We present a method to numerically calculate the dynamics driven by arbitrary Hamiltonians, in particular those with symmetry. The method enables us to study quantum state and entanglement transmission through a uniformly coupled two-dimensional square lattice with XY-type interaction. Significantly, we find that the central symmetry between sending and receiving nodes plays a crucial role in attaining maximal fidelity and entanglement transmission. In other words, the quality of a two-dimensional transmission is determined by the geometry of the nodes involved.

Device independent protocols rely on the violation of Bell inequalities to certify properties of the resources available. The violation of the inequalities is meaningless without a few well-known assumptions. One of these is measurement independence, the property that the source of the states measured in an inequality is uncorrelated from the measurements selected. Since this assumption cannot be confirmed, we consider the consequences of relaxing it and find that the definition chosen is critically important to the observed behavior. Considering a definition that is a bound on the min-entropy of the measurement settings, we find lower bounds on the min-entropy of the source used to choose the inputs required to deduce any quantum or nonlocal behavior from a Bell inequality violation. These bounds are significantly more restrictive than the ones obtained by endowing the measurement-input source with the further structure of a Santha-Vazirani source. We also outline a procedure for finding tight bounds and study the set of probabilities that can result from relaxing measurement dependence.

An all-linear-optical scheme for a fully featured quantum router is presented. This device directs the signal photonic qubit according to the state of one control photonic qubit. In the introduction we formulate the list of requirements imposed on a fully quantum router. Then we describe our proposal, showing the exact principle of operation on a linear-optical scheme. Subsequently we provide a generalization of the scheme in order to optimize the success probability by means of a tunable controlled-phase gate. Finally, we show how one can modify the device to route multiple signal qubits using the same control qubit.

We report a cluster of results regarding the difficulty of finding approximate ground states to typical instances of the quantum satisfiability problem $k$-body quantum satisfiability ($k$-QSAT) on large random graphs. As an approximation strategy, we optimize the solution space over “classical” product states, which in turn introduces a novel autonomous classical optimization problem, PSAT, over a space of continuous degrees of freedom rather than discrete bits. Our central results are (i) the derivation of a set of bounds and approximations in various limits of the problem, several of which we believe may be amenable to a rigorous treatment; (ii) a demonstration that an approximation based on a greedy algorithm borrowed from the study of frustrated magnetism performs well over a wide range in parameter space, and its performance reflects the structure of the solution space of random $k$-QSAT. Simulated annealing exhibits metastability in similar “hard” regions of parameter space; and (iii) a generalization of belief propagation algorithms introduced for classical problems to the case of continuous spins. This yields both approximate solutions, as well as insights into the free energy “landscape” of the approximation problem, including a so-called dynamical transition near the satisfiability threshold. Taken together, these results allow us to elucidate the phase diagram of random $k$-QSAT in a two-dimensional energy-density–clause-density space.

The dynamics of ionic fragmentation of CH${}_4$ molecules under impact of 10-keV electrons has been studied. The technique of recoil ion momentum spectroscopy is employed to obtain information about the kinetic energy release and the dissociation mechanisms of different pathways arising from the fragmentation of a CH${}_4$ dication. The results show that there are altogether eight dissociation pathways that arise from the complete and the incomplete Coulomb explosions of the CH${}_4$${}^{2+}$ molecular ions. The kinetic energy release for these pathways is compared with earlier data from the literature for the impact of different charged particles, photons, and their impact energies. The present results indicate that mostly the lower electronic states of CH${}_4$${}^{2+}$ are involved for the observed dissociation channels. Also, the dissociation mechanisms associated with these channels are suggested and discussed. Further, we have also estimated the relative ion intensities of different channels of fragmentation of CH${}_4$ dication produced under impact of considered energy of electrons.

