Eigenvalues of the time-delay matrix in overlapping resonances

We discuss the properties of the lifetime or the time-delay matrix Q(E) for multichannel scattering, which is related to the scattering matrix S(E) by Q = i?S(dS†/dE). For two overlapping resonances occurring at energies E with widths G(? = 1, 2), with an energy-independent background, only two eigenvalues of Q(E) are proved to be different from zero and to show typical avoided-crossing behaviour. These eigenvalues are expressible in terms of the four resonance parameters (E , G) and a parameter representing the strength of the interaction of the resonances. An example of the strong and weak interaction in an overlapping double resonance is presented for the positronium negative ion. When more than two resonances overlap (? = 1, ..., N), no simple representation of each eigenvalue has been found. However, the formula for the trace of the Q-matrix leads to the expression d(E) = -?arctan[(G/2)/(E - E)] + d(E) for the eigenphase sum d(E) and the background eigenphase sum d(E), in agreement with the known form of the state density. The formulae presented in this paper are useful in a parameter fitting of overlapping resonances. © 2006 IOP Publishing Ltd.

Information theoretic measures of UHG graphs with low computational complexity

We introduce a novel graph class we call universal hierarchical graphs (UHG) whose topology can be found numerously in problems representing, e.g., temporal, spacial or general process structures of systems. For this graph class we show, that we can naturally assign two probability distributions, for nodes and for edges, which lead us directly to the definition of the entropy and joint entropy and, hence, mutual information establishing an information theory for this graph class. Furthermore, we provide some results under which conditions these constraint probability distributions maximize the corresponding entropy. Also, we demonstrate that these entropic measures can be computed efficiently which is a prerequisite for every large scale practical application and show some numerical examples. (c) 2007 Elsevier Inc. All rights reserved.

Entanglement detection in hybrid optomechanical systems

We study a device formed by a Bose-Einstein condensate (BEC) coupled to the field of a cavity with a moving end mirror and find a working point such that the mirror-light entanglement is reproduced by the BEC-light quantum correlations. This provides an experimentally viable tool for inferring mirror-light entanglement with only a limited set of assumptions. We prove the existence of tripartite entanglement in the hybrid device, persisting up to temperatures of a few milli-Kelvin, and discuss a scheme to detect it.

Probing magnetic order in ultracold lattice gases

A forthcoming challenge in ultracold lattice gases is the simulation of quantum magnetism. That involves both the preparation of the lattice atomic gas in the desired spin state and the probing of the state. Here we demonstrate how a probing scheme based on atom-light interfaces gives access to the order parameters of nontrivial quantum magnetic phases, allowing us to characterize univocally strongly correlated magnetic systems produced in ultracold gases. This method, which is also nondemolishing, yields spatially resolved spin correlations and can be applied to bosons or fermions. As a proof of principle, we apply this method to detect the complete phase diagram displayed by a chain of (rotationally invariant) spin-1 bosons.

Spontaneous nucleation of structural defects in inhomogeneous ion chains

Structural defects in ion crystals can be formed during a linear quench of the transverse trapping frequency across the mechanical instability from a linear chain to a zigzag structure. The density of defects after the sweep can be conveniently described by the Kibble-Zurek mechanism (KZM). In particular, the number of kinks in the zigzag ordering can be derived from a time-dependent Ginzburg-Landau equation for the order parameter, here the zigzag transverse size, under the assumption that the ions are continuously laser cooled. In a linear Paul trap, the transition becomes inhomogeneous, since the charge density is larger in the center and more rarefied at the edges. During the linear quench, the mechanical instability is first crossed in the center of the chain, and a front, at which the mechanical instability is crossed during the quench, is identified that propagates along the chain from the center to the edges. If the velocity of this front is smaller than the sound velocity, the dynamics become adiabatic even in the thermodynamic limit and no defect is produced. Otherwise, the nucleation of kinks is reduced with respect to the case in which the charges are homogeneously distributed, leading to a new scaling of the density of kinks with the quenching rate. The analytical predictions are verified numerically by integrating the Langevin equations of motion of the ions, in the presence of a time-dependent transverse confinement. We argue that the non-equilibrium dynamics of an ion chain in a Paul trap constitutes an ideal scenario to test the inhomogeneous extension of the KZM, which lacks experimental evidence to date.

