Numerical simulations of fs laser propagation in water have been made to explain the small-scale filaments in water we have observed by a nonlinear fluorescence technique. Some analytical descriptions combined with numerical simulations show that a space-frequency coupling mainly from the interplay among self-phase modulation, dispersion and phase mismatching will reshape the laser beam into a conical wave which plays a major role of energy redistribution and can prevent laser beam from self-guiding over a long distance. An effective group velocity dispersion is introduced to explain the pulse broadening and compression in the filamentation.

We propose an easy implementable prepare-and-measure protocol for robust quantum key distribution with photon polarization. The protocol is fault tolerant against collective random unitary channel noise. The protocol does not need any collective quantum measurement or quantum memory. A security proof and a specific linear optical realization using spontaneous parametric down conversion are given.

We re-examine the status of the weak value of a quantum mechanical observable as an objective physical concept, addressing its physical interpretation and general domain of applicability. We show that the weak value can be regarded as a definite mechanical effect on a measuring probe specifically designed to minimize the back reaction on the measured system. We then present an interesting framework for general measurement conditions (where the back reaction on the system may not be negligible) in which the measurement outcomes can still be interpreted as quantum averages of weak values. We show that in the classical limit, there is a direct correspondence between quantum averages of weak values and posterior expectation values of classical dynamical properties according to the classical inference framework.

Contrary to the usual assumption that the experimental preparation of pure entangled states can be described by mixed states due to white noise, a more realistic description for polarization-entangled states produced by parametric down-conversion is that they are mixed states due to decoherence in a preferred polarization basis. This distinction between white and colored noise is crucial when we look for maximal violations of Bell’s inequalities for two-qubit and two-qutrit entangled states. We find that violations of Bell’s inequalities with realistic noise for polarization-entangled photons are extremely robust for colored noise, whereas this is not the case for white noise. In addition, we study the difference between white and colored noise for maximal violations of Bell’s inequalities for three- and four-qubit entangled states.

Real parallel computing with a quantum computer attracts vast interest due to its extreme high potential. We propose a neuromorphic quantum computation algorithm based on an adiabatic Hamiltonian evolution with energy dissipation. This algorithm can be applied to problems if a cost function can be expressed in a quadratic form. This requirement results from the fact that our Hamiltonian is designed by following a method similar to an artificial neural network (ANN). The state of an ANN is often trapped at local minima, and the network outputs an error. Since the state of a quantum system with the proposed algorithm is always in the ground state according to the adiabatic theorem, it is not necessary to be concerned that the quantum state is trapped at local minima. However, there is no guarantee that a quantum algorithm based on an adiabatic Hamiltonian evolution with degeneration or level crossing is successfully executed. We show successful numerical simulation results with the proposed algorithm by introducing energy dissipation to keep the quantum state staying in the ground state, and then we show an application to the $n$-queen problem, which is one of the combinatorial optimization problems.

A private shared Cartesian frame is a novel form of private shared correlation that allows for both private classical and quantum communication. Cryptography using a private shared Cartesian frame has the remarkable property that asymptotically, if perfect privacy is demanded, the private classical capacity is three times the private quantum capacity. We demonstrate that if the requirement for perfect privacy is relaxed, then it is possible to use the properties of random subspaces to nearly triple the private quantum capacity, almost closing the gap between the private classical and quantum capacities.

My previous calculations of the Lamb shift in muonic hydrogen are repeated for muonic deuterium.

The doubly excited singlet states of He below the $N=2$ threshold may decay by autoionization or fluorescence. In the fluorescence decay channel, most decay cascades consist of emission of three photons, of which the first is a VUV photon, the second is in or near the visible range, and the last is another VUV photon. We have studied the fluorescence channel decay dynamics of the $(2,0_{\mathrm{n}})$, $(2,1_{\mathrm{n}})$ and $(2,-1_{\mathrm{n}})$ ${}^1\mathrm{P}$, $n=3–7$, states by wavelength dispersed photon-induced fluorescence spectroscopy. We have detected the photons in the second step of the cascade and determined the branching ratios for the strongest lines in this step. From these data we are able to calculate the branching ratios of the first step in the cascade. The results are in good agreement with calculations of the main decay channels of the higher resonances, but about 20–30 % lower, and so we are able to describe quantitatively the whole fluorescence cascade of the above-mentioned doubly excited states.

