Spontaneous Fluxoid Formation in Superconducting Loops

We report on the first experimental verification of the Zurek-Kibble scenario in an isolated superconducting ring over a wide parameter range. The probability of creating a single flux quantum spontaneously during the fast normal-superconducting phase transition of a wide Nb loop clearly follows an allometric dependence on the quenching time $\tau_{Q}$, as one would expect if the transition took place as fast as causality permits. However, the observed Zurek-Kibble scaling exponent $\sigma = 0.62\pm0.15$ is two times larger than anticipated for large loops. Assuming Gaussian winding number densities we show that this doubling is well-founded for small annuli.Comment: 10 pages, 2 figures, submitted to Phys. Rev. Lett

Quantum rotor description of the Mott-insulator transition in the Bose-Hubbard model

We present the novel approach to the Bose-Hubbard model using the $\mathrm{U}(1)$ quantum rotor description. The effective action formalism allows us to formulate a problem in the phase only action and obtain an analytical formulas for the critical lines. We show that the nontrivial $\mathrm{U}(1)$ phase field configurations have an impact on the phase diagrams. The topological character of the quantum field is governed by terms of the integer charges - winding numbers. The comparison presented results to recently obtained quantum Monte Carlo numerical calculations suggests that the competition between quantum effects in strongly interacting boson systems is correctly captured by our model.Comment: accepted to PR

Zurek-Kibble Mechanism for the Spontaneous Vortex Formation in Nb−Al/Alox/NbNb-Al/Al_{ox}/Nb Josephson Tunnel Junctions: New Theory and Experiment

New scaling behavior has been both predicted and observed in the spontaneous production of fluxons in quenched $Nb-Al/Al_{ox}/Nb$ annular Josephson tunnel junctions as a function of the quench time, $\tau_{Q}$. The probability $f_{1}$ to trap a single defect during the N-S phase transition clearly follows an allometric dependence on $\tau_{Q}$ with a scaling exponent $\sigma = 0.5$, as predicted from the Zurek-Kibble mechanism for {\it realistic} JTJs formed by strongly coupled superconductors. This definitive experiment replaces one reported by us earlier, in which an idealised model was used that predicted $\sigma = 0.25$, commensurate with the then much poorer data. Our experiment remains the only condensed matter experiment to date to have measured a scaling exponent with any reliability.Comment: Four pages, one figur

Spontaneous Fluxon Production in Annular Josephson Tunnel Junctions in the Presence of a Magnetic Field

We report on the spontaneous production of fluxons in the presence of a symmetry-breaking magnetic field for annular Josephson tunnel junctions during a thermal quench. The dependence on field intensity $B$ of the probability $\bar{f_1}$ to trap a single defect during the N-S phase transition drastically depends on the sample circumferences. We show that the data can be understood in the framework of the Kibble-Zurek picture of spontaneous defect formation controlled by causal bounds.Comment: Submitted to Phys. Rev. B with 5 figures on Nov. 15, 200

New Experiments for Spontaneous Vortex Formation in Josephson Tunnel Junctions

It has been argued by Zurek and Kibble that the likelihood of producing defects in a continuous phase transition depends in a characteristic way on the quench rate. In this paper we discuss an improved experiment for measuring the Zurek-Kibble scaling exponent $\sigma$ for the production of fluxons in annular symmetric Josephson Tunnel Junctions. We find $\sigma \simeq 0.5$. Further, we report accurate measurements of the junction gap voltage temperature dependence which allow for precise monitoring of the fast temperature variations during the quench.Comment: 12 pages, 5 figures, submitted to Phys. Rev.

Extremely Correlated Quantum Liquids

We formulate the theory of an extremely correlated electron liquid, generalizing the standard Fermi liquid. This quantum liquid has specific signatures in various physical properties, such as the Fermi surface volume and the narrowing of electronic bands by spin and density correlation functions. We use Schwinger's source field idea to generate equations for the Greens function for the Hubbard operators. A local (matrix) scale transformation in the time domain to a quasiparticle Greens function, is found to be optimal. This transformation allows us to generate vertex functions that are guaranteed to reduce to the bare values for high frequencies, i.e. are ``asymptotically free''. The quasiparticles are fractionally charged objects, and we find an exact Schwinger Dyson equation for their Greens function. We find a hierarchy of equations for the vertex functions, and further we obtain Ward identities so that systematic approximations are feasible. An expansion in terms of the density of holes measured from the Mott Hubbard insulating state follows from the nature of the theory. A systematic presentation of the formalism is followed by some preliminary explicit calculations.Comment: 40 pages, typos remove

Testing the Kibble-Zurek Scenario with Annular Josephson Tunnel Junctions

In parallel with Kibble's description of the onset of phase transitions in the early universe, Zurek has provided a simple picture for the onset of phase transitions in condensed matter systems, strongly supported by agreement with experiments in He3. In this letter we show how experiments with annular Josephson tunnel Junctions can and do provide further support for this scenario.Comment: Revised version with correct formula for the Swihart velocity. The results are qualitatively the same as with the previous version but differ quantitatively. 4 pages, RevTe

Zurek-Kibble domain structures: The Dynamics of Spontaneous Vortex formation in Annular Josephson Tunnel Junctions

Phase transitions executed in a finite time show a domain structure with defects, that has been argued by Zurek and Kibble to depend in a characteristic way on the quench rate. In this letter we present an experiment to measure the Zurek-Kibble scaling exponent sigma. Using symmetric and long Josephson Tunnel Junctions, for which the predicted index is sigma = 0.25, we find sigma = 0.27 +/- 0.05. Further, there is agreement with the ZK prediction for the overall normalisation.Comment: To be published in Phys. Rev. Lett

Suppression of Bremsstrahlung at Non-Zero Temperature

The first-order bremsstrahlung emission spectrum is $\alpha d\omega/\omega$ at zero temperature. If the radiation is emitted into a region that contains a thermal distribution of photons, then the rate is increased by a factor $1+N(\omega)$ where $N(\omega)$ is the Bose-Einstein function. The stimulated emission changes the spectrum to $\alpha Td\omega/\omega^{2}$ for $\omega\ll T$. If this were correct, an infinite amount of energy would be radiated in the low frequency modes. This unphysical result indicates a breakdown of perturbation theory. The paper computes the bremsstrahlung rate to all orders of perturbation theory, neglecting the recoil of the charged particle. When the perturbation series is summed, it has a different low-energy behavior. For $\omega\ll\alpha T$, the spectrum is independent of $\omega$ and has a value proportional to $d\omega/\alpha T$ .Comment: 16 pages (plain TeX), figures available on reques

Slow 4He^{4}He Quenches Produce Fuzzy, Transient Vortices

We examine the Zurek scenario for the production of vortices in quenches of liquid $^{4}He$ in the light of recent experiments. Extending our previous results to later times, we argue that short wavelength thermal fluctuations make vortices poorly defined until after the transition has occurred. Further, if and when vortices appear, it is plausible that that they will decay faster than anticipated from turbulence experiments, irrespective of quench rates.Comment: 4 pages, Revtex file, no figures Apart from a more appropriate title, this paper differs from its predecessor by including temperature, as well as pressure, quenche