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arXiv:cond-mat/0503655

Using Annular Josephson Tunnel Junctions to Monitor Causal Horizon

R. Monaco, R. J. Rivers

Published Mar 29, 2005• 0 citations
arXivHTMLPDF

Abstract

If systems change as fast as possible as they pass through a phase transition then the initial domain structure is constrained by causality. We shall show how we can trace these causal horizons by measuring the spontaneous production of flux in annular Josephson Tunnel Junctions as a function of the quench time $τ_{Q}$ into the superconducting phase. A specific test of our analysis is that the probability P$_{1}$ to trap a single fluxon at the N-S transition clearly follows an allometric dependence on $τ_{Q}$ as $P_1 = a τ_Q^{-σ}$, with a scaling exponent $σ= 0.25$, in agreement with the data.

DOI
10.48550/arxiv.cond-mat/0503655

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If systems change as fast as possible as they pass through a phase transition then the initial domain structure is constrained by causality. We shall show how we can trace these causal horizons by measuring the spontaneous production of flux in annular Josephson Tunnel Junctions as a function of the quench time τQτ_{Q}τQ​ into the superconducting phase. A specific test of our analysis is that the probability P1_{1}1​ to trap a single fluxon at the N-S transition clearly follows an allometric dependence on τQτ_{Q}τQ​ as P1=aτQ−σP_1 = a τ_Q^{-σ}P1​=aτQ−σ​, with a scaling exponent σ=0.25σ= 0.25σ=0.25, in agreement with the data.
In order to mimic the phase changes in the primordial Big Bang, several cosmological solid-state experiments have been conceived, during the last decade, to investigate the spontaneous symmetry breaking in superconductors and superfluids cooled through their transition temperature. In one of such experiments, the number of magnetic flux quanta spontaneously trapped in a superconducting loop was measured by means of a long Josephson tunnel junction built on top of the loop itself. We have analyzed this system and found a number of interesting features not occurring in the conventional case with simply connected electrodes. In particular, the fluxoid quantization results in a frustration of the Josephson phase, which, in turn, reduces the junction critical current. Further, the possible stable states of the system are obtained by a self-consistent application of the principle of minimum energy. The theoretical findings are supported by measurements on a number of samples having different geometrical configuration. The experiments demonstrate that a very large signal-to-noise ratio can be achieved in the flux quanta detection.
Long Josephson tunnel junctions are non-linear transmission lines that allow propagation of current vortices (fluxons) and electromagnetic waves and are used in various applications within superconductive electronics. Recently, the Josephson vortex has been proposed as a new superconducting qubit. We describe a simple method to create a double-well potential for an individual fluxon trapped in a long elliptic annular Josephson tunnel junction characterized by an intrinsic non-uniform width. The distance between the potential wells and the height of the inter-well potential barrier are controlled by the strength of an in-plane magnetic field. The manipulation of the vortex states can be achieved by applying a proper current ramp across the junction. The read-out of the state is accomplished by measuring the vortex depinning current in a small magnetic field. An accurate one-dimensional sine-Gordon model for this strongly non-linear system is presented, from which we calculate the position-dependent fluxon rest-mass, its Hamiltonian density and the corresponding trajectories in the phase space. We examine the dependence of the potential properties on the annulus eccentricity and its electrical parameters and address the requirements for observing quantum-mechanical effects, as discrete energy levels and tunneling, in this two-state system.
Experiments towards realizing a readout of superconducting qubits by using ballistic Josephson vortices are reported. We measured the microwave radiation induced by a fluxon moving in an annular Josephson junction. By coupling a flux qubit as a current dipole to the annular junction, we detect periodic variations of the fluxon's oscillation frequency versus magnetic flux through the qubit. We found that the scattering of a fluxon on a current dipole can lead to the acceleration of a fluxon regardless of a dipole polarity. We use the perturbation theory and numerical simulations of the perturbed sine-Gordon equation to analyze our results.
Quantum mechanics constrains conjugate observables from being simultaneously measurable with arbitrary precision. In a Josephson junction, these are the transferred electric charge and the quantum-mechanical phase difference between the superconducting domains. Which of them fluctuates determines the supercurrent: a dissipative trickle of single Cooper pairs in one limit, a coherent dissipationless flow in the other. Bridging both regimes in one device remained elusive because the Josephson and charging energies are fixed at fabrication. Here, we use the tunable tunnel junction of a scanning tunneling microscope at millikelvin temperature to vary their ratio continuously over many orders of magnitude. In this way, we monitor the smooth transition between incoherent and coherent Cooper pair flow in a single junction, revealing the quantum-to-classical transition in a controlled way.
High-resolution (sub-microsecond to nanosecond) time-resolved measurements of the dynamics of superconducting electronic devices, such as Josephson tunnel junctions and SQUIDs, are indispensable for fundamental physics research, such as quantum mechanics of macroscopic variables. We describe the development of a time-resolved measurement technique that enables direct measurements, in the time domain, of the temporal evolution of Josephson junctions with a nanosecond resolution. The technique was applied to study escape dynamics of Josephson junctions, as macroscopic quantum systems, in the quantum tunnelling regime. The measured probability of junctions remaining in the initial metastable state—the survival probability—as a function of time decayed exponentially, agrees very well with the theoretical prediction of the incoherent tunnelling process.
An experiment demonstrating a link between classical single-flux quantum digital logic and a superconducting quantum circuit is reported. We implement coupling between a moving Josephson vortex (fluxon) and a flux qubit by reading out of a state of the flux qubit through a frequency shift of the fluxon oscillations in an annular Josephson junction. The energy spectrum of the flux qubit is measured using this technique. The implemented hybrid scheme opens an opportunity to readout quantum states of superconducting qubits with the classical fluxon logic circuits.