An entanglement-witness approach to quantum coherent-state key distribution and a system for its practical implementation are described. In this approach, eavesdropping can be detected by a change in sign of either of two witness functions: an entanglement witness $\mathcal{S}$ or an eavesdropping witness $\mathcal{W}$. The effects of loss and eavesdropping on system operation are evaluated as a function of distance. Although the eavesdropping witness $\mathcal{W}$ does not directly witness entanglement for the system, its behavior remains related to that of the true entanglement witness $\mathcal{S}$. Furthermore, $\mathcal{W}$ is easier to implement experimentally than $\mathcal{S}$. $\mathcal{W}$ crosses the axis at a finite distance, in a manner reminiscent of entanglement sudden death. The distance at which this occurs changes measurably when an eavesdropper is present. The distance dependence of the two witnesses due to amplitude reduction and due to increased variance resulting from both ordinary propagation losses and possible eavesdropping activity is provided. Finally, the information content and secure key rate of a continuous variable protocol using this witness approach are given.

We investigate the behavior of genuine multipartite entanglement of paradigmatic frustrated quantum spin systems. We consider six different spin models, whose frustration ranges from being very high to very low. We find that the highly frustrated quantum spin systems are near-maximally genuine multipartite entangled, while those with low frustration do not possess a similar definite behavior with regard to their genuine multipartite entanglement.

Two–electron atoms embedded in a plasma environment are studied with screened and exponential cosine screened Coulomb model potentials. Within a configuration interaction approach, and using parameter–free explicitly correlated basis functions, we have calculated the ground-state and first excited-state energies (and other mean values) for H${}^{-}$, He, and Li${}^{+}$. We analyze their evolution with the screening parameter and provide simple fits, which allow for practical and rapid evaluations for example in plasma applications.

The basic physics of $e^{+},e^{-}$ creation and annihilation is overviewed. It is shown that for atomic hydrogen targets electron capture by a free positron to form positronium is vastly more probable than in-flight annihilation. Cross sections are presented using the classical trajectory Monte Carlo (CTMC) approach for the charge-exchange process: $$e^{+}+A^{q+}\to Ps+A^{(q+1)+},$$where $A^{q+}$ is some target ion of charge $q$. Charge-exchange cross sections for hydrogenic ion targets are presented. It is found that while the CTMC gives adequate results for positronium formation for $e^{+}$-hydrogen and $e^{+}$-cesium collisions, its high-energy behavior for hydrogenic ions is not in agreement with quantum mechanical predictions. Since we are interested in situations where many multicharged ions will be present we have looked for an alternative approach. Scaling rules are proposed and used to estimate the charge-exchange cross sections for both neutral atoms and multicharged ions.

We present theoretical predictions of high-order-harmonic generation resulting from the interaction of short femtosecond laser pulses with metal nanotips. It is demonstrated that high-energy electrons can be generated using nanotips as sources; furthermore, the recollision mechanism is proven to be intrinsically linked to this high-energy tail. If recollision exists, it should be possible to convert the energy gained by the electron in the continuum in a high-energy photon. Consequently, the emission of harmonic radiation appears to be viable. We employ a quantum mechanical time-dependent approach to model the electron dipole moment including both the laser experimental conditions and the bulk matter properties. The use of metal tips should provide an alternative way of generating coherent XUV light with a femtosecond laser field.

A setup to frequency-convert an arbitrary image encoded in the spatial profile of a probe field onto a signal field using four-wave mixing in a thermal atom vapor is proposed. The atomic motion is exploited to cancel diffraction of both signal and probe fields simultaneously. We show that an incoherent probe field can be used to enhance the transverse momentum bandwidth which can be propagated without diffraction, such that smaller structures with higher spatial resolution can be transmitted. It furthermore compensates linear absorption with nonlinear gain, to improve the four-wave mixing performance since the propagation dynamics of the various field intensities is favorably modified.

Cavity soliton lasers in a vertical-cavity surface-emitting laser with a saturable absorber can spontaneously move provided that a proper ratio of the carrier lifetimes in the amplifier and in the absorber is considered. Use is made of this fact to propose a scheme based on which a tunable all-optical delay line can be demonstrated. This easy-to-realize delay device exhibits high delay range, a very good delay resolution, and a wide extent of available data bandwidth. Also it is shown that the ratio of delay time to pulse duration (fractional delay) can be as large as 2300.