The three-dimensional time-dependent quantum wave packet dynamics $(J=0)$ using a Hamiltonian for a triatomic molecule in Radau coordinates is employed to study laser pulse excitation of the OClO molecule. The fast Fourier transform (FFT) and the split operator methods are applied to propagate the wave packet. The vibronic excitations $A{}^{2}A_2({\nu }_1,{\nu }_2,{\nu }_3)\leftarrow X{}^{2}B_1(0,0,0)$ of the triatomic molecule OClO using femtosecond laser pulses of varying intensities are investigated. With an ultrashort laser pulse of certain FWHM (full width at half maximum), the vibrational level can be selectively excited. The changes in the vibrational population distributions caused by simple variation of the pulse are remarkable.

We image the dynamics of diatomic and triatomic molecules with sub-$5\mathrm{fs}$ and sub-Å resolution using laser Coulomb explosion imaging with $8\mathrm{fs}$ pulses. We obtain image information by measuring the vector momenta of all atomic ions produced by explosion of a single molecule. We image vibrating $\mathrm{D}_2{}^{+}$ and of dissociating $\mathrm{S}\mathrm{O}_2{}^{2+}$ and $\mathrm{S}\mathrm{O}_2{}^{3+}$. Images taken at 0 and $60\mathrm{fs}$ show that the dissociation of $\mathrm{S}\mathrm{O}_2{}^{2+}$ produces an $\mathrm{S}{\mathrm{O}}^{+}$ rotational wave packet.

Electron capture and loss cross sections have been measured for fast light projectile ions of $0.5\mathrm{MeV}$ ${\mathrm{H}}^{0,1+}$ and $0.5–2.0\mathrm{MeV}$ ${}^4\mathrm{He}^{0,1+,2+}$ in collisions with ${\mathrm{C}}_{60}$. The gaseous target of ${\mathrm{C}}_{60}$ was prepared by heating ${\mathrm{C}}_{60}$ powder in a target cell to temperatures of $300–500°\mathrm{C}$, and outgoing charge fractions were measured as a function of the cell temperature. Absolute cross sections are deduced by using two different vapor-pressure data available in literature. Experimental cross sections are examined in comparison with theoretical values obtained from various conventional formulas proposed for atomic targets. In addition, single- and double-electron capture cross sections are also calculated on the basis of a classical model by taking account of the local electron density of ${\mathrm{C}}_{60}$. From a complete set of our experimental cross sections, equilibrium charge fractions are also deduced and found to be essentially the same as carbon-foil data, indicating no gas-solid difference.

In the collisional region at finite temperatures, the collective modes of superfluids are described by the Landau two-fluid hydrodynamic equations. This region can now be probed over the entire BCS–Bose-Einstein-condensate crossover in trapped Fermi superfluids with a Feshbach resonance, including the unitarity region. Building on the approach initiated by Zaremba, Nikuni, and Griffin in 1999 for trapped atomic Bose gases, we present a variational formulation of two-fluid hydrodynamic collective modes based on the work of Zilsel in 1950 developed for superfluid helium. Assuming a simple variational Ansatz for the superfluid and normal fluid velocities, the frequencies of the hydrodynamic modes are given by solutions of coupled algebraic equations, with constants only involving spatial integrals over various equilibrium thermodynamic derivatives. This variational approach is both simpler and more physical than a direct attempt to solve the Landau two-fluid differential equations. Our two-fluid results are shown to reduce to those of Pitaevskii and Stringari for a pure superfluid at $T=0$.

We analyze mechanisms of high-order harmonic generation from two-center molecules at large internuclear separations in linearly polarized laser fields. Since laser-driven electrons acquire instantaneous kinetic energies of up to 8 times the ponderomotive potential $U_{\mathrm{p}}$, recombination at an appropriately placed nucleus leads to ultrahigh-order harmonic emission [P. Moreno, L. Plaja, and L. Roso, Phys. Rev. A 55, R1593 (1997)]. By solving the time-dependent Schrödinger equation for model systems, we show that this mechanism is only efficient if the single-particle orbital of the electron is coherently delocalized over the two potential wells. This is realized in the ground state of a one-electron molecular ion. In a neutral molecule or in a molecular ion created by ionization of a neutral molecule at large internuclear distance, the coherence is destroyed by electron-electron correlation.

