Optimal purification of a generic n-qudit state

We propose a quantum algorithm for the purification of a generic mixed state $\rho$ of a $n$-qudit system by using an ancillary $n$-qudit system. The algorithm is optimal in that (i) the number of ancillary qudits cannot be reduced, (ii) the number of parameters which determine the purification state $|\Psi>$ exactly equals the number of degrees of freedom of $\rho$, and (iii) $|\Psi>$ is easily determined from the density matrix $\rho$. Moreover, we introduce a quantum circuit in which the quantum gates are unitary transformations acting on a $2n$-qudit system. These transformations are determined by parameters that can be tuned to generate, once the ancillary qudits are disregarded, any given mixed $n$-qudit state.Comment: 8 pages, 9 figures, remarks adde

Luttinger liquid of trimers in Fermi gases with unequal masses

We investigate one dimensional attractive Fermi gases in spin-dependent optical lattices. We show that three-body bound states - "trimers" - exist as soon as the two tunneling rates are different. We calculate the binding energy and the effective mass of a single trimer. We then show numerically that for finite and commensurate densities $n_\uparrow=n_\downarrow/2$ an energy gap appears, implying that the gas is a one-component Luttinger liquid of trimers with suppressed superfluid ordering. The boundaries of this novel phase are given. We discuss experimental situations to test our predictions.Comment: 4 pages, 4 figures. Final accepted versio

Reversible and irreversible dynamics of a qubit interacting with a small environment

We analyze the dynamics of a system qubit interacting by means a sequence of pairwise collisions with an environment consisting of just two qubits. We show that the density operator of the qubits approaches a common time averaged equilibrium state, characterized by large fluctuations, only for a random sequence of collisions. For a regular sequence of collisions the qubitstates of the system and of the reservoir undergo instantaneous periodic oscillations and do not relax to a common state. Furthermore we show that pure bipartite entanglement is developed only when at least two qubits are initially in the same purestate while otherwise also genuine multipartite entanglement builds up.Comment: 5 pages, 4 figure

O2 signature in thin and thick O2-H2O ices

Aims. In this paper we investigate the detectability of the molecular oxygen in icy dust grain mantles towards astronomical objects. Methods. We present a systematic set of experiments with O2-H2O ice mixtures designed to disentangle how the molecular ratio affects the O2 signature in the mid- and near-infrared spectral regions. All the experiments were conducted in a closed-cycle helium cryostat coupled to a Fourier transform infrared spectrometer. The ice mixtures comprise varying thicknesses from 8 $\times$ 10$^{-3}$ to 3 $\mu$m. The absorption spectra of the O2-H2O mixtures are also compared to the one of pure water. In addition, the possibility to detect the O2 in icy bodies and in the interstellar medium is discussed. Results. We are able to see the O2 feature at 1551 cm$^{-1}$ even for the most diluted mixture of H2O : O2 = 9 : 1, comparable to a ratio of O2/H2O = 10 % which has already been detected in situ in the coma of the comet 67P/Churyumov-Gerasimenko. We provide an estimate for the detection of O2 with the future mission of the James Webb Space Telescope (JWST).Comment: 11 pages, 10 figures, article in press, to appear in A&A 201

Josephson current through a long quantum wire

The dc Josephson current through a long SNS junction receives contributions from both Andreev bound states localized in the normal region as well as from scattering states incoming from the superconducting leads. We show that in the limit of a long junction, this current, at low temperatures, can be expressed entirely in terms of properties of the Andreev bound states at the Fermi energy: the normal and Andreev reflection amplitudes at the left-hand and at the right-hand S-N interface. This has important implications for treating interactions in such systems.Comment: 25 pages, 5 figure

LITTLE THINGS in 3D: robust determination of the circular velocity of dwarf irregular galaxies

Dwarf Irregular galaxies (dIrrs) are the smallest stellar systems with extended HI discs. The study of the kinematics of such discs is a powerful tool to estimate the total matter distribution at these very small scales. In this work, we study the HI kinematics of 17 galaxies extracted from the `Local Irregulars That Trace Luminosity Extremes, The HI Nearby Galaxy Survey' (LITTLE THINGS). Our approach differs significantly from previous studies in that we directly fit 3D models (two spatial dimensions plus one spectral dimension) using the software $^\text{3D}$BAROLO, fully exploiting the information in the HI datacubes. For each galaxy we derive the geometric parameters of the HI disc (inclination and position angle), the radial distribution of the surface density, the velocity-dispersion ($\sigma_v$) profile and the rotation curve. The circular velocity (V$_{\text{c}}$), which traces directly the galactic potential, is then obtained by correcting the rotation curve for the asymmetric drift. As an initial application, we show that these dIrrs lie on a baryonic Tully-Fisher relation in excellent agreement with that seen on larger scales. The final products of this work are high-quality, ready-to-use kinematic data ($\textrm{V}_\textrm{c}$ and $\sigma_v$) that we make publicly available. These can be used to perform dynamical studies and improve our understanding of these low-mass galaxies.Comment: 36 pages, 28 figures, 2 tables. Submitted to MNRAS (revised version after the referee report). The final rotation curves can be downloaded from http://www.filippofraternali.com/styled-9/index.htm

Pairing of Cooper pairs in a Josephson junction network containing an impurity

We show how to induce pairing of Cooper pairs (and, thus, $4e$ superconductivity) as a result of local embedding of a quantum impurity in a Josephson network fabricable with conventional junctions. We find that a boundary double Sine-Gordon model provides an accurate description of the dc Josephson current patterns, as well as of the stable phases accessible to the network. We point out that tunneling of pairs of Cooper pairs is robust against quantum fluctuations, as a consequence of the time reversal invariance, arising when the central region of the network is pierced by a dimensionless magnetic flux $\phi = \pi$. We find that, for $\phi = \pi$, a stable attractive finite coupling fixed point emerges and point out its relevance for engineering a two level quantum system with enhanced coherence.Comment: 5 Pages, 5 Figures. Small modifications, ref.[11] added. To appear in EP

Thermodynamic Bounds on Efficiency for Systems with Broken Time-reversal Symmetry

We show that for systems with broken time-reversal symmetry the maximum efficiency and the efficiency at maximum power are both determined by two parameters: a "figure of merit" and an asymmetry parameter. In contrast to the time-symmetric case, the figure of merit is bounded from above; nevertheless the Carnot efficiency can be reached at lower and lower values of the figure of merit and far from the so-called strong coupling condition as the asymmetry parameter increases. Moreover, the Curzon-Ahlborn limit for efficiency at maximum power can be overcome within linear response. Finally, always within linear response, it is allowed to have simultaneously Carnot efficiency and non-zero power.Comment: Final version, 4 pages, 3 figure

A simple representation of quantum process tomography

We show that the Fano representation leads to a particularly simple and appealing form of the quantum process tomography matrix $\chi_{_F}$, in that the matrix $\chi_{_F}$ is real, the number of matrix elements is exactly equal to the number of free parameters required for the complete characterization of a quantum operation, and these matrix elements are directly related to evolution of the expectation values of the system's polarization measurements. These facts are illustrated in the examples of one- and two-qubit quantum noise channels.Comment: 5 page

A Bridging Mechanism in the Homogenization of Brittle Composites with Soft Inclusions

We provide a homogenisation result for the energy-functional associated with a purely brittle composite whose microstructure is characterised by soft periodic inclusions embedded in a stiffer matrix. We show that the two constituents as above can be suitably arranged on a microscopic scale \u3b5 to obtain, in the limit as \u3b5 tends to zero, a homogeneous macroscopic energy-functional explicitly depending on the opening of the crack