Frustration of decoherence in YY-shaped superconducting Josephson networks

We examine the possibility that pertinent impurities in a condensed matter system may help in designing quantum devices with enhanced coherent behaviors. For this purpose, we analyze a field theory model describing Y- shaped superconducting Josephson networks. We show that a new finite coupling stable infrared fixed point emerges in its phase diagram; we then explicitly evidence that, when engineered to operate near by this new fixed point, Y-shaped networks support two-level quantum systems, for which the entanglement with the environment is frustrated. We briefly address the potential relevance of this result for engineering finite-size superconducting devices with enhanced quantum coherence. Our approach uses boundary conformal field theory since it naturally allows for a field-theoretical treatment of the phase slips (instantons), describing the quantum tunneling between degenerate levels.Comment: 11 pages, 5 .eps figures; several changes in the presentation and in the figures, upgraded reference

Finite-Temperature Renormalization Group Analysis of Interaction Effects in 2D Lattices of Bose-Einstein Condensates

By using a renormalization group analysis, we study the effect of interparticle interactions on the critical temperature at which the Berezinskii-Kosterlitz-Thouless (BKT) transition occurs for Bose-Einstein condensates loaded at finite temperature in a 2D optical lattice. We find that the critical temperature decreases as the interaction energy decreases; when U/J=36/\pi one has a vanishing critical temperature, signaling the possibility of a quantum phase transition of BKT type

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

Inhomogeneous Superconductivity in Comb-Shaped Josephson Junction Networks

We show that some of the Josephson couplings of junctions arranged to form an inhomogeneous network undergo a non-perturbative renormalization provided that the network's connectivity is pertinently chosen. As a result, the zero-voltage Josephson critical currents $I_c$ turn out to be enhanced along directions selected by the network's topology. This renormalization effect is possible only on graphs whose adjacency matrix admits an hidden spectrum (i.e. a set of localized states disappearing in the thermodynamic limit). We provide a theoretical and experimental study of this effect by comparing the superconducting behavior of a comb-shaped Josephson junction network and a linear chain made with the same junctions: we show that the Josephson critical currents of the junctions located on the comb's backbone are bigger than the ones of the junctions located on the chain. Our theoretical analysis, based on a discrete version of the Bogoliubov-de Gennes equation, leads to results which are in good quantitative agreement with experimental results.Comment: 4 pages, 2 figures, revte

Chiral Symmetry Breaking on the Lattice: a Study of the Strongly Coupled Lattice Schwinger Model

We revisit the strong coupling limit of the Schwinger model on the lattice using staggered fermions and the hamiltonian approach to lattice gauge theories. Although staggered fermions have no continuous chiral symmetry, they posses a discrete axial invari ance which forbids fermion mass and which must be broken in order for the lattice Schwinger model to exhibit the features of the spectrum of the continuum theory. We show that this discrete symmetry is indeed broken spontaneously in the strong coupling li mit. Expanding around a gauge invariant ground state and carefully considering the normal ordering of the charge operator, we derive an improved strong coupling expansion and compute the masses of the low lying bosonic excitations as well as the chiral co ndensate of the model. We find very good agreement between our lattice calculations and known continuum values for these quantities already in the fourth order of strong coupling perturbation theory. We also find the exact ground state of the antiferromag netic Ising spin chain with long range Coulomb interaction, which determines the nature of the ground state in the strong coupling limit.Comment: 24 pages, Latex, no figure

Confinement-Deconfinement Transition in 3-Dimensional QED

We argue that, at finite temperature, parity invariant non-compact electrodynamics with massive electrons in 2+1 dimensions can exist in both confined and deconfined phases. We show that an order parameter for the confinement-deconfinement phase transition is the Polyakov loop operator whose average measures the free energy of a test charge that is not an integral multiple of the electron charge. The effective field theory for the Polyakov loop operator is a 2-dimensional Euclidean scalar field theory with a global discrete symmetry $Z$, the additive group of the integers. We argue that the realization of this symmetry governs confinement and that the confinement-deconfinement phase transition is of Berezinskii-Kosterlitz-Thouless type. We compute the effective action to one-loop order and argue that when the electron mass $m$ is much greater than the temperature $T$ and dimensional coupling $e^2$, the effective field theory is the Sine-Gordon model. In this limit, we estimate the critical temperature, $T_{\rm crit.}=e^2/8\pi(1-e^2/12\pi m+\ldots)$.Comment: 11 pages, latex, no figure

Mean Field Theory of Josephson Junction Arrays with Charge Frustration

Using the path integral approach, we provide an explicit derivation of the equation for the phase boundary for quantum Josephson junction arrays with offset charges and non-diagonal capacitance matrix. For the model with nearest neighbor capacitance matrix and uniform offset charge $q/2e=1/2$, we determine, in the low critical temperature expansion, the most relevant contributions to the equation for the phase boundary. We explicitly construct the charge distributions on the lattice corresponding to the lowest energies. We find a reentrant behavior even with a short ranged interaction. A merit of the path integral approach is that it allows to provide an elegant derivation of the Ginzburg-Landau free energy for a general model with charge frustration and non-diagonal capacitance matrix. The partition function factorizes as a product of a topological term, depending only on a set of integers, and a non-topological one, which is explicitly evaluated.Comment: LaTex, 24 pages, 8 figure

Topological Excitations in Compact Maxwell-Chern-Simons Theory

We construct a lattice model of compact (2+1)-dimensional Maxwell-Chern- Simons theory, starting from its formulation in terms of gauge invariant quantities proposed by Deser and Jackiw. We thereby identify the topological excitations and their interactions. These consist of monopolo- antimonopole pairs bounded by strings carrying both magnetic flux and electric charge. The electric charge renders the Dirac strings observable and endows them with a finite energy per unit length, which results in a linearly confining string tension. Additionally, the strings interact via an imaginary, topological term measuring the (self-) linking number of closed strings.Comment: harvmac, CERN-TH. 6906/93, DFUPG 80/9

The Strongly Coupled 't Hooft Model on the Lattice

We study the strong coupling limit of the one-flavor and two-flavor massless 't Hooft models, $large-{\cal N}_c$-color $QCD_2$, on a lattice. We use staggered fermions and the Hamiltonian approach to lattice gauge theories. We show that the one-flavor model is effectively described by the antiferromagnetic Ising model, whose ground state is the vacuum of the gauge model in the infinite coupling limit; expanding around this ground state we derive a strong coupling expansion and compute the lowest lying hadron masses as well as the chiral condensate of the gauge theory. Our lattice computation well reproduces the results of the continuum theory. Baryons are massless in the infinite coupling limit; they acquire a mass already at the second order in the strong coupling expansion in agreement with the Witten argument that baryons are the $QCD$ solitons. The spectrum and chiral condensate of the two-flavor model are effectively described in terms of observables of the quantum antiferromagnetic Heisenberg model. We explicitly write the lowest lying hadron masses and chiral condensate in terms of spin-spin correlators on the ground state of the spin model. We show that the planar limit (${\cal N}_c\longrightarrow \infty$) of the gauge model corresponds to the large spin limit ($S\longrightarrow \infty$) of the antiferromagnet and compute the hadron mass spectrum in this limit finding that, also in this model, the pattern of chiral symmetry breaking of the continuum theory is well reproduced on the lattice.Comment: LaTex, 25 pages, no figure