The non-negative Wigner function of all quantum states involved in teleportation of Gaussian states using the standard continuous-variable teleportation protocol means that there is a local realistic phase-space description of the process. This includes the coherent states teleported up to now in experiments. We extend the phase-space description to teleportation of non-Gaussian states using the standard protocol and conclude that teleportation of non-Gaussian pure states with a fidelity of $2/3$ is a “gold standard” for this kind of teleportation.

We study the asymmetric simple exclusion process with open boundaries and derive the exact form of the joint probability function for the occupation number and the current through the system. We further consider the thermodynamic limit, showing that the resulting distribution is non-Gaussian and that the density fluctuations have a discontinuity at the continuous phase transition, while the current fluctuations are continuous. The derivations are performed by using the standard operator algebraic approach and by the introduction of new operators satisfying a modified version of the original algebra.

We propose an approach to optical quantum computation in which a deterministic entangling quantum gate may be performed using, on average, a few hundred coherently interacting optical elements (beam splitters, phase shifters, single photon sources, and photodetectors with feedforward). This scheme combines ideas from the optical quantum computing proposal of Knill, Laflamme, and Milburn [Nature (London) 409, 46 (2001)], and the abstract cluster-state model of quantum computation proposed by Raussendorf and Briegel [Phys. Rev. Lett. 86, 5188 (2001)].

We investigate strongly interacting atomic Fermi-Bose mixtures in inhomogeneous and random optical lattices. We derive an effective Hamiltonian for the system and discuss its low temperature physics. We demonstrate the possibility of controlling the interactions at local level in inhomogeneous but regular lattices. Such a control leads to the achievement of Fermi glass, quantum Fermi spin-glass, and quantum percolation regimes involving bare and/or composite fermions in random lattices.

We show that by choosing appropriate distributions of the randomness the search for optimal paths links diverse problems of disordered media, such as directed percolation, invasion percolation, and directed and nondirected spanning polymers. We also introduce a simple and efficient algorithm, which solves the $d$-dimensional model numerically in $\mathcal{O}\left(N^{1+d_f/d}\right)$ steps, where $d_f$ is the fractal dimension of the path. Using extensive simulations in two dimensions, we identify the phase boundaries of the di­rected polymer universality class. A new strong-disorder phase occurs where the optimum paths are self-affine with parameter-dependent scaling exponents. Furthermore, the phase diagram contains directed and nondirected percolation as well as the directed random walk models at specific points and lines.

Here we demonstrate how parahydrogen can be used to prepare a two-spin system in an almost pure state which is suitable for implementing nuclear magnetic resonance quantum computation. A 12 ns laser pulse is used to initiate a chemical reaction involving pure parahydrogen (the nuclear spin singlet of ${\mathrm{H}}_2$). The product, formed on the $\mu \mathrm{s}$ time scale, contains a hydrogen-derived two-spin system with an effective spin-state purity of 0.916. To achieve a comparable result by direct cooling would require an unmanageable (in the liquid state) temperature of 6.4 mK or an impractical magnetic field of 0.45 MT at room temperature. The resulting spin state has an entanglement of formation of 0.822 and cannot be described by local hidden variable models.

We present a numerical method to simulate the time evolution, according to a generic Hamiltonian made of local interactions, of quantum spin chains and systems alike. The efficiency of the scheme depends on the amount of entanglement involved in the simulated evolution. Numerical analysis indicates that this method can be used, for instance, to efficiently compute time-dependent properties of low-energy dynamics in sufficiently regular but otherwise arbitrary one-dimensional quantum many-body systems. As by-products, we describe two alternatives to the density matrix renormalization group method.

We propose the scaled Schrödinger equation and the related principles, and construct a general method of calculating the exact wave functions of atoms and molecules in analytical forms. The nuclear and electron singularity problems no longer occur. Test applications to hydrogen atom, helium atom, and hydrogen molecule are satisfactory, implying a high potentiality of the proposed method.

We demonstrate the possibility of creating and controlling an ideal and trimerized optical Kagomé lattice, and study the low temperature physics of various atomic gases in such lattices. In the trimerized Kagomé lattice, a Bose gas exhibits a Mott transition with fractional filling factors, whereas a spinless interacting Fermi gas at $2/3$ filling behaves as a quantum magnet on a triangular lattice. Finally, a Fermi-Fermi mixture at half-filling for both components represents a frustrated quantum antiferromagnet with a resonating-valence-bond ground state and quantum spin liquid behavior dominated by a continuous spectrum of singlet and triplet excitations. We discuss the method of preparing and observing such a quantum spin liquid employing molecular Bose condensates.

