Low temperature decoherence and relaxation in charge Josephson-junction qubits

In this lectures, we have described some essential features of loss of coherence by a qubit coupled to the environment. We have first presented well known semiclassical arguments that relate both decoherence and relaxation to the environmental noise. Then we have shown that models with pure decoherence (but no relaxation in qubit states) can be exactly solvable. As an example, we have treated in detail the model of fluctuating background charges which is believed to describe one of the most important channels for decoherence for the charge Josephson junction qubit. We have shown that the decoherence rate saturates at `high' temperatures while becoming linear in T at low temperatures and showing in all regimes a non-monotonic behaviour as a function of the coupling of the qubit to the fluctuating background charges. We have also considered, albeit only perturbatively, the qubit relaxation by the background charges and demonstrated that a quasi-linear behaviour of the spectral density of noise deduced from the measurements of the relaxation rate can be qualitatively explained.Comment: Lecture notes for International workshop on mesoscopic and nanoscopic systems, Kolkata, India, February 2006, to be published by Springe

Low-Temperature Decoherence of Qubit Coupled to Background Charges

We have found an exact expression for the decoherence rate of a Josephson charge qubit coupled to fluctuating background charges. At low temperatures $T$ the decoherence rate ${\Gamma}$ is linear in $T$ while at high temperatures it saturates in agreement with a known classical solution which, however, reached at surprisingly high $T$. In contrast to the classical picture, impurity states spread in a wide interval of energies ($\gg T$) may essentially contribute to ${\Gamma}$.Comment: Both figures are changed to illustrate a more generic case of impurity states spread in wide interval of energies. Some changes have been made to the abstract and the introductio

Local impurity in a multichannel Luttinger liquid

We investigate the stability of conducting and insulating phases in multichannel Luttinger liquids with respect to embedding a single impurity. We devise a general approach for finding critical exponents of the conductance in the limits of both weak and strong scattering. In contrast to the one-channel Luttinger liquid, the system state in certain parametric regions depends on the scattering strength which results in the emergence of a bistability. Focusing on the two-channel liquid, the method developed here enables us to provide a generic analysis of phase boundaries governed by the most relevant (i.e., not necessarily single-particle) scattering mechanism. The present approach is applicable to channels of different nature as in fermion-boson mixtures, or to identical ones as on the opposite edges of a topological insulator. We show that interaction per se cannot provide protection in the particular case of topological insulators realized in narrow Hall bars

Berezinskii - Kosteriltz - Thouless transition in disordered multichannel Luttinger liquids.

We study the phase transition between conducting and insulating states taking place in disordered multichannel Luttinger liquids with interchannel interactions. We derive renormalization-group equations which are perturbative in disorder but nonperturbative in interaction. In the vicinity of the simultaneous phase transition in all channels, these equations become a set of coupled Berezinskii-Kosterlitz-Thouless equations, which we analyze within two models: an array of identical wires and a two-channel model with distinct channels. We show that a competition between disorder and interaction results in a variety of phases, expected to be observable at intermediate temperatures where the interaction and disorder are relevant but weak hybridization and the charge-density-wave interaction may be ignored

Coulomb staircase in an asymmetrically coupled quantum dot

We investigate the Coulomb blockade in quantum dots asymmetrically coupled to the leads for an arbitrary voltage bias focusing on the regime where electrons do not thermalise during their dwell time in the dot. By solving the quantum kinetic equation, we show that the current-voltage characteristics are crucially dependent on the ratio of the Fermi energy to charging energy on the dot. In the standard regime when the Fermi energy is large, there is a Coulomb staircase which is practically the same as in the thermalised regime. In the opposite case of the large charging energy, we identify a new regime in which only one step is left in the staircase, and we anticipate experimental confirmation of this finding.Comment: 12 pages, 2 figure

Loss Fluctuations and Temporal Correlations in Network Queues

We consider data losses in a single node of a packet-switched Internet-like network. We employ two distinct models, one with discrete and the other with continuous one-dimensional random walks, representing the state of a queue in a router. Both models {have} a built-in critical behavior with {a sharp} transition from exponentially small to finite losses. It turns out that the finite capacity of a buffer and the packet-dropping procedure give rise to specific boundary conditions which lead to strong loss rate fluctuations at the critical point even in the absence of such fluctuations in the data arrival process.Comment: 6 pages, 2 figures; an invited talk at the 1st Workshop on Physics-Inspired Paradigms in Wireless Communications and Networks, April 4th, 2008, Berlin, German

Metal-insulator transition in a sliding Luttinger liquid with line defects

We investigate the effect of both strong and weak potential scattering caused by local impurities and extended (line) defects in an array of Luttinger liquid wires. We find that in both cases a finite range interwire interaction stabilizes the metallic state. Based on calculations of the scaling dimensions of one-particle scattering operators, we construct a phase diagram for low-temperature transport along the array.We find that unlike the local impurity case where only conducting and insulating states are realized (metal-insulator transition driven by interactions), the extended line defects may bring the system into a mixed state where conducting or insulating behavior can be observed depending on bare strength of the scatterer (metal-insulator transition driven by disorder)