We describe a continuous-variable coherent-states quantum-key distribution system working at $1550\mathrm{nm}$, and entirely made of standard fiber optics and telecommunications components, such as integrated-optics modulators, couplers and fast InGaAs photodiodes. The setup is composed of an emitter randomly modulating a coherent state in the complex plane with a doubly Gaussian distribution, and a receiver based on a shot-noise limited time-resolved homodyne detector. By using a reverse reconciliation protocol, the device can transfer a raw key rate up to $1\mathrm{Mbit}∕\mathrm{s}$, with a proven security against Gaussian or non-Gaussian attacks. The dependence of the secret information rate of the present fiber setup is studied as a function of the line transmission and excess noise.

We describe an atom trap for Bose-Einstein condensates of ${}^{87}\mathrm{Rb}$ to be used in atom interferometry experiments. The trap is based on a time-orbiting potential waveguide. It supports the atoms against gravity while providing weak confinement to minimize interaction effects. We observe harmonic oscillation frequencies $({\omega }_x,{\omega }_y,{\omega }_z)$ as low as $2\pi \times (6.0,1.2,3.3)\mathrm{Hz}$. Up to $2\times {10}^4$ condensate atoms have been loaded into the trap, at estimated temperatures as low as $850\mathrm{pK}$. We anticipate that interferometer measurement times of $1\mathrm{s}$ or more should be achievable in this device.

We have created a Bose-Einstein condensate whose spin orientation is metastable. Condensates were transferred into a quadrupole magnetic trap, where Majorana transitions limited the lifetime to a few hundred milliseconds, about 30 times the trapping period. Atoms held in the trap frequently displayed a ring-shaped time-of-flight distribution. We speculate that such a ring could be either a quantized vortex or a feature of the Majorana loss dynamics in the quantum regime.

We analyze how a maximally entangled state of two qubits (e.g., the singlet ${\psi }_s$) is affected by the action of local channels described by completely positive maps $\mathcal{E}$. We analyze the concurrence and the purity of states ${\varrho }_{\mathcal{E}}=\mathcal{E}\otimes \mathcal{I}\left[{\psi }_s\right]$. Using the concurrence-versus-purity phase diagram we characterize local channels $\mathcal{E}$ by their action on the singlet state ${\psi }_s$. We specify a region of the concurrence-versus-purity diagram that is achievable from the singlet state via the action of unital channels. We show that even the most general (including nonunital) local channels acting just on a single qubit of the original singlet state cannot generate the maximally entangled mixed states. We study in detail various time evolutions of the original singlet state induced by local Markovian semigroups. We show that the decoherence process is represented in the concurrence-versus-purity diagram by a line that forms the lower bound of the achievable region for unital maps. On the other hand, the depolarization process is represented by a line that forms the upper bound of the region of maps induced by unital maps.

We consider completely positive maps that describe noisy, multiparticle unitary operations. We show that by random single-particle operations the completely positive maps can be depolarized to a standard form with a reduced number of parameters describing the noise process in such a way that the noiseless (unitary) part of the evolution is not altered. A further reduction of the parameters, in many cases even to a single one (i.e., global white noise), is possible by tailoring the decoherence process and increasing the amount of noise. We generalize these results to the dynamical case where the noisy evolution is described by a master equation of Lindblad form, and the noiseless evolution is specified by an interaction Hamiltonian. The resulting standard forms may be used to compute lower bounds on channel capacities, to simplify quantum process tomography or to derive error thresholds for entanglement purification and quantum computation.

We prepared polarization-entangled photon pairs and sent one of the photons through a Mach-Zehnder interferometer. The apparatus was arranged so that when going through each arm of the interferometer the pairs were in a different Bell state. The distinguishability of the interferometer paths was determined by projecting the entangled state of the two photons with a polarizer placed in the path of the photon that does not go through the interferometer. As a consequence, actions on the remote photon determined nonlocally the visibility of the interference pattern. We present a full theoretical analysis and experimental results that confirm the theoretical predictions.