A new perturbative expansion of the time evolution operator associated with a quantum system

A novel expansion of the evolution operator associated with a -- in general, time-dependent -- perturbed quantum Hamiltonian is presented. It is shown that it has a wide range of possible realizations that can be fitted according to computational convenience or to satisfy specific requirements. As a remarkable example, the quantum Hamiltonian describing a laser-driven trapped ion is studied in detail.Comment: 32 pages; modified version with examples of my previous paper quant-ph/0404056; to appear on the J. of Optics B: Quantum and Semiclassical Optics, Special Issue on 'Optics and Squeeze Transformations after Einstein

Coarse grained and fine dynamics in trapped ion Raman schemes

A novel result concerning Raman coupling schemes in the context of trapped ions is obtained. By means of an operator perturbative approach, it is shown that the complete time evolution of these systems (in the interaction picture) can be expressed, with a high degree of accuracy, as the product of two unitary evolutions. The first one describes the time evolution related to an effective coarse grained dynamics. The second is a suitable correction restoring the {\em fine} dynamics suppressed by the coarse graining performed to adiabatically eliminate the nonresonantly coupled atomic level.Comment: 12 pages, no figure

Spring 2009 water mass distribution, mixing and transport in the southern Adriatic after a low production of winter dense waters

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SU(1,1) symmetry of multimode squeezed states

We show that a class of multimode optical transformations that employ linear optics plus two-mode squeezing can be expressed as SU(1,1) operators. These operations are relevant to state-of-the-art continuous variable quantum information experiments including quantum state sharing, quantum teleportation, and multipartite entangled states. Using this SU(1,1) description of these transformations, we obtain a new basis for such transformations that lies in a useful representation of this group and lies outside the often-used restriction to Gaussian states. We analyze this basis, show its application to a class of transformations, and discuss its extension to more general quantum optical networks

An Algebraic Approach to Linear-Optical Schemes for Deterministic Quantum Computing

Linear-Optical Passive (LOP) devices and photon counters are sufficient to implement universal quantum computation with single photons, and particular schemes have already been proposed. In this paper we discuss the link between the algebraic structure of LOP transformations and quantum computing. We first show how to decompose the Fock space of N optical modes in finite-dimensional subspaces that are suitable for encoding strings of qubits and invariant under LOP transformations (these subspaces are related to the spaces of irreducible unitary representations of U(N)). Next we show how to design in algorithmic fashion LOP circuits which implement any quantum circuit deterministically. We also present some simple examples, such as the circuits implementing a CNOT gate and a Bell-State Generator/Analyzer.Comment: new version with minor modification

On the classical capacity of quantum Gaussian channels

The set of quantum Gaussian channels acting on one bosonic mode can be classified according to the action of the group of Gaussian unitaries. We look for bounds on the classical capacity for channels belonging to such a classification. Lower bounds can be efficiently calculated by restricting to Gaussian encodings, for which we provide analytical expressions.Comment: 10 pages, IOP style. v2: minor corrections, close to the published versio

Earth-Moon Lagrangian points as a testbed for general relativity and effective field theories of gravity

We first analyse the restricted four-body problem consisting of the Earth, the Moon and the Sun as the primaries and a spacecraft as the planetoid. This scheme allows us to take into account the solar perturbation in the description of the motion of a spacecraft in the vicinity of the stable Earth-Moon libration points L4 and L5 both in the classical regime and in the context of effective field theories of gravity. A vehicle initially placed at L4 or L5 will not remain near the respective points. In particular, in the classical case the vehicle moves on a trajectory about the libration points for at least 700 days before escaping away. We show that this is true also if the modified long-distance Newtonian potential of effective gravity is employed. We also evaluate the impulse required to cancel out the perturbing force due to the Sun in order to force the spacecraft to stay precisely at L4 or L5. It turns out that this value is slightly modified with respect to the corresponding Newtonian one. In the second part of the paper, we first evaluate the location of all Lagrangian points in the Earth-Moon system within the framework of general relativity. For the points L4 and L5, the corrections of coordinates are of order a few millimeters and describe a tiny departure from the equilateral triangle. After that, we set up a scheme where the theory which is quantum corrected has as its classical counterpart the Einstein theory, instead of the Newtonian one. In other words, we deal with a theory involving quantum corrections to Einstein gravity, rather than to Newtonian gravity. By virtue of the effective-gravity correction to the long-distance form of the potential among two point masses, all terms involving the ratio between the gravitational radius of the primary and its separation from the planetoid get modified. Within this framework, for the Lagrangian points of stable equilibrium, we find quantum corrections of order two millimeters, whereas for Lagrangian points of unstable equilibrium we find quantum corrections below a millimeter. In the latter case, for the point L1, general relativity corrects Newtonian theory by 7.61 meters, comparable, as an order of magnitude, with the lunar geodesic precession of about 3 meters per orbit. The latter is a cumulative effect accurately measured at the centimeter level through the lunar laser ranging positioning technique. Thus, it is possible to study a new laser ranging test of general relativity to measure the 7.61-meter correction to the L1 Lagrangian point, an observable never used before in the Sun-Earth-Moon system. Performing such an experiment requires controlling the propulsion to precisely reach L1, an instrumental accuracy comparable to the measurement of the lunar geodesic precession, understanding systematic effects resulting from thermal radiation and multi-body gravitational perturbations. This will then be the basis to consider a second-generation experiment to study deviations of effective field theories of gravity from general relativity in the Sun-Earth-Moon system

