We show that a concentration of light at a metal tip allows near-field optical imaging of single fluorescent dye molecules at very high resolution, despite strong quenching effects. Details as small as 10 nm were observed in the fluorescence patterns of single Cy-3 dyes bound to the termini of DNA. Data evaluation by model fitting determines the positions of the dyes to an accuracy even better than 1 nm and also yields their 3D orientation. The metal tip simultaneously provides high-resolution topographic imaging complementing the optical signal for a detailed surface examination.

We investigate a possibility of superfluidity in a trapped gas of Fermi atoms with a repulsive interaction in the presence of an optical lattice. Applying the exact diagonalization method to a one-dimensional Hubbard model including the trap potential, we find that, when the strength of the repulsive interaction exceeds a critical value, the binding energy of two Fermi atoms becomes negative below the half-filling case, indicating that an attractive interaction effectively works between Fermi atoms. In this case, a “Mott insulating core” appears in the center of the trap, where each site is occupied by one atom. The Cooper-pair correlation strongly develops between atoms in the left- and right-hand sides of this core.

Quantum mechanics forbids deterministic discrimination among nonorthogonal states. Nonetheless, the capability to distinguish nonorthogonal states unambiguously is an important primitive in quantum information processing. In this work, we experimentally implement generalized measurements in an optical system and demonstrate the first optimal unambiguous discrimination between three nonorthogonal states, with a success rate of 55%, to be compared with the 25% maximum achievable using projective measurements. Furthermore, we present the first realization of unambiguous discrimination between a pure state and a nonorthogonal mixed state.

We derive tight Bell's inequalities for $N>2$ observers involving more than two alternative measurement settings. We give a necessary and sufficient condition for a general quantum state to violate the new inequalities. The inequalities are violated by some classes of states, for which all standard Bell’s inequalities with two measurement settings per observer are satisfied.

We determine the ground state properties of inhomogeneous mixtures of bosons and fermions in cubic lattices and parabolic confining potentials. For finite hopping we determine the domain boundaries between Mott-insulator plateaux and hopping-dominated regions for lattices of arbitrary dimension within mean-field and perturbation theory. The results are compared with a new numerical method that is based on a Gutzwiller variational approach for the bosons and an exact treatment for the fermions. The findings can be applied as a guideline for future experiments with trapped atomic Bose-Fermi mixtures in optical lattices.

We study arrays of mechanical oscillators in the quantum domain and demonstrate how the motions of distant oscillators can be entangled without the need for control of individual oscillators and without a direct interaction between them. These oscillators are thought of as being members of an array of nanoelectromechanical resonators with a voltage being applicable between neighboring resonators. Sudden nonadiabatic switching of the interaction results in a squeezing of the states of the mechanical oscillators, leading to an entanglement transport in chains of mechanical oscillators. We discuss spatial dimensions, $Q$ factors, temperatures and decoherence sources in some detail, and find a distinct robustness of the entanglement in the canonical coordinates in such a scheme. We also briefly discuss the challenging aspect of detection of the generated entanglement.

We evaluate the frequencies of collective modes and the anisotropic expansion rate of a harmonically trapped Fermi superfluid at varying coupling strengths across a Feshbach resonance driving a BCS-BEC crossover. The equations of motion for the superfluid are obtained from a microscopic mean-field expression for the compressibility and are solved within a scaling ansatz. Our results confirm nonmonotonic behavior in the crossover region and are in quantitative agreement with current measurements of the transverse breathing mode by Kinast et al. [Phys. Rev. Lett. 92, 150402 (2004)] and of the axial breathing mode by Bartenstein et al. [Phys. Rev. Lett. 92, 203201 (2004)].

Closed-form analytic expressions are derived for the density profile of a harmonically trapped noninteracting Fermi gas in $d$ dimensions. Shell structure effects are included to leading order in $1/N$, where $N$ is the number of particles. These corrections to the local density approximation scale as $\delta n/n\sim N^{-\alpha }$, where $\alpha =(1+1/d)/2$.

We generalize the quantum random walk protocol for a particle in a one-dimensional chain, by using several types of biased quantum coins, arranged in aperiodic sequences, in a manner that leads to a rich variety of possible wave-function evolutions. Quasiperiodic sequences, following the Fibonacci prescription, are of particular interest, leading to a sub-ballistic wave-function spreading. In contrast, random sequences lead to diffusive spreading, similar to the classical random walk behavior. We also describe how to experimentally implement these aperiodic sequences.

We establish an explicit correspondence between ergodicity breaking in a system described by power-law tail distributions and the divergence of the moments of these distributions.