We study a quantum theory in terms of action decomposed function (ADF), a class of quantum wave function, towards many-dimensional applications to quantum dynamics of heavy particles as in chemical reactions. The equation of motion for the complex-valued amplitude of ADF represents a coupling between the internal diffusive motion of a wave packet and dynamics of its group velocity in a hierarchical manner ascending from classical to purely quantum mechanics via semiclassical dynamics. We attempt to solve this equation of motion dividing it into two stages: a semiclassical level and beyond. In this paper, as the first stage, we develop a semiclassical approximation in the Lagrange picture of classical phase flow. In the Euler picture (as in the standard WKB picture), continuous integration of the stability matrix along the paths is required. By adopting the Lagrange picture, on the other hand, we represent the semiclassical amplitude in terms of what we call deviation determinant, which can be evaluated readily in many-dimensional systems. Numerical tests show that ADF reproduces quantum wave packets at each space-time point along classical paths very well. However, the ADF in this stage is not free of the semiclassical singularity. In other words, the wave functions diverge at turning points or caustics, depending on the initial conditions chosen. This divergence is known to take place at points where classical paths smoothly distributed in phase space have “focuses” in configuration space (or momentum space) and reflects an intrinsic relationship between quantum and classical mechanics. Therefore, it is by studying the mechanism of removing the singularity that the essential feature of quantum mechanics will be clarified. This aspect will be discussed in a companion paper [K. Takatsuka and S. Takahashi, Phys. Rev. A 89, 012109 (2014)] as the second stage of many-body quantum theory.

A theory of many-dimensional real-time quantum dynamics is studied in terms of action decomposed function (ADF), a class of quantum wave function. In the preceding companion paper [S. Takahashi and K. Takatsuka, Phys. Rev. A 89, 012108 (2014)], we showed that semiclassical dynamics for ADF in the Lagrange picture of phase flow can be described in terms of what we call deviation determinant and associated quantum phases without use of the stability matrix. Consequently, the Hessian of the involved potential functions is not required in this formalism. This paper is devoted to an analysis of the mechanism of quantum diffusion (quantum smoothing) that removes the singularity inherent in the semiclassical ADF: We derive a Lorentzian form for the amplitude factor of ADF. The real part of its denominator comes from the deviation determinant, while the imaginary part reflects quantum diffusion and is proportional to the Planck constant. The presence of the nonzero imaginary part smooths out the singularity and removes the divergence. Besides, this imaginary part can be obtained through a Wronskian relation with the deviation vectors, which can be solved rather easily at each space-time point on a classical trajectory. A number of theoretical advantages of the Lorentzian form and the Wronskian relation are illustrated theoretically and numerically. It turns out that there is no essential difficulty in applications to many-dimensional heavy-particle systems such as molecules. The theory is examined with stringent numerical tests.

Evolution by the Gross-Pitaevskii equation, which describes Bose-Einstein condensates under certain conditions, solves the unstructured search problem more efficiently than does the Schrödinger equation, because it includes a cubic nonlinearity, proportional to ${\left|\psi \right|}^2\psi$. This is not the only nonlinearity of the form $f\left(\right|\psi {|}^2)\psi$ that arises in effective equations for the evolution of real quantum physical systems, however: The cubic-quintic nonlinear Schrödinger equation describes light propagation in nonlinear Kerr media with defocusing corrections, and the logarithmic nonlinear Schrödinger equation describes Bose liquids under certain conditions. Analysis of computation with such systems yields some surprising results; for example, when time-measurement precision is included in the resource accounting, searching a “database” when there is a single correct answer may be easier than searching when there are multiple correct answers. In each of these cases the nonlinear equation is an effective approximation to a multiparticle Schrödinger equation, for search by which Grover's algorithm is optimal. Thus our results lead to quantum information-theoretic bounds on the physical resources required for these effective nonlinear theories to hold, asymptotically.

We study strong-field molecular ionization with shaped ultrafast laser pulses. We measure both photoions and photoelectrons as a function of laser pulse shape using a velocity map imaging spectrometer. We analyze correlations between photoelectrons and photoions as a function of photoelectron energy and ionic fragment mass-to-charge ratio. Our analysis focuses on resonant structures in the photoelectron spectrum known as Freeman resonances, and highlights both direct and indirect ionization to multiple states of the molecular cation.

We investigate the effects of atomic interaction and artificial gauge potential in a quantum simulation of classical magnetism via ultracold bosonic atoms in triple wells. The system can be mapped into a transverse-field spin chain with Ising interaction under a twisted boundary condition. It undergoes a phase transition from planar to three-dimensional spin configurations, similar to the para-to-antiferromagnetic phase transition in the transverse-field Ising model, and the artificial gauge potential can tune this phase transition. The phase diagram is obtained, including ferromagnetic and spiral phases, similar to those simulated in Struck et al. [Struck, Ölschläger, Targat, Soltan-Panahi, Eckardt, Lewenstein, Windpassinger, and Sengstock, Science 333, 996 (2011)].

We investigate finite number effects in collisions between two states of an initially well defined number of identical bosons with attractive contact interactions, oscillating in the presence of harmonic confinement in one dimension. We investigate two $N/2$ atom bound states, which are initially displaced (symmetrically) from the trap center, and then left to freely evolve. For sufficiently attractive interactions, these bound states are like those found through use of the Bethe ansatz (quantum solitons). However, unlike the free case, the integrability is lost due to confinement, and collisions can cause mixing into different bound-state configurations. We study the system numerically for the simplest case of $N=4$, via an exact diagonalization of the Hamiltonian within a finite basis, investigating left-right number uncertainty as our primary measure of entanglement. We find that for certain interaction strengths, a phase-matching condition leads to resonant transfer to different bound-state configurations with highly non-Poissonian relative number statistics.

