The time- and frequency-resolved nonlinear light scattering (NLS) signals from a time-evolving charge distribution of valence electrons prepared by impulsive x-ray pulses are calculated using a superoperator Green's function formalism. The signal consists of a coherent $\sim$$N^2$-scaling difference-frequency-generation and an incoherent fluorescence $\sim$$N$-scaling component, where $N$ is the number of active molecules. The former is given by the classical Larmor formula based on the time-dependent charge density. The latter carries additional information about the electronic structure and may be recast in terms of transition amplitudes representing quantum matter pathways.

We theoretically investigate the propagation of a paraxial beam in two-dimensional media with spatial dispersion. Based on the spatial dispersion theory and the ($1+1$)-dimensional paraxial wave equation, we get an expression which determines the diffraction of the beam. By fitting the dispersion surface of a typical spatial dispersion medium (a photonic crystal) calculated by the plane-wave-expansion method, the value of the diffraction term is determined, with which one can predict the diffraction of the paraxial beam that propagates in such media. Numerical simulations based on the finite-difference time-domain method confirm the theoretical results.

We study the stability of a quasi-one-dimensional dipolar Bose-Einstein condensate that is perturbed by a weak lattice potential along its axis. Our numerical simulations demonstrate that systems exhibiting a roton-maxon structure destabilize readily when the lattice wavelength equals either half the roton wavelength or a low roton subharmonic. We apply perturbation theory to the Gross-Pitaevskii and Bogoliubov–de Gennes equations to illustrate the mechanisms behind the instability threshold. The features of our stability diagram may be used as a direct measurement of the roton wavelength for quasi-one-dimensional geometries.

This paper presents an exact Grassmann stochastic Schrödinger equation for the dynamics of an open fermionic quantum system coupled to a reservoir consisting of a finite or infinite number of fermions. We use this stochastic Schrödinger equation as a generic open system tool to derive the exact master equation for an electronic system strongly coupled to fermionic reservoirs. The generality and applicability of this Grassmann stochastic approach are justified and exemplified by several quantum fermionic system problems concerning quantum coherence coupled to vacuum or finite-temperature fermionic reservoirs. Our studies show that the quantum coherence property of a quantum dot system can be profoundly modified by the environmental memory.

We investigate the time dynamics of quantum correlations of the anisotropic Heisenberg model in a time-dependent magnetic field in one-dimensional, ladder, and two-dimensional lattices. We find that quantum correlation measures in the entanglement-separability paradigm are ergodic in these systems irrespective of system parameters. However, information-theoretic quantum correlation measures can also be nonergodic and exhibit a transition from nonergodic to ergodic behavior with the change of interaction strength in the direction of the magnetic field. We also observe that the transition point changes drastically as we go from one-dimensional and ladder lattices to the two-dimensional one.

We show that the classical capacity of a quantum state, as quantified by its ability to perform dense coding, respects an exclusion principle, for arbitrary pure or mixed three-party states in any dimension. This states that no two bipartite states which are reduced states of a common tripartite quantum state can have simultaneous quantum advantage in dense coding. The exclusion principle is robust against noise. Such a principle also holds for an arbitrary number of parties. This exclusion principle is independent of the content and distribution of entanglement in the multipartite state.

We report on a scanning microscopy technique for atom-number-resolved imaging of excited-state atoms. A tightly focused laser beam leads to local autoionization and the resulting ions are counted electronically. Scanning the beam across the cloud builds up an image of the density distribution of excited atoms, with access to the full counting statistics at each spatial sampling point and an overall detection efficiency of $21\%$. We apply this technique to the measurement of a spatially inhomogeneous electric field with a spatial resolution of 50 $\mu$m and a sensitivity to electric-field gradients of 0.04 V cm${}^{-2}$.

Self-testing is a device-independent approach to estimate the state and measurement operators without the need to assume the dimension of our quantum system. In this paper, we show that one can self-test black boxes into any pure entangled two-qubit state by performing simple Bell-type experiments. The approach makes use of only one family of Bell inequalities with two inputs and two outputs. Furthermore, we outline the sufficient conditions for one to self-test any dimensional bipartite entangled state. All these methods are robust to small but inevitable experimental errors.