Structural Defects in Ion Chains by Quenching the External Potential: The Inhomogeneous Kibble-Zurek Mechanism

The nonequilibrium dynamics of an ion chain in a highly anisotropic trap is studied when the transverse trap frequency is quenched across the value at which the chain undergoes a continuous phase transition from a linear to a zigzag structure. Within Landau theory, an equation for the order parameter, corresponding to the transverse size of the zigzag structure, is determined when the vibrational motion is damped via laser cooling. The number of structural defects produced during a linear quench of the transverse trapping frequency is predicted and verified numerically. It is shown to obey the scaling predicted by the Kibble-Zurek mechanism, when extended to take into account the spatial inhomogeneities of the ion chain in a linear Paul trap.

Quantum ground state of self-organized atomic crystals in optical resonators

Cold atoms, driven by a laser and simultaneously coupled to the quantum field of an optical resonator, may self-organize in periodic structures. These structures are supported by the optical lattice, which emerges from the laser light they scatter into the cavity mode and form when the laser intensity exceeds a threshold value. We study theoretically the quantum ground state of these structures above the pump threshold of self-organization by mapping the atomic dynamics of the self-organized crystal to a Bose-Hubbard model. We find that the quantum ground state of the self-organized structure can be the one of a Mott insulator, depending on the pump strength of the driving laser. For very large pump strengths, where the intracavity-field intensity is maximum and one would expect a Mott-insulator state, we find intervals of parameters where the phase is compressible. These states could be realized in existing experimental setups.

Collective decoherence of cold atoms coupled to a Bose-Einstein condensate

We examine the time evolution of cold atoms (impurities) interacting with an environment consisting of a degenerate bosonic quantum gas. The impurity atoms differ from the environment atoms, being of a different species. This allows one to superimpose two independent trapping potentials, each being effective only on one atomic kind, while transparent to the other. When the environment is homogeneous and the impurities are confined in a potential consisting of a set of double wells, the system can be described in terms of an effective spin-boson model, where the occupation of the left or right well of each site represents the two (pseudo)-spin states. The irreversible dynamics of such system is here studied exactly, i.e. not in terms of a Markovian master equation. The dynamics of one and two impurities is remarkably different in respect of the standard decoherence of the spin-boson system. In particular, we show: (i) the appearance of coherence oscillations, (ii) the presence of super and subdecoherent states that differ from the standard ones of the spin-boson model, and (iii) the persistence of coherence in the system at long times. We show that this behaviour is due to the fact that the pseudospins have an internal spatial structure. We argue that collective decoherence also prompts information about the correlation length of the environment. In a one-dimensional (1D) configuration, one can change even more strongly the qualitative behaviour of the dephasing just by tuning the interaction of the bath.

Thermal and quantum fluctuations in chains of ultracold polar molecules

Ultracold polar molecules, in highly anisotropic traps and interacting via a repulsive dipolar potential, may form one-dimensional chains at high densities. According to classical theory, at low temperatures there exists a critical value of the density at which a second-order phase transition from a linear to a zigzag chain occurs. We study the effect of thermal and quantum fluctuations on these self-organized structures using classical and quantum Monte Carlo methods, by means of which we evaluate the pair correlation function and the static structure factor. Depending on the parameters, these functions exhibit properties typical of a crystalline or of a liquid system. We compare the thermal and the quantum results, identifying analogies and differences. Finally, we discuss experimental parameter regimes where the effects of quantum fluctuations on the linear-zigzag transition can be observed.

Ground state of low-dimensional dipolar gases: Linear and zigzag chains

We study the ground-state phase diagram of ultracold dipolar gases in highly anisotropic traps. Starting from a one-dimensional geometry, by ramping down the transverse confinement along one direction, the gas reaches various planar distributions of dipoles. At large linear densities, when the dipolar gas exhibits a crystal-like phase, critical values of the transverse frequency exist below which the configuration exhibits transverse patterns. These critical values are found by means of a classical theory, and are in full agreement with classical Monte Carlo simulations. The study of the quantum system is performed numerically with Monte Carlo techniques and shows that the quantum fluctuations smoothen the transition and make it completely disappear in a gas phase. These predictions could be experimentally tested and would allow one to reveal the effect of zero-point motion on self-organized mesoscopic structures of matter waves, such as the transverse pattern of the zigzag chain.

Density Matrix Renormalization Group for Dummies

We describe the Density Matrix Renormalization Group algorithms for time dependent and time independent Hamiltonians. This paper is a brief but comprehensive introduction to the subject for anyone willing to enter in the field or write the program source code from scratch. An open source version of the code can be found at: http://www.dmrg.it.

A geometric analysis of the effects of noise on Berry phase

In this work we describe the effect of classical and quantum noise on the Berry phase. It is not a topical review article but rather an overview of our work in this field aiming at giving a simple pictorial intuition of our results.