We perform a rigorous computation of the specific heat of the Ashkin-Teller model in the case of small interaction and we explain how the universality-nonuniversality crossover is realized when the isotropic limit is reached. We prove that, even in the region where universality for the specific heat holds, anomalous critical exponents appear: for instance, we predict the existence of a previously unknown anomalous exponent, continuously varying with the strength of the interaction, describing how the difference between the critical temperatures rescales with the anisotropy parameter.

We study the current relaxation of a wave packet in a nonlinear random sample coupled to the continuum and show that the survival probability decays as $P(t)\sim 1/t^{\alpha }$. For intermediate times $t<t^{*}$, the exponent $\alpha$ satisfies a scaling law $\alpha =f(\Lambda =\chi /l_{\infty })$, where $\chi$ is the nonlinearity strength and $l_{\infty }$ is the localization length of the corresponding random system with $\chi =0$. For $t\gg t^{*}$ and $\chi >{\chi }_{\mathrm{c}\mathrm{r}}$ we find a universal decay with $\alpha =2/3$ which is a signature of the nonlinearity-induced delocalization. Experimental evidence should be observable in coupled nonlinear optical waveguides.

A method of phase control of entanglement in two-qubit systems is proposed. We show that by changing a relative phase of the pulses that drive the transitions in a two-qubit system with closed-loop couplings, one can control entanglement at will. The method relies on adiabatic dynamics via time-delayed pulse sequences and can be implemented with both resonant and nonresonant transitions.

We show that, within mean-field theory, the density profile of a rapidly rotating harmonically trapped Bose-Einstein condensate is of the Thomas-Fermi form as long as the number of vortices is much larger than unity. Two forms of the condensate wave function are explored: (i) the lowest Landau level (LLL) wave function with a regular lattice of vortices multiplied by a slowly varying envelope function, which gives rise to components in higher Landau levels; (ii) the LLL wave function with a nonuniform vortex lattice. From variational calculations, we find it most favorable energetically to retain the LLL form of the wave function but to allow the vortices to deviate slightly from a regular lattice. The predicted distortions of the lattice are small, but in accord with recent measurements at lower rates of rotation.

For percolation on $(RL)\times L$ two-dimensional rectangular domains with a width $L$ and aspect ratio $R$, we propose that the existence probability of the percolating cluster $E_p(L,\epsilon ,R)$ as a function of $L$, $R$, and deviation from the critical point $\epsilon$ can be expressed as $F(\epsilon L^{y_t}{R}^a)$, where $y_t\equiv 1/\nu$ is the thermal scaling power, $a$ is a new exponent, and $F$ is a scaling function. We use Monte Carlo simulation of bond percolation on square lattices to test our proposal and find that it is well satisfied with $a=0.14(1)$ for $R>2$. We also propose superscaling for other critical quantities.

I show that two distant parties can transform pure entangled states to arbitrary pure states by stochastic local operations and classical communication (SLOCC) at the single copy level, if they share bound entangled states. This is the effect of bound entanglement since this entanglement processing is impossible by SLOCC alone. A similar effect of bound entanglement exists in three qubits where two incomparable entangled states of GHZ (Greenberger, Horne, and Zeilinger) and $W$ can be interconverted. In general, multipartite settings composed by $N$ distant parties, all $N$-partite pure entangled states are interconvertible by SLOCC with the assistance of bound entangled states with positive partial transpose.

We consider the Dirac equation in one space dimension in the presence of a symmetric potential well. We connect the scattering phase shifts at $E=+m$ and $E=-m$ to the number of states that have left the positive energy continuum or joined the negative energy continuum, respectively, as the potential is turned on from zero.

We show that formulating the quantum time of arrival problem in a segment of the real line suggests rephrasing the quantum time of arrival problem to finding states that evolve to unitarily collapse at a given point at a definite time. For the spatially confined particle, we show that the problem admits a solution in the form of an eigenvalue problem of a compact and self-adjoint time of arrival operator derived by a quantization of the classical time of arrival, which is canonically conjugate with the Hamiltonian in a closed subspace of the Hilbert space.

A probability of electron-positron pair production by photons in strong nonuniform fields is derived by applying a model trajectory method in the frame of a semiclassical approach. In addition to the well known invariant field parameter $\chi$, a new invariant parameter $\nu$ is introduced to characterize the nonuniformity of the field. For $\nu \gg 1$, the obtained expression is reduced to the uniform-field approximation while it approaches the Bethe-Heitler formula for $\nu \ll 1$. The pair production is predicted for relatively weak external fields where the uniform-field approximation gives no effect. The theory agrees well with the experimental results of crystal-assisted pair production.

By introducing fractional Gaussian noise into the generalized Langevin equation, the subdiffusion of a particle can be described as a stationary Gaussian process with analytical tractability. This model is capable of explaining the equilibrium fluctuation of the distance between an electron transfer donor and acceptor pair within a protein that spans a broad range of time scales, and is in excellent agreement with a single-molecule experiment.