Reconfigurable Josephson Phase Shifter

Phase shifter is one of the key elements of quantum electronics. In order to facilitate operation and avoid decoherence, it has to be reconfigurable, persistent, and nondissipative. In this work, we demonstrate prototypes of such devices in which a Josephson phase shift is generated by coreless superconducting vortices. The smallness of the vortex allows a broad-range tunability by nanoscale manipulation of vortices in a micron-size array of vortex traps. We show that a phase shift in a device containing just a few vortex traps can be reconfigured between a large number of quantized states in a broad [−3π, +3π] range.


Samples
Studied devices contain planar JJ's. They are made from bi-layer films with a 70 nm top Nb layer and thin nonsuperconducting metallic bottom layer. Devices in Figs. 1 (d), 2 and 3 are made using a paramagnetic CuNi alloy, the SQUID from Fