The physics of vortex lines in dipolar condensates is studied. Because of the nonlocality of the dipolar interaction, the 3D character of the vortex plays a more important role in dipolar gases than in typical short-range interacting ones. In particular, the dipolar interaction significantly affects the stability of the transverse modes of the vortex line. Remarkably, in the presence of a periodic potential along the vortexline, the spectrum of transverse modes shows a rotonlike minimum, which eventually destabilizes the straight vortex when the BEC as a whole is still stable, opening the possibility for new scenarios for vortex-line configurations in dipolar gases.

We show theoretically that entangled photon pairs can be produced on demand through the biexciton decay of a quantum dot strongly coupled to the modes of a photonic crystal. The strong coupling allows us to tune the energy of the mixed exciton-photon (polariton) eigenmodes and to overcome the natural splitting existing between the exciton states coupled with different linear polarizations of light. Polariton states are moreover well protected against dephasing due to their lifetime of ten to a hundred times shorter than that of a bare exciton. Our analysis shows that the scheme proposed is achievable with the present technology.

It is shown analytically that the output of the standard model for complex, nonlocal hysteresis, the Preisach model, exhibits long-time tails under quite general conditions. For uncorrelated input signals the exponent of the algebraic output correlation decay is determined solely by the tails of the input and the Preisach density. Correspondingly we identify universality classes leading to identical algebraic tails. These results predict the occurrence of $1/f$ noise for a large class of hysteretic systems.

Time of flight images reflect the momentum distribution of the atoms in the trap, but the spatial noise in the image holds information on more subtle correlations. Using bosonization, we study such correlations in generic 1D systems of ultracold fermions. We show how pairing as well as spin and charge density wave correlations may be identified and extracted from time of flight images. These incipient orders manifest themselves as power-law singularities in the noise correlations, that depend on the Luttinger parameters, which suggests a general experimental technique to obtain them.

We investigate the properties of strongly interacting heteronuclear boson-boson mixtures loaded in realistic optical lattices, with particular emphasis on the physics of interfaces. In particular, we numerically reproduce the recent experimental observation that the addition of a small fraction of ${}^{41}\mathrm{K}$ induces a significant loss of coherence in ${}^{87}\mathrm{Rb}$, providing a simple explanation. We then investigate the robustness against the inhomogeneity typical of realistic experimental realizations of the glassy quantum emulsions recently predicted to occur in strongly interacting boson-boson mixtures on ideal homogeneous lattices.

The exact formula of the one-level distribution of the Schmidt eigenvalues is obtained for dynamical formation of entanglement in quantum chaos. The formula is based on the random matrix theory of the fixed-trace ensemble, and is derived using the theory of the holonomic system of differential equations. We confirm that the formula describes the universality of the distribution of the Schmidt eigenvalues in quantum chaos.

We present an analytical strong-disorder renormalization group theory of the quantum phase transition in the dissipative random transverse-field Ising chain. For Ohmic dissipation, we solve the renormalization flow equations analytically, yielding asymptotically exact results for the low-temperature properties of the system. We find that the interplay between quantum fluctuations and Ohmic dissipation destroys the quantum critical point by smearing. We also determine the phase diagram and the behavior of observables in the vicinity of the smeared quantum phase transition.

A universal quantum work relation is proved for isolated time-dependent Hamiltonian systems in a magnetic field as the consequence of microreversibility. This relation involves a functional of an arbitrary observable. The quantum Jarzynski equality is recovered in the case this observable vanishes. The Green-Kubo formula and the Casimir-Onsager reciprocity relations are deduced thereof in the linear response regime.

Starting from microscopic mechanics, we derive thermodynamic relations for heat conducting nonequilibrium steady states. The extended Clausius relation enables one to experimentally determine nonequilibrium entropy to the second order in the heat current. The associated Shannon-like microscopic expression of the entropy is suggestive. When the heat current is fixed, the extended Gibbs relation provides a unified treatment of thermodynamic forces in the linear nonequilibrium regime.

The exact stochastic decomposition of non-Markovian dissipative quantum dynamics is combined with the time-dependent semiclassical initial value formalism. It is shown that even in the challenging regime of moderate friction and low temperatures, where non-Markovian effects are substantial, this approach allows for the accurate description of dissipative dynamics in anharmonic potentials over many oscillation periods until thermalization is reached. The problem of convergence of the stochastic average at long times, which plagues full quantum mechanical implementations, is avoided through a joint sampling of the stochastic noise and the semiclassical phase-space distribution.