Typical applications of the fast-atom diffraction technique exploit incidence along low-index directions to extract accurate structural information on surfaces from the diffraction pattern. The data interpretation in this case is well developed and simplified by the axial channeling conditions, where the three-dimensional projectile-surface interaction appears effectively averaged over the fast-motion direction. We study theoretically the diffraction of fast-atom beams that are significantly misaligned with respect to a low-index direction at the surface. With full quantum wave-packet calculations, we address He atom scattering from the LiF(001) surface within a wide range of azimuthal and polar incidence angles. In particular, we are interested in the transitions between low-index directions upon the azimuthal rotation of the beam, and in the question of the choice of an adequate axial channeling approximation. We make use of the energy criterion to analyze the diffraction patterns and to discuss how the momentum exchange projected on the beam direction affects the diffraction.

Compared with the macrosystem case, the phase transition occurring in fragmenting cluster systems depicts a much richer story. However, most experimental observations have been restricted to an extremely partial view of this picture due to the technical limitations of a large-range scan of the energy deposited in a selected cluster system. Here, taking charge-selected C${}_{60}$${}^{3+}$ and C${}_{60}$${}^{4+}$ as model systems, we experimentally explore the fragmentation phase transition (FPT) over a large energy range and directly observe some of the most important features of the FPT, the multistage transformation, and the charge effect.

Calculations of the photoexcitation spectra of ortho-positronium Rydberg states with principal quantum numbers between 10 and 30 are presented. The effects of Doppler broadening and saturation of the corresponding electric-dipole transitions are studied, together with the role of static and motionally induced electric fields. This is done in the context of recent measurements reported by Cassidy et al. [Phys. Rev. Lett. 108, 043401 (2012)], and with regard to experiments involving the production of antihydrogen by charge-exchange between Rydberg positronium and cold antiprotons.

We present an exact solution to the stationary coupled nonlinear Gross-Pitaevskii equations, which govern the motion of the spinor Bose-Einstein condensates. The solitonic solution is a twisted half-skyrmion in 3D space. By making a map from the Cartesian coordinates to the toroidal coordinates, we demonstrate it is a linked half-unknot with a fractional topological charge.

We present a many-body description for two-component ultracold bosonic gases when one of the species is in the weakly interacting regime and the other is either weakly or strongly interacting. In the one-dimensional limit the latter is a hybrid in which a Tonks-Girardeau gas is immersed in a Bose-Einstein condensate, which is an example of a class of quantum system involving a tunable, superfluid environment. We describe the process of phase separation microscopically as well as semiclassically in both situations and show that quantum correlations are maintained even in the separated phase.

We discuss a general scheme for creating atomic spin-orbit coupling (SOC) such as the Rashba or Dresselhaus types using magnetic-field-gradient pulses. In contrast to conventional schemes based on adiabatic center-of-mass motion with atomic internal states restricted to a dressed-state subspace, our scheme works for the complete subspace of a hyperfine-spin manifold by utilizing the coupling between the atomic magnetic moment and external magnetic fields. A space-dependent pulsed magnetic field acts as an internal-state-dependent impulse, thereby coupling the atomic internal spin with its orbital center-of-mass motion, as in the Einstein–de Haas effect. This effective coupling can be dynamically manipulated to synthesize SOC of any type (Rashba, Dresselhaus, or any linear combination thereof). Our scheme can be realized with most experimental setups of ultracold atoms and is especially suited for atoms with zero nuclear spins.

We examine the prospect of demonstrating Einstein-Podolsky-Rosen (EPR) entanglement for massive particles using spin-changing collisions in a spinor Bose-Einstein condensate. Such a demonstration has recently been attempted by Gross et al. [Nature (London) 480, 219 (2011)] using a condensate of ${}^{\text{87}}$Rb atoms trapped in an optical lattice potential. For the condensate initially prepared in the $(F,m_F)=(2,0)$ hyperfine state, with no population in the $m_F=\pm 1$ states, we predict a significant suppression of the product of inferred quadrature variances below the Heisenberg uncertainty limit, implying strong EPR entanglement. However, such EPR entanglement is lost when the collisions are initiated in the presence of a small (currently undetectable) thermal population ${\overline{n}}_{\mathrm{th}}$ in the $m_F=\pm 1$ states. For condensates containing 150–200 atoms, we predict an upper bound of ${\overline{n}}_{\mathrm{th}}\simeq 1$ that can be tolerated in this experiment before EPR entanglement is lost.

