The entanglement between two arbitrary subsystems of random pure states is studied via properties of the density matrix's partial transpose ${\rho }_{12}^{T_2}$. The density of states of ${\rho }_{12}^{T_2}$ is close to the semicircle law when both subsystems have dimensions which are not too small and are of the same order. A simple random matrix model for the partial transpose is found to capture the entanglement properties well, including a transition across a critical dimension. Log negativity is used to quantify entanglement between subsystems and analytic formulas for this are derived based on the simple model. The skewness of the eigenvalue density of ${\rho }_{12}^{T_2}$ is derived analytically, using the average of the third moment over the ensemble of random pure states. The third moment after partial transpose is also shown to be related to a generalization of the Kempe invariant. The smallest eigenvalue after partial transpose is found to follow the extreme value statistics of random matrices; namely, the Tracy-Widom distribution. This distribution, with relevant parameters obtained from the model, is found to be useful in calculating the fraction of entangled states at critical dimensions. These results are tested in a quantum dynamical system of three coupled standard maps, where one finds that if the parameters represent a strongly chaotic system, the results are close to those of random states, although there are some systematic deviations at critical dimensions.

Besides two strong ${\pi }_{\perp 1}^{*}$ and ${\pi }_{\parallel }^{*}$ resonances in the 398- to 400-eV energy range, N 1$s$ near edge x-ray absorption fine structure spectra of acrylonitrile molecules have a less intense 401- to 403-eV doublet. The two components correspond to the N 1$s$ $\to$ ${\pi }_{\perp 2}^{*}$ and N 1$s$ $\to$ $D_{\parallel }^{*}$ transitions, where $D_{\parallel }^{*}$ is a diffuse state with strong Rydberg character. The vibrational analysis shows that in the $D_{\parallel }^{*}$ excited state, two low-energy $\mathit{out}$-$\mathit{of}$-$\mathit{plane}$ normal modes are strongly excited. The ${\pi }_{\perp 2}^{*}$ excitation triggers a set of $\mathit{\text{in}}$-$\mathit{plane}$ vibrations, in particular, two C=C–C$\equiv$N bendings of the molecule.

Allowed vibronic transitions to the two lowest singlet electronic terms induced by electron impact in the cesium dimer are theoretically investigated in the frame of the semiclassical impact parameter method. All relevant quantities characterizing the transitions, i.e., transition dipole moments, Franck-Condon factors, and vibronic moments, are derived and compared with results in the literature. Total and vibrationally resolved cross sections for excitations initiated from ${\upsilon }^{\prime \prime }=0$–45 vibrational levels of the ground electronic state are calculated and the role of vibrational excitation is discussed.

We investigate to which extend a terahertz laser pulse can be used to produce field-free molecular orientation at high temperature. We consider laser pulses that can be implemented with the state of the art technology and we show that the efficiency of the control scheme crucially depends on the parameters of the molecule. We analyze the temperature effects on molecular dynamics and we demonstrate that for some molecules a noticeable orientation can be achieved at high temperature.

We obtain approximations for the time-independent Gross-Pitaevskii (GP) and complex GP equation in two and three spatial dimensions by generalizing the divergence-free WKB method. The results include an explicit expression of a uniformly valid approximation for the condensate density of an ultracold Bose gas confined in a harmonic trap that extends into the classically forbidden region. This provides an accurate approximation of the condensate density that includes healing effects at leading order that are missing in the widely adopted Thomas-Fermi approximation. The results presented herein allow us to formulate useful approximations to a range of experimental systems including the equilibrium properties of a finite-temperature Bose gas and the steady-state properties of a two-dimensional nonequilibrium condensate. Comparisons between our asymptotic and numerical results for the conservative and forced-dissipative forms of the GP equations as applied to these systems show excellent agreement between the two sets of solutions, thereby illustrating the accuracy of these approximations.

The striped state of ultracold bosons with Rashba spin-orbit coupling in a homogeneous infinite system has, as we show, a constant particle flow, which in a finite-size system would accumulate particles at the boundaries; it is thus not a physical steady state of the system. We propose, as a variational ansatz, a condensate wave function for a weakly trapped system which behaves similarly to the striped state near the center, but does not have particle flow at the boundaries. This state has a line of unquantized coreless vortices. We show, by minimizing the total energy, that our modified striped state has lower energy than the conventional striped state and it is thus a physically appropriate starting point to analyze striped states in finite systems.