It has been widely assumed that one-qubit gates in spin-based quantum computers suffer from severe technical difficulties. We show that one-qubit gates can, in fact, be generated using only modest and presently feasible technological requirements. Our solution uses only global magnetic fields and controllable Heisenberg exchange interactions, thus circumventing the need for single-spin addressing.

We have investigated how the decay dynamics of an unstable quantum system is affected by a false measurement, where the decay is monitored by detecting a decay product but the active energy band of the detector does not match the energy of the decay product. It is shown that, although such a measurement is ineffective and has almost no effect if the detector response is slow, the detectability of decay is increased and the decay is accelerated considerably if the response is fast. This is due to the new decay channel, which is generated as a counteraction of measurement.

The boundary $\beta$ function generates the renormalization group acting on the universality classes of one-dimensional quantum systems with boundary which are critical in the bulk but not critical at the boundary. We prove a gradient formula for the boundary $\beta$ function, expressing it as the gradient of the boundary entropy $s$ at fixed nonzero temperature. The gradient formula implies that $s$ decreases under renormalization, except at critical points (where it stays constant). At a critical point, the number $\exp \left(s\right)$ is the “ground-state degeneracy,” $g$, of Affleck and Ludwig, so we have proved their long-standing conjecture that $g$ decreases under renormalization, from critical point to critical point. The gradient formula also implies that $s$ decreases with temperature, except at critical points, where it is independent of temperature. It remains open whether the boundary entropy is always bounded below.

It is shown that electromagnetic vortices can act as beam guides for charged particles. The confinement in the transverse directions is due to the rotation of the electric and magnetic fields around the vortex line. A large class of exact solutions describing various types of relativistic beams formed by an electromagnetic wave with a simple vortex line is found both in the classical and in the quantum case. In the second case, the motion in the transverse direction is fully quantized. Particle trajectories trapped by a vortex are very similar to those in a helical undulator.

We demonstrate that the temporal peak generated by specific electromagnetic pulses may arrive at different positions simultaneously in an absorbing waveguide. The effect can be used for triggering several devices all at once at unknown distances from the sender or generally to transmit information so that it arrives at the same time to receivers at different, unknown locations. This simultaneity cannot be realized by the standard transmission methods.

Starting from the Boltzmann equation, we study the center-of-mass oscillation of a harmonically trapped normal Fermi gas in the presence of a one-dimensional periodic potential. We show that for values of the Fermi energy above the first Bloch band the center of mass motion is overdamped in the collisional regime due to umklapp processes. This should be contrasted with the behavior of a superfluid where one instead expects the occurrence of persistent Josephson-like oscillations.

We show that in an atomic Bose gas near a Feshbach resonance a quantum phase transition occurs between a phase with only a molecular Bose-Einstein condensate and a phase with both an atomic and a molecular Bose-Einstein condensate. We show that the transition is characterized by an Ising order parameter. We also determine the phase diagram of the gas as a function of magnetic field and temperature: the quantum critical point extends into a line of finite temperature Ising transitions.

By miniaturizing electrode geometries high electric fields can be produced using modest voltages. A planar array of $20\mu \mathrm{m}$ wide gold electrodes, spaced $20\mu \mathrm{m}$ apart, is made on a sapphire substrate. A voltage difference of up to 350 V is applied to adjacent electrodes, generating an electric field that decreases exponentially with distance from the substrate. This microstructured array can be used as a mirror for polar molecules and can be rapidly switched on and off. This is demonstrated by retro­reflecting a beam of state-selected ammonia molecules with a forward velocity of about $30\mathrm{m}/\mathrm{s}$.

We report the first experimental demonstration of a quantum controlled-NOT gate for different photons, which is classically feed forwardable. In the experiment, we achieved this goal with only the use of linear optics, an entangled ancillary pair of photons, and postselection. The techniques developed in our experiment are of significant importance for quantum information processing with linear optics.

We investigate multiparty communication scenarios where information is sent from several senders to several receivers. We establish a relation between the quantum capacity of multiparty communication channels and their distillability properties, which enables us to show that the quantum capacity of such channels is not additive.

We study the equilibrium properties of a monomer-monomer $A+B\to \emptyset$ reaction on a two-dimensional substrate containing randomly placed catalytic bonds. Interacting $A$ and $B$ species undergo continuous exchanges with particle reservoirs and react as soon as a pair of unlike particles appears on sites connected by a catalytic bond. For annealed disorder in the placement of catalytic bonds the model is mapped onto a general spin $S=1$ model and solved exactly for the pressure in a particular case. At equal activities of the two species a second order phase transition is revealed.