It is well known that jammed soft materials will flow if sheared above their yield stress - think mayonnaise spread on bread - but a complete microscopic description of this seemingly sim- ple process has yet to emerge. What remains elusive is a micr
oscopic framework that explains the macroscopic flow, derived from a 3-D spatially resolved analysis of the dynamics of the droplets or particles that compose the soft material. By combining confocal-rheology experiments on compressed emulsions and numerical simulations, we unravel that the primary microscopic mechanisms for flow are strongly influenced by the rate of the imposed deformation. When shearing fast, small coordinated clusters of droplets move collectively as in a conga line, while at low rates the flow emerges from bursts of droplet rearrangements, correlated over large domains. These regions exhibit complex spatio-temporal correlation patterns that reflect the long range elasticity embedded in the jammed material. These results identify the three-dimensional structure of microscopic rearrangements within sheared soft solids, revealing that the characteristic shape and dynamics of these structures are strongly determined by the rate of the external shear.
We report spectroscopic measurements of discrete two-level systems (TLSs) coupled to a dc SQUID phase qubit with a 16 mum2 area Al/AlOx/Al junction. Applying microwaves in the 10 GHz to 11 GHz range, we found eight avoided level crossings with splitt
ing sizes from 10 MHz to 200 MHz and spectroscopic lifetimes from 4 ns to 160 ns. Assuming the transitions are from the ground state of the composite system to an excited state of the qubit or an excited state of one of the TLS states, we fit the location and spectral width to get the energy levels, splitting sizes and spectroscopic coherence times of the phase qubit and TLSs. The distribution of splittings is consistent with non-interacting individual charged ions tunneling between random locations in the tunnel barrier and the distribution of lifetimes is consistent with the AlOx in the junction barrier having a frequency-independent loss tangent. To check that the charge of each TLS couples independently to the voltage across the junction, we also measured the spectrum in the 20-22 GHz range and found tilted avoided level crossings due to the second excited state of the junction and states in which both the junction and a TLS were excited.
We present Rabi oscillation measurements of a Nb/AlOx/Nb dc superconducting quantum interference device (SQUID) phase qubit with a 100 um^2 area junction acquired over a range of microwave drive power and frequency detuning. Given the slightly anharm
onic level structure of the device, several excited states play an important role in the qubit dynamics, particularly at high power. To investigate the effects of these levels, multiphoton Rabi oscillations were monitored by measuring the tunneling escape rate of the device to the voltage state, which is particularly sensitive to excited state population. We compare the observed oscillation frequencies with a simplified model constructed from the full phase qubit Hamiltonian and also compare time-dependent escape rate measurements with a more complete density-matrix simulation. Good quantitative agreement is found between the data and simulations, allowing us to identify a shift in resonance (analogous to the ac Stark effect), a suppression of the Rabi frequency, and leakage to the higher excited states.
We report measurements of Rabi oscillations and spectroscopic coherence times in an Al/AlOx/Al and three Nb/AlOx/Nb dc SQUID phase qubits. One junction of the SQUID acts as a phase qubit and the other junction acts as a current-controlled nonlinear i
solating inductor, allowing us to change the coupling to the current bias leads in situ by an order of magnitude. We found that for the Al qubit a spectroscopic coherence time T2* varied from 3 to 7 ns and the decay envelope of Rabi oscillations had a time constant T = 25 ns on average at 80 mK. The three Nb devices also showed T2* in the range of 4 to 6 ns, but T was 9 to 15 ns, just about 1/2 the value we found in the Al device. For all the devices, the time constants were roughly independent of the isolation from the bias lines, implying that noise and dissipation from the bias leads were not the principal sources of dephasing and inhomogeneous broadening.
We report measurements of spectroscopic linewidth and Rabi oscillations in three thin-film dc SQUID phase qubits. One device had a single-turn Al loop, the second had a 6-turn Nb loop, and the third was a first order gradiometer formed from 6-turn wo
und and counter-wound Nb coils to provide isolation from spatially uniform flux noise. In the 6 - 7.2 GHz range, the spectroscopic coherence times for the gradiometer varied from 4 ns to 8 ns, about the same as for the other devices (4 to 10 ns). The time constant for decay of Rabi oscillations was significantly longer in the single-turn Al device (20 to 30 ns) than either of the Nb devices (10 to 15 ns). These results imply that spatially uniform flux noise is not the main source of decoherence or inhomogenous broadening in these devices.
Rabi oscillations have been observed in many superconducting devices, and represent prototypical logic operations for quantum bits (qubits) in a quantum computer. We use a three-level multiphoton analysis to understand the behavior of the superconduc
ting phase qubit (current-biased Josephson junction) at high microwave drive power. Analytical and numerical results for the ac Stark shift, single-photon Rabi frequency, and two-photon Rabi frequency are compared to measurements made on a dc SQUID phase qubit with Nb/AlOx/Nb tunnel junctions. Good agreement is found between theory and experiment.
We have investigated the fidelity and speed of single-shot current-pulse measurements of the three lowest energy states of the dc SQUID phase qubit. We apply a short (2ns) current pulse to one junction of a Nb/AlOx/Nb SQUID that is in the zero voltag
e state at 25 mK and measure if the system switches to the finite voltage state. By plotting the switching rate versus pulse size we can determine average occupancy of the levels down to 0.01%, quantify small levels of leakage, and find the optimum pulse condition for single-shot measurements. Our best error rate is 3% with a measurement fidelity of 94%. By monitoring the escape rate during the pulse, the pulse current in the junction can be found to better than 10 nA on a 0.1 ns time scale. Theoretical analysis of the system reveals switching curves that are in good agreement with the data, as well as predictions that the ultimate single-shot error rate for this technique can reach 0.4% and the fidelity 99.2%.
