Decoherence in Josephson-Junction Qubits due to Critical Current Fluctuations

We compute the decoherence caused by 1/f fluctuations at low frequency f in the critical current I_0 of Josephson junctions incorporated into flux, phase, charge and hybrid flux-charge superconducting quantum bits (qubits). The dephasing time \tau_{\phi} scales as I_0/ \Omega \Lambda S_{I_0}^{1/2}(1 Hz),where \Omega / 2\pi is the energy level splitting frequency, S_{I_0}(1 Hz) is the spectral density of the critical current noise at 1 Hz, and \Lambda \equiv |I_0 d \Omega / \Omega d I_0| is a parameter computed for given parameters for each type of qubit that specifies the sensitivity of the level splitting to critical current fluctuations. Computer simulations show that the envelope of the coherent oscillations of any qubit after time t scales as \exp (-t^2/ 2 \tau_{\phi}^2) when the dephasing due to critical current noise dominates the dephasing from all sources of dissipation. We compile published results for fluctuations in the critical current of Josephson tunnel junctions fabricated with different technologies and a wide range in I_0 and A, and show that their values of S_{I_0}(1 Hz) scale to within a factor of three of [ 144 (I_0/\mu{\rm A})^2/ (A/ \mu{\rm m}^2)](pA)^2/Hz at 4.2 K. We empirically extrapolate S_{I_0}^{1/2}(1 Hz) to lower temperatures using a scaling T(K)/4.2. Using this result, we find that the predicted values of \tau_{\phi} at 100 mK range from 0.8 to 12 \mus, and are usually substantially longer than values measured experimentally at lower temperatures

Phase Coherence and Andreev Reflection in Topological Insulator Devices

Topological insulators (TIs) have attracted immense interest because they host helical surface states. Protected by time-reversal symmetry, they are robust to non-magnetic disorder. When superconductivity is induced in these helical states, they are predicted to emulate p-wave pairing symmetry, with Majorana states bound to vortices. Majorana bound states possess non-Abelian exchange statistics which can be probed through interferometry. Here, we take a significant step towards Majorana interferometry by observing pronounced Fabry-Perot oscillations in a TI sandwiched between a superconducting and normal lead. For energies below the superconducting gap, we observe a doubling in the frequency of the oscillations, arising from the additional phase accumulated from Andreev reflection. When a magnetic field is applied perpendicular to the TI surface, a number of very sharp and gate-tunable conductance peaks appear at or near zero energy, which has consequences for interpreting spectroscopic probes of Majorana fermions. Our results demonstrate that TIs are a promising platform for exploring phase-coherent transport in a solid-state system.Comment: 9 pages, 7 figure

On a Possibility to Measure Thermoelectric Power in SNS Structures

Two dissimilar Josephson junctions, which are connected to a heater can act as precise batteries. Because of the difference in thermoelectric power of these batteries, circuit with two dissimilar batteries, under heat flow $\Delta T\sim 10^{-5}K$ would have a net EMF $10^{-11} V$ around the zero-resistance loop leading to a loop's magnetic flux oscillating in time. It is shown its theoretical value is proportional to both the temperature difference as well as the disparity in the thermoelectric powers of the two junctions.Comment: 5 page

Evidence for an anomalous current phase relation in topological insulator Josephson junctions

Josephson junctions with topological insulator weak links can host low energy Andreev bound states giving rise to a current phase relation that deviates from sinusoidal behaviour. Of particular interest are zero energy Majorana bound states that form at a phase difference of $\pi$. Here we report on interferometry studies of Josephson junctions and superconducting quantum interference devices (SQUIDs) incorporating topological insulator weak links. We find that the nodes in single junction diffraction patterns and SQUID oscillations are lifted and independent of chemical potential. At high temperatures, the SQUID oscillations revert to conventional behaviour, ruling out asymmetry. The node lifting of the SQUID oscillations is consistent with low energy Andreev bound states exhibiting a nonsinusoidal current phase relation, coexisting with states possessing a conventional sinusoidal current phase relation. However, the finite nodal currents in the single junction diffraction pattern suggest an anomalous contribution to the supercurrent possibly carried by Majorana bound states, although we also consider the possibility of inhomogeneity.Comment: 6 pages, 4 figure

Dynamical Gate Tunable Supercurrents in Topological Josephson Junctions

Josephson junctions made of closely-spaced conventional superconductors on the surface of 3D topological insulators have been proposed to host Andreev bound states (ABSs) which can include Majorana fermions. Here, we present an extensive study of the supercurrent carried by low energy ABSs in Nb/Bi$_2$Se$_3$/Nb Josephson junctions in various SQUIDs as we modulate the carrier density in the Bi$_2$Se$_3$ barriers through electrostatic top gates. As previously reported, we find a precipitous drop in the Josephson current at a critical value of the voltage applied to the top gate. This drop has been attributed to a transition where the topologically trivial 2DEG at the surface is nearly depleted, causing a shift in the spatial location and change in nature of the helical surface states. We present measurements that support this picture by revealing qualitative changes in the temperature and magnetic field dependence of the critical current across this transition. In particular, we observe pronounced fluctuations in the critical current near total depletion of the 2DEG that demonstrate the dynamical nature of the supercurrent transport through topological low energy ABSs.Comment: 6 pages, 6 figure