We numerically simulate strongly correlated ultracold bosons coupled to a high-finesse cavity field, pumped by a laser beam in the transverse direction. Assuming a weak $\mathit{classical}$ optical lattice added in the cavity direction, we model this system by a generalized Bose-Hubbard model, which is solved by means of bosonic dynamical mean-field theory. The complete phase diagram is established, which contains two novel self-organized quantum phases, lattice supersolid and checkerboard solid, in addition to conventional phases such as superfluid and Mott insulator. At finite but low temperature, thermal fluctuations are found to enhance the buildup of the self-organized phases. We demonstrate that cavity-mediated long-range interactions can give rise to stable lattice supersolid and checkerboard solid phases even in the regime of strong $s$-wave scattering. In the presence of a harmonic trap, we discuss coexistence of these self-organized phases, as relevant to experiments.

We present a protocol for measuring Bohmian, or the mathematically equivalent hydrodynamic, velocities based on an ensemble of two position measurements, defined from a positive operator-valued measure, separated by a finite time interval. The protocol is very accurate and robust as long as the first measurement uncertainty divided by the finite time interval between measurements is much larger than the Bohmian velocity, and the system evolves under flat potential between measurements. The difference between the Bohmian velocity of the unperturbed state and the measured one is predicted to be much smaller than $1\%$ in a large range of parameters. Counterintuitively, the measured velocity is that at the final time and not a time-averaged value between measurements.

Bohr's complementarity principle is one of the central concepts in quantum mechanics which restricts joint measurement for certain observables. Of course, later development shows that joint measurement could be possible for such observables with the introduction of a certain degree of unsharpness or fuzziness in the measurement. In this paper, we show that the optimal degree of unsharpness, which guarantees the joint measurement of all possible pairs of dichotomic observables, determines the degree of nonlocality in quantum mechanics as well as in more general no-signaling theories.

We study a class of Bell inequalities and find their maximum quantum violation. These inequalities involve $n$ parties, two measurements per party, with each measurement having two outcomes. The $n=2$ case corresponds to the Clauser-Horne inequality. We use the method of Jordan bases to find the maximum quantum violations. Results are found for the cases $n=2$ through $n=7$.

Entanglement-purification protocols, developed for the sake of high-fidelity communication through noisy quantum channels, are highly nonlinear quantum operations and can offer a very useful context to studies of nonlinear complex maps. Recently it was demonstrated that the feedback mechanism used in a typical purification protocol can cause the evolution dynamics of qubits to exhibit chaos [Kiss et al., Phys. Rev. Lett. 107, 100501 (2011)]. In this work we extend the investigation by considering the natural time evolution of qubits during a purification process, leading to a number of interesting findings that reflect the competition between the natural unitary evolution of qubits and nonlinear purification operations. As a result, the overall evolution dynamics of entanglement can be much richer. Possible applications are also proposed.

Composite pulses, originally developed in nuclear magnetic resonance (NMR), have found widespread use in experimental quantum information processing (QIP) to reduce the effects of systematic errors. Most pulses used so far have simply been adapted from existing NMR designs, and while techniques have been developed for designing composite pulses with arbitrary precision, the results have been quite complicated and have found little application. Here, I describe techniques for designing short but effective composite pulses to implement robust not gates, bringing together existing insights from NMR and QIP, and present some composite pulses.

We present an analytical description for ultracold collisions between two spin-$\frac{1}{2}$ fermions with isotropic spin-orbit coupling (SOC) of the Rashba type. We show that regardless of how weak the SOC may be, at sufficiently low energies the collision properties are significantly modified. The ubiquitous low energy Wigner threshold behavior is changed and its modified form for ground-state neutral atoms is given. The particles are further found to scatter preferentially into the lower-energy helicity states due to the breaking of parity conservation. This latter point establishes interaction with SOC as one mechanism for the spontaneous emergence of handedness. Our theory is applicable both to elementary spin-$\frac{1}{2}$ fermions such as electrons in condensed matter and to ultracold pseudo-spin-$\frac{1}{2}$ atoms such as ${}^6$Li in its ground hyperfine state.