We derive the Schrödinger equation for a spinless charged particle constrained to move on a curved surface in the presence of an electric and magnetic field. The particle is confined on the surface using a thin-layer procedure, which gives rise to the well-known geometric potential. The electric and magnetic fields are included via the four potential. We find that there is no coupling between the fields and the surface curvature and that, with a proper choice of the gauge, the surface and transverse dynamics are exactly separable. Finally, we derive an analytic form of the Hamiltonian for spherical, cylindrical, and toroidal surfaces.

We predict the possibility to generate a finite stationary spin current by applying an unbiased ac driving to a quasi-one-dimensional asymmetric periodic structure with Rashba spin-orbit interaction and strong dissipation. We show that under a finite coupling strength between the orbital degrees of freedom the electron dynamics at low temperatures exhibits a pure spin ratchet behavior, i.e., a finite spin current and the absence of charge transport in spatially asymmetric structures. It is also found that the equilibrium spin currents are not destroyed by the presence of strong dissipation.

We apply the configuration-interaction method to calculate the spectra of two-component Fermi systems in a harmonic trap, studying the convergence of energies at the unitary interaction limit. We find that for a fixed regularization of the two-body interaction the convergence is exponential or better in the truncation parameter of the many-body space. However, the conventional regularization is found to have poor convergence in the regularization parameter, with an error that scales as a low negative power of this parameter. We propose a new regularization of the two-body interaction that produces exponential convergence for systems of three and four particles. We estimate the ground-state energy of the four-particle system to be $(5.045\pm 0.003)\hslash \omega$.

We propose a cheat sensitive quantum protocol to perform a private search on a classical database which is efficient in terms of communication complexity. It allows a user to retrieve an item from the database provider without revealing which item he or she retrieved: if the provider tries to obtain information on the query, the person querying the database can find it out. The protocol ensures also perfect data privacy of the database: the information that the user can retrieve in a single query is bounded and does not depend on the size of the database. With respect to the known (quantum and classical) strategies for private information retrieval, our protocol displays an exponential reduction in communication complexity and in running-time computational complexity.

How correlated are two quantum systems from the perspective of a third? We answer this by providing an optimal “quantum state redistribution” protocol for multipartite product sources. Specifically, given an arbitrary quantum state of three systems, where Alice holds two and Bob holds one, we identify the cost, in terms of quantum communication and entanglement, for Alice to give one of her parts to Bob. The communication cost gives the first known operational interpretation to quantum conditional mutual information. The optimal procedure is self-dual under time reversal and is perfectly composable. This generalizes known protocols such as the state merging and fully quantum Slepian-Wolf protocols, from which almost every known protocol in quantum Shannon theory can be derived.

We report on a Bell experiment with spacelike separation assuming that the measurement time is related to gravity-induced state reduction. Two energy-time entangled photons are sent through optical fibers and directed into unbalanced interferometers at two receiving stations separated by 18 km. At each station, the detection of a photon triggers the displacement of a macroscopic mass. The timing ensures spacelike separation from the moment a photon enters its interferometer until the mass has moved. Two-photon interference fringes with a visibility of up to 90.5% are obtained, leading to a violation of the Bell inequality.

We show how to implement cryptographic primitives based on the realistic assumption that quantum storage of qubits is noisy. We thereby consider individual-storage attacks; i.e., the dishonest party attempts to store each incoming qubit separately. Our model is similar to the model of bounded-quantum storage; however, we consider an explicit noise model inspired by present-day technology. To illustrate the power of this new model, we show that a protocol for oblivious transfer is secure for any amount of quantum-storage noise, as long as honest players can perform perfect quantum operations. Our model also allows us to show the security of protocols that cope with noise in the operations of the honest players and achieve more advanced tasks such as secure identification.

We study the effect of noise-induced dephasing on collisional phase diffusion in the two-site Bose-Hubbard model. Dephasing of the quasimomentum modes may slow down phase diffusion in the quantum Zeno limit. Remarkably, the degree of suppression is enhanced by a bosonic factor of order $N/\log N$ as the particle number $N$ increases.

We show that when a suitable entanglement-generating unitary operator depending on a parameter is applied on $N$ qubits in parallel, a precision of the order of $2^{-N}$ in estimating the parameter may be achieved. This exponentially improves the precision achievable in classical and in quantum nonentangling strategies.

We report an experimental test of quantum complementarity with single-photon pulses sent into a Mach-Zehnder interferometer with an output beam splitter of adjustable reflection coefficient $R$. In addition, the experiment is realized in Wheeler’s delayed-choice regime. Each randomly set value of $R$ allows us to observe interference with visibility $V$ and to obtain incomplete which-path information characterized by the distinguishability parameter $D$. Measured values of $V$ and $D$ are found to fulfill the complementarity relation $V^2+D^2\le 1$.