Models of environment and T_1 relaxation in Josephson Charge Qubits

A theoretical interpretation of the recent experiments of Astafiev et. al. on the T_1-relaxation rate in Josephson Charge Qubits is proposed. The experimentally observed reproducible nonmonotonic dependence of T_1 on the splitting E_J of the qubit levels suggests further specification of the previously proposed models of the background charge noise. From our point of view the most promising is the ``Andreev fluctuator'' model of the noise. In this model the fluctuator is a Cooper pair that tunnels from a superconductor and occupies a pair of localized electronic states. Within this model one can naturally explain both the average linear T_1(E_J) dependence and the irregular fluctuations. The role of fluctuators in the formation of strong resonant peaks in this dependence is also discussed.Comment: 4 pages, 3 figure

Analysis of high quality superconducting resonators: consequences for TLS properties in amorphous oxides

$1/f$ noise caused by microscopic Two-Level Systems (TLS) is known to be very detrimental to the performance of superconducting quantum devices but the nature of these TLS is still poorly understood. Recent experiments with superconducting resonators indicates that interaction between TLS in the oxide at the film-substrate interface is not negligible. Here we present data on the loss and $1/f$ frequency noise from two different Nb resonators with and without Pt capping and discuss what conclusions can be drawn regarding the properties of TLS in amorphous oxides. We also estimate the concentration and dipole moment of the TLS.Comment: 8 pages, 5 figure

Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves

We extend the Keldysh technique to enable the computation of out-of-time order correlators. We show that the behavior of these correlators is described by equations that display initially an exponential instability which is followed by a linear propagation of the decoherence between two initially identically copies of the quantum many body systems with interactions. At large times the decoherence propagation (quantum butterfly effect) is described by a diffusion equation with non-linear dissipation known in the theory of combustion waves. The solution of this equation is a propagating non-linear wave moving with constant velocity despite the diffusive character of the underlying dynamics. Our general conclusions are illustrated by the detailed computations for the specific models describing the electrons interacting with bosonic degrees of freedom (phonons, two-level-systems etc.) or with each other

Magnetism in SQUIDs at Millikelvin Temperatures

We have characterized the temperature dependence of the flux threading dc SQUIDs cooled to millikelvin temperatures. The flux increases as 1/T as temperature is lowered; moreover, the flux change is proportional to the density of trapped vortices. The data is compatible with the thermal polarization of surface spins in the trapped fields of the vortices. In the absence of trapped flux, we observe evidence of spin-glass freezing at low temperature. These results suggest an explanation for the "universal" 1/f flux noise in SQUIDs and superconducting qubits.Comment: 4 pages, 4 figure

Entanglement detection for electrons via witness operators

We discuss an implementation of the entanglement witness, a method to detect entanglement with few local measurements, in systems where entangled electrons are generated both in the spin and orbital degrees of freedom. We address the efficiency of this method in various setups, including two different particle-hole entanglement structures, and we demonstrate that it can also be used to infer information on the possible dephasing afflicting the devices.Comment: 12 pages, 5 figures; published versio

Decoherence due to discrete noise in Josephson qubits

We study decoherence produced by a discrete environment on a charge Josephson qubit by introducing a model of an environment of bistable fluctuators. In particular we address the effect of $1/f$ noise where memory effects play an important role. We perform a detailed investigation of various computation procedures (single shot measurements, repeated measurements) and discuss the problem of the information needed to characterize the effect of the environment. Although in general information beyond the power spectrum is needed, in many situations this results in the knowledge of only one more microscopic parameter of the environment. This allows to determine which degrees of freedom of the environment are effective sources of decoherence in each different physical situation considered.Comment: 20 pages, 11 figure

Phenomenological noise model for superconducting qubits: two-state fluctuators and 1=f noise

We present a general phenomenological model for superconducting qubits subject to noise produced by two-state fluctuators whose couplings to the qubit are all roughly the same. In flux qubit experiments where the working point can be varied, it is possible to extract both the form of the noise spectrum and the number of fluctuators. We find that the noise has a broad spectrum consistent with 1=f noise and that the number of fluctuators with slow switching rates is surprisingly small: less than 100. If the fluctuators are interpreted as unpaired surface spins, then the size of their magnetic moments is surprisingly large.Comment: 7 pages, 2 figures, 1 tabl

Non-Abelian phases, charge pumping, and quantum computation with Josephson junctions

Non-Abelian geometric phases can be generated and detected in certain superconducting nanocircuits. Here we consider an example where the holonomies are related to the adiabatic charge dynamics of the Josephson network. We demonstrate that such a device can be applied both for adiabatic charge pumping and as an implementation of a quantum computer.Comment: 11 pages RevTex, 3 figures in eps format, revised versio