Combining Litter Observations with a Regional Ocean Model to Identify Sources and Sinks of Floating Debris in a Semi-enclosed Basin: The Adriatic Sea

Visual ship transect surveys provide crucial information about the density, and spatial distribution of floating anthropogenic litter in a basin. However, such observations provide a ‘snapshot’ of local conditions at a given time and cannot be used to deduce the provenance of the litter or to predict its fate, crucial information for management and mitigation policies. Particle tracking techniques have seen extensive use in these roles, however, most previous studies have used simplistic initial conditions based on bulk average inputs of debris to the system. Here, observations of floating anthropogenic macro debris in the Adriatic Sea are used to define initial conditions (number of particles, location, and time) in a Lagrangian particle tracking model. Particles are advected backward and forward in time for 60 days (120 days total) using surface velocities from an operational regional ocean model. Sources and sinks for debris observed in the central and southern Adriatic in May 2013 and March 2015 included the Italian coastline from Pescara to Brindisi, the Croatian island of Mljet, and the coastline from Dubrovnik through Montenegro to Albania. Debris observed in the northern Adriatic originated from the Istrian peninsula to the Italian city of Termoli, as well as the Croatian island of Cres and the Kornati archipelago. Particles spent a total of roughly 47 days afloat. Coastal currents, notably the eastern and western Adriatic currents, resulted in large alongshore displacements. Our results indicate that anthropogenic macro debris originates largely from coastal sources near population centers and is advected by the cyclonic surface circulation until it strands on the southwest (Italian) coast, exits the Adriatic, or recirculates in the southern gyreVersión del edito

Alternative commutation relations, star products and tomography

Invertible maps from operators of quantum obvservables onto functions of c-number arguments and their associative products are first assessed. Different types of maps like Weyl-Wigner-Stratonovich map and s-ordered quasidistribution are discussed. The recently introduced symplectic tomography map of observables (tomograms) related to the Heisenberg-Weyl group is shown to belong to the standard framework of the maps from quantum observables onto the c-number functions. The star-product for symbols of the quantum-observable for each one of the maps (including the tomographic map) and explicit relations among different star-products are obtained. Deformations of the Moyal star-product and alternative commutation relations are also considered.Comment: LATEX plus two style files, to appear in J. Phys.

Detection of minimal residual disease identifies differences in treatment response between T-ALL and precursor B-ALL

We performed sensitive polymerase chain reaction-based minimal residual disease (MRD) analyses on bone marrow samples at 9 follow-up time points in 71 children with T-lineage acute lymphoblastic leukemia (T-ALL) and compared the results with the precursor B-lineage ALL (B-ALL) results (n = 210) of our previous study. At the first 5 follow-up time points, the frequency of MRD-positive patients and the MRD levels were higher in T-ALL than in precursor-B-ALL, reflecting the more frequent occurrence of resistant disease in T-ALL. Subsequently, patients were classified according to their MRD level at time point 1 (TP1), taken at the end of induction treatment (5 weeks), and at TP2 just before the start of consolidation treatment (3 months). Patients were considered at low risk if TP1 and TP2 were MRD negative and at high risk if MRD levels at TP1 and TP2 were 10(-3) or higher; remaining patients were considered at intermediate risk. The relative distribution of patients with T-ALL (n = 43) over the MRD-based risk groups differed significantly from that of precursor B-ALL (n = 109). Twenty-three percent of patients with T-ALL and 46% of patients with precursor B-ALL were classified in the low-risk group (P =.01) and had a 5-year relapse-free survival (RFS) rate of 98% or greater. In contrast, 28% of patients with T-ALL were classified in the MRD-based high-risk group compared to only 11% of patients with precursor B-ALL (P =.02), and the RFS rates were 0% and 25%, respectively (P =.03). Not only was the distribution of patients with T-ALL different over the MRD-based risk groups, the prognostic value of MRD levels at TP1 and TP2 was higher in T-ALL (larger RFS gradient), and consistently higher RFS rates were found for MRD-negative T-ALL patients at the first 5 follow-up time points