We study the dynamics of a single vortex and a pair of vortices in quasi two-dimensional Bose-Einstein condensates at finite temperatures. To this end, we use the stochastic Gross–Pitaevskii equation, which is the Langevin equation for the Bose–Einstein condensate. For a pair of vortices, we study the dynamics of both the vortex-vortex and vortex-antivortex pairs, which are generated by rotating the trap and moving the Gaussian obstacle potential, respectively. Due to thermal fluctuations, the constituent vortices are not symmetrically generated with respect to each other at finite temperatures. This initial asymmetry coupled with the presence of random thermal fluctuations in the system can lead to different decay rates for the component vortices of the pair, especially in the case of two corotating vortices.

It is known that cross correlation between the random intensity fluctuations of two lasers forming electromagnetically induced transparency (EIT) exhibits a transition from correlation to anticorrelation. We study the linewidth behavior of this transition and have found the linewidth is below the (effective) coherence lifetime limit and is limited only by competing noises. We established a numerical model which reveals the linewidth dependence on laser linewidth and laser power. Our experiments using lasers with different linewidth showed results in qualitative agreement with the model. This result is useful for quantum optics using EIT and may also have applications in spectroscopy and precision measurements.

We study cooperative single-photon spontaneous emission from $N$ multilevel atoms for different atomic distributions in optical vector theory. Instead of the average approximation for interatomic distance or the continuum approximation (sums over atoms replaced by integrals) for atomic distribution, the positions of every atom are taken into account by numerical calculation. It is shown that the regularity of atomic distribution has considerable influence on cooperative spontaneous emission. For a small atomic sample (compared with radiation wavelength), obtaining strong superradiance requires not only the uniform excitation (the Dicke state) but also the uniform atomic distribution. For a large sample, the uniform atomic distribution is beneficial to subradiance of the Dicke state, while the influence of atomic distribution on the timed Dicke state is weak and its time evolution obeys exponential decay approximately. In addition, we also investigate the corresponding emission spectrum and verify the directed emission for the timed Dicke state for a large atomic sample.

Wigner function is a “quasidistribution” that provides a representation of the state of a quantum mechanical system in the phase space of position and momentum. In this paper we find a relation between the Wigner function and appropriate measurements involving the system's position and momentum which generalize the von Neumann model of measurement. We introduce two probes coupled successively in time to projectors associated with the system's position and momentum. We show that one can relate the Wigner function to the Kirkwood joint quasidistribution of position and momentum, the latter, in turn, being a particular case of successive measurements. We first consider the case of a quantum mechanical system described in a continuous Hilbert space and then turn to the case of a discrete, finite-dimensional Hilbert space.

A model of an arbitrary spin coupled to a bath of spins $\frac{1}{2}$ in a star configuration is considered. The exact reduced dynamics of the central spin is found for the case of noncorrelated initial conditions of the system and the bath. The exact solution is used to test two approximation techniques, namely, the Nakajima-Zwanzig projection operator technique and the time-convolutionless projection operator technique corresponding to the second order of the coupling constant. Two types of projection operators are used for deriving the master equations, and the results are compared with the exact solution for a central spin equal to one. It is shown that the approximate master equations reproduce the exact dynamics on time scales $1/\left(A\sqrt{N}\right)$, where $A$ is the coupling constant and $N$ is the number of spins in the bath.

We investigate the systematic use of the Schwinger representation, by virtue of which two boson fields are equivalent to an effective spin, for casting multimode squeezed states into multipartite spin entangled states. The motivation for this endeavor is the following established fact: finitely squeezed, two-mode entangled states can be recast into maximally entangled bipartite spin states, irrespective of their level of squeezing (in the lossless case). This work explores the generalization of this interesting property to multipartite entanglement. While we found that the generalization of multipartite Gaussian entanglement to multipartite spin entanglement is not straightforward, there are nonetheless interesting features and entangled states to be found. Here we study a few continuous-variable entangled states already realized experimentally, and show that some of them correspond to multipartite spin entangled states.

Quantum energy teleportation (QET) is, from the operational viewpoint of distant protocol users, energy transportation via local operations and classical communication. QET has various links to fundamental research fields including black-hole physics, the quantum theory of Maxwell's demon, and quantum entanglement in condensed-matter physics. However, the energy that has been extracted using a previous QET protocol is limited by the distance between two protocol users; the upper bound of the energy being inversely proportional to the distance. In this paper, we prove that introducing squeezed vacuum states with local vacuum regions between the two protocol users overcomes this limitation, allowing energy teleportation over practical distances.