We explore the feasibility of producing ultracold diatomic molecules with nonzero electric and magnetic dipole moments by magnetically associating two atoms, one with zero electron spin and one with nonzero spin. Feshbach resonances arise through the dependence of the hyperfine coupling on internuclear distance. We survey the Feshbach resonances in diatomic systems combining the nine stable alkali-metal isotopes with those of Yb, focusing on the illustrative examples of RbYb and CsYb. We show that the resonance widths may expressed as a product of physically comprehensible terms in the framework of Fermi's golden rule. The resonance widths depend strongly on the background scattering length, which may be adjusted by selecting the Yb isotope, and on the hyperfine coupling constant and the magnetic field. In favorable cases the resonances may be over 100 mG wide.

We have measured the double-differential cross sections (DDCS) for electron emission in ionization of H${}_2$O molecules under the impact of $4.5$-MeV/u O${}^{8+}$ ions. The data were collected between 1 and 600 eV, in an angular range of ${20}^{\circ }$–${150}^{\circ }$ by using an electrostatic hemispherical analyzer. In the experiment we used the H${}_2$O vapor in a static gas condition which allowed us to deduce the absolute value of the cross sections. The single-differential cross sections (SDCS) and the total cross sections have also been obtained. The DDCS as well as the SDCS spectra are compared with the continuum-distorted-wave eikonal-initial-state (CDW-EIS) calculations for both the prior as well as the post forms of the scattering matrix. The initial state is represented within the complete neglect of differential overlap approximation, where the molecular orbitals are expressed in terms of atomic orbitals of the atomic constituents. The overall agreement with the CDW-EIS model is quite good as far as the energy dependence is concerned. The prior form of the model is found to provide a better understanding of the data compared to the post version. In particular, excellent agreement between the theory and experiment has been observed for the angular distribution data at forward angles.

We propose a ground-state cavity-mediated cooling scheme for a trapped atom, which is in the $\Lambda$ configuration and confined inside a high-finesse optical cavity, using a standing-wave cooling laser. The carrier transition can be prohibited by placing the atom at the node of the cavity field, and the blue-sideband transition can be simultaneously eliminated by exploiting quantum interference via tuning the frequency of the cooling laser. As a consequence, the ground-state cooling for the trapped atom can be achieved. Moreover, we numerically demonstrate the superiority by placing the atom at the antinode of the standing-wave cooling laser as compared with the running-wave cooling laser, and the robustness of the scheme using the standing-wave laser. Meanwhile, the cooling rate can reach the same order of magnitude as that obtained in the cavity–electromagnetically-induced-transparency cooling scheme, and the explicit expression for the final phonon number in higher order is also presented.

Interacting bosonic atoms under strong gauge fields undergo a series of phase transitions that take the cloud from a simple Bose-Einstein condensate all the way to a family of fractional-quantum-Hall-type states [M. Popp, B. Paredes, and J. I. Cirac, Phys. Rev. A 70, 053612 (2004)]. In this work we demonstrate that the Hall response of the atoms can be used to locate the phase transitions and characterize the ground state of the many-body state. Moreover, the same response function reveals within some regions of the parameter space, the structure of the spectrum and the allowed transitions to excited states. We verify numerically these ideas using exact diagonalization for a small number of atoms, and provide an experimental protocol to implement the gauge fields and probe the linear response using a periodically driven optical lattice. Finally, we discuss our theoretical results in relation to recent experiments with condensates in artificial magnetic fields [L. J. LeBlanc, K. Jimenez-Garcia, R. A. Williams, M. C. Beeler, A. R. Perry, W. D. Phillips, and I. B. Spielman, Proc. Natl. Acad. Sci. USA 109, 10811 (2012)] and we analyze the role played by vortex states in the Hall response.

We study the properties of an ultracold Fermi gas loaded in a square optical lattice and subjected to an external and classical non-Abelian gauge field. We calculate the energy spectrum of the system and show that the Dirac points in the energy spectrum will remain quite stable under on-site interaction of certain strength. Once the on-site interaction grows stronger than a critical value, the Dirac points will no longer be stable and merge into a single hybrid point. This merging implies a quantum phase transition from a semimetallic phase to a band insulator. The on-site interaction between ultracold fermions could be conveniently controlled by Feshbach resonances in current experiments. We propose that this interaction-induced merging of Dirac points may be observed in the ultracold-Fermi-gas experiments.