In this paper a method is presented for calculating the subcycle rate for transitions of electrons between two bands of a sinusoidal band structure. A simple closed-form expression for the rate is derived. We show that transition dynamics are sensitive to the shape of the band structure away from the minima of the conduction band. A model of high-order-harmonic generation in periodic solids that incorporates the subcycle dynamics of transitions across the band gap is described. Harmonic emission is found to be highly sensitive to the temporal shape of the transition rate. Destructive interference of electron currents in the conduction band due to subcycle transition dynamics is described.

We show that the rate of switching between the vibrational states of a modulated nonlinear oscillator is characterized by a quantum critical temperature $T_{c1}\propto {\hslash }^2$. Above $T_{c1}$ there emerges a quantum crossover region where the switching rate displays a steep and characteristic temperature dependence, followed by a qualitatively different temperature dependence for higher $T$. In contrast to the crossover between tunneling and thermal activation in equilibrium systems, here the crossover occurs between different regimes of switching activated by quantum fluctuations. The results go beyond the standard real-time instanton technique of the large-deviation theory.

Quantum state tomography relies on the ability to perform well-characterized unitary operations, which are not always available. This places restrictions on which physical systems can be characterized using such techniques. We develop a formalism that circumvents the requirement for well-characterized unitary operations by treating unknown parameters in the state and unitary process on the same footing, thereby simultaneously performing state and partial process tomography. Our formalism is generalized to $d$-level systems, and we provide a specific example for a $\mathsf{V}$-type three-level atomic system whose transition dipole moments are not known. We show that it is always possible to retrieve not only the unknown state but also the process parameters, except for a set of zero measure in the state-parameter space.

Quantum process tomography is a necessary tool for verifying quantum gates and diagnosing faults in architectures and gate design. We show that the standard approach of process tomography is grossly inaccurate in the case where the states and measurement operators used to interrogate the system are generated by gates that have some systematic error, a situation all but unavoidable in any practical setting. These errors in tomography cannot be fully corrected through oversampling or by performing a larger set of experiments. We present an alternative method for tomography to reconstruct an entire library of gates in a self-consistent manner. The essential ingredient is to define a likelihood function that assumes nothing about the gates used for preparation and measurement. In order to make the resulting optimization tractable, we linearize about the target, a reasonable approximation when benchmarking a quantum computer as opposed to probing a black-box function.

We introduce the concept of monogamy deficit for quantum correlation by combining two types of monogamy inequalities depending on different measurement sides. For tripartite pure states, we demonstrate a relation which connects two types of monogamy inequalities for quantum discord and provide the difference between them. By using this relation, we obtain a unified physical interpretation for these two monogamy deficits. In addition, we find the interesting fact that there is a general monogamy condition for several quantum correlations for tripartite pure states. We then provide a necessary and sufficient condition for the establishment of one kind of monogamy inequality for tripartite mixed states and generalize it to multipartite quantum states.

We study the effects of diffusion on a $\Lambda$-gradient echo memory, which is a coherent optical quantum memory, using thermal gases. The efficiency of this memory is high for short storage time, but decreases exponentially due to decoherence as the storage time is increased. We study the effects of both longitudinal and transverse diffusion in this memory system, and give both analytical and numerical results that are in good agreement. Our results show that diffusion has a significant effect on the efficiency. Further, we suggest ways to reduce these effects to improve storage efficiency. We also report on a mechanism by which the rate of expansion of the transverse width of the beam is reduced compared to the naive expectation of diffusive effects, as observed in recent experiments.