I derive a loop representation for the canonical and grand-canonical partition functions for an interacting four-component Fermi gas in one spatial dimension and an arbitrary external potential. The representation is free of the “sign problem” irrespective of population imbalance, mass imbalance, and to a degree, sign of the interaction strength. This property is in sharp contrast with the analogous three-dimensional, two-component interacting Fermi gas, which exhibits a sign problem in the case of unequal masses, chemical potentials, and repulsive interactions. The one-dimensional system is believed to exhibit many phenomena in common with its three-dimensional counterpart, including an analog of the BCS-BEC crossover, and nonperturbative, universal few- and many-body physics at scattering lengths much larger than the range of interaction, making the theory an interesting candidate for numerical study. Positivity of the probability measure for the partition function allows for a mean-field treatment of the model; here, I present such an analysis for the interacting Fermi gas in the SU(4) (unpolarized, mass-symmetric) limit and demonstrate that there exists a phase in which a continuum limit may be defined.

The induced intraspecies interactions among the majority species, mediated by the minority species, is computed for a population-imbalanced two-component Fermi gas. Although the Feshbach-resonance mediated interspecies interaction is dominant for equal populations, leading to singlet $s$-wave pairing, we find that, in the strongly imbalanced regime, the induced intraspecies interaction leads to $p$-wave pairing and superfluidity of the majority species. Thus, we predict that the observed spin-polaron Fermi-liquid state in this regime is unstable to $p$-wave superfluidity, in accordance with the results of Kohn and Luttinger, below a temperature that, near unitarity, we find to be within current experimental capabilities. We present possible experimental signatures of the $p$-wave state using radiofrequency spectroscopy as well as density-density correlations after free expansion.

We study, analytically and numerically, the dynamics of a matter-wave soliton formed by a Bose-Einstein condensate with an attractive interatomic interaction confined in a one-dimensional harmonic trap and subjected to a flashing weak periodic potential. Within the framework of the Gross-Pitaevski equation, we show that efficient energy transfer to the soliton occurs within two distinct frequency regimes: (a) on resonance with the trapping frequency and (b) on resonance with the internal mode of the soliton. We find that the former regime is well described within the soliton-as-particle approximation, while the latter relies on the extended nature of the localized state and involves strong excitations of the width coupled to translational motion.

We propose a scheme to controllably convert the wave front of an arbitrary incident beam into a helical one by compact transformation slabs, thus enabling the output beam to carry a desirable orbital angular momentum (OAM). First, based on transformation optics, a three-dimensional (3D) phase transformation between any two wave fronts by flat transformation media is established and then used to mold the wave front of a Gaussian beam into a helical one. Second, 3D finite-difference time-domain simulations are performed to confirm the spiraling evolutions of the resultant field and phase, clearly demonstrating the OAM generated. Further theoretical analyses show that the refractive index exhibiting a helical distribution leads to the oppositely spiral phase front and that it is feasible to produce a desirable OAM by generators of the unit OAM. The results not only provide an additional way to manipulate the phase and photon OAM but also reciprocally shed further light on the phase structure of helical beams, which leads to a new means of transformation by a surface.

Plasmons on the surface of a metal increase the light intensity by several orders of magnitude. To quantify the consequences of this phenomenon in quantum processes, we calculate the excitation probability for atoms near the surface, which are excited by a single-photon pulse. Using quantum electrodynamics in the presence of absorbing dielectrics, we predict that nonradiative decay in the metal will limit the excitation probability to about one-half of the maximum that could be achieved in the absence of such losses.

We quantify precisely the maximum secure information capacity of photons entangled in high dimensions for entanglement in the orbital angular momentum and angular degrees of freedom. Our analysis takes careful account of the influence of experimental imperfections, such as nonunity detection efficiency, on the degree of Einstein-Podolsky-Rosen (EPR) entanglement and hence on the secure information capacity of the photon pairs. We find that there is is an optimal dimension that maximizes the secure information capacity whose value can be predicted analytically from the knowledge of only a few experimental parameters.

We present approximate but nevertheless highly accurate similariton solutions to the generalized nonlinear Schrödinger equation (NLSE) with varying parameters describing pulses propagating in fiber amplifiers and lasers with normal and anomalous dispersion. We also derive the analytical similariton solutions of the NLSE for the case when the pulses have a rectangular or “smooth rectangular” shape and when they have a kink and antikink shape. Numerical simulations are in excellent agreement with these analytical solutions describing self-similar linearly chirped pulses showing that they can be observed in realistic fiber geometries.

The beat time ${\tau }_{\mathrm{fpt}}$ associated with the energy transfer between two coupled oscillators is dictated by the bandwidth theorem which sets a lower bound ${\tau }_{\mathrm{fpt}}\sim 1/\delta \omega$. We show, both experimentally and theoretically, that two coupled active LRC electrical oscillators with parity-time ($\mathcal{PT}$) symmetry bypass the lower bound imposed by the bandwidth theorem, reducing the beat time to zero while retaining a real valued spectrum and fixed eigenfrequency difference $\delta \omega$. Our results foster design strategies which lead to (stable) pseudounitary wave evolution, and may allow for ultrafast computation, telecommunication, and signal processing.

We study qubit decoherence under generalized dispersive readout, i.e., we investigate a qubit coupled to a resonantly driven dissipative harmonic oscillator. We provide a complete picture by allowing for arbitrarily large qubit-oscillator detuning and by considering also a coupling to the square of the oscillator coordinate, which is relevant for flux qubits. Analytical results for the decoherence time are obtained by a transformation of the qubit-oscillator Hamiltonian to the dispersive frame and a subsequent master equation treatment beyond the Markov limit. We predict a crossover from Markovian decay to a decay with Gaussian shape. Our results are corroborated by the numerical solution of the full qubit-oscillator master equation in the original frame.

Verification of entanglement is an important tool to characterize sources and devices for use in quantum computing and communication applications. In a vast majority of experiments entanglement witnesses (EWs) are used in order to prove the presence of entanglement in a quantum state. EWs can be constructed from available measurement results and do not require a reconstruction of the whole density matrix (full tomography), which is especially valuable for high-dimensional systems. We provide a method to construct accessible nonlinear EWs, which incorporate two important properties. First, they improve on linear EWs in the sense that each nonlinear EW detects more entangled states than its linear counterpart and therefore allows the verification of entanglement without critical dependence on having found the “right” linear witness. Second, they can be evaluated using exactly the same data as for the evaluation of the original linear witness. This allows a reanalysis of published experimental data to strengthen statements about entanglement verification without the requirement to perform additional measurements. These particular properties make the accessible nonlinear EWs attractive for the implementations in current experiments, for they can also enhance the statistical significance of the entanglement verification.

String-net condensate is a new class of materials which exhibits quantum topological order. Here we study the measurement-based quantum computation on the simplest example of string-net condensate, namely the $Z_2$ gauge string-net condensate on the two-dimensional hexagonal lattice, by using the framework of quantum computational tensor network. We show that universal measurement-based quantum computation is possible by coupling two correlation space wires with a physical two-body interaction. We also show that universal measurement-based quantum computation is possible solely with single-qubit measurements if the sign of the coefficient of each closed-loop configuration in the state is tuned. These results suggest that even the simplest example of string-net condensate is equipped with the correlation space that has the capacity for the application to quantum information processing.

We describe a possible architecture to implement a universal bosonic simulator using trapped ions. Single ions are confined in individual traps, and their motional states represent the bosonic modes. Single-mode linear operators, nonlinear phase shifts, and linear beam splitters can be realized by precisely controlling the trapping potentials. All the processes in a bosonic simulation, except the initialization and the readout, can be conducted beyond the Lamb-Dicke regime. Aspects of our proposal can also be applied to split adiabatically a pair of ions in a single trap.

Quantum interference in spontaneous emission from a four-level atom is investigated with the counter-rotating terms and the energy shifts included. The atom has two upper levels which are coupled to a common lower level by the same vacuum modes and are driven by a coherent field to an auxiliary level. The effect of the counter-rotating terms in the coupling through the vacuum modes is taken into account by a unitary transformation method. We show how the quantum interference due to the energy shifts affects the spontaneous emission.

The recently developed method combining the configuration interaction and the coupled-cluster method was demonstrated to provide accurate treatment of correlation corrections in divalent atomic systems [Safronova, Kozlov, and Clark, Phys. Rev. Lett. 107, 143006 (2011)]. We have extended this approach to the calculation of quadrupole polarizabilities ${\alpha }_2$ and applied it to evaluate ${\alpha }_2$ for the ground state of Mg and Mg-like Si${}^{2+}$. Performing the calculations in three different approximations of increasing accuracy allowed us to place the upper bounds on the uncertainty of the final results. The recommended values ${\alpha }_2\left(3s^2{}^1{S}_0\right)=35.86\left(13\right)$ a.u. for Si${}^{2+}$ and ${\alpha }_2\left(3s^2{}^1{S}_0\right)=814\left(3\right)$ a.u. for Mg are estimated to be accurate to $0.4\%$. Differences in quadrupole polarizability contributions in neutral Mg and Si${}^{2+}$ ion are discussed.