously observed resonances were investigated [Kiyan et al., Phys. Rev. Lett. 84, 5979 (2000)]. A greatly increased modulation of the signal was obtained by detecting in the K($7{}^{2}S$) channel instead of the K($5{}^{2}S$) channel used in the previous study. Furthermore, the shapes of the cross sections in the threshold regions are discussed. A detailed description of the apparatus and the experimental procedure employed is presented in the paper.

We present a theoretical model for describing the interaction of an electron, weakly bound in a short-range potential, with an intense, few-cycle laser pulse. General definitions for the differential probability of above-threshold ionization and for the yield of high-order-harmonic generation (HHG) are presented. For HHG we then derive detailed analytic expressions for the spectral density of generated radiation in terms of the key laser parameters, including the number $N$ of optical cycles in the pulse and the carrier-envelope phase (CEP). In particular, in the tunneling approximation, we provide detailed derivations of the closed-form formulas presented briefly by M. V. Frolov et al. [Phys. Rev. A 83, 021405(R) (2011)], which were used to describe key features of HHG by both H and Xe atom targets in an intense, few-cycle laser pulse. We then provide a complete analysis of the dependence of the HHG spectrum on both $N$ and the CEP $\phi$ of an $N$-cycle laser pulse. Most importantly, we show analytically that the structure of the HHG spectrum stems from interference between electron wave packets originating from electron ionization from neighboring half-cycles near the peak of the intensity envelope of the few-cycle laser pulse. Such interference is shown to be very sensitive to the CEP. The usual HHG spectrum for a monochromatic driving laser field (comprising harmonic peaks at odd multiples of the carrier frequency and spaced by twice the carrier frequency) is shown analytically to occur only in the limit of very large $N$, and begins to form, as $N$ increases, in the energy region beyond the HHG plateau cutoff.

We describe a model of dynamic Bose-Einstein condensates near a Feshbach resonance that is computationally feasible under assumptions of spherical or cylindrical symmetry. Simulations in spherical symmetry approximate the experimentally measured time to collapse of an unstably attractive condensate only when the molecular binding energy in the model is correct, demonstrating that quantum fluctuations and coupling between atoms and (un)bound pairs of atoms included in the model are the dominant mechanisms during collapse. Simulations of condensates with repulsive interactions find some quantitative disagreement, suggesting that pairing and quantum fluctuations are not the only significant factors for condensate loss or burst formation. Inclusion of three-body recombination was found to be inconsequential in all of our simulations, although we do not consider recent experiments [Phys. Rev. A 84, 033632 (2011)] conducted at over an order of magnitude higher density.

The effects of disorder on the quantum coherence for many-boson systems are studied in a double-well model. For the ground state, the disorder enhances the quantum coherence. In the deep Mott regime, dynamical evolution reveals periodical collapses and revivals of the quantum coherence, which is robust against the disorder. The average over variations in both the on-site energy and the interaction reveals a beat phenomenon of the coherence-decoherence oscillation in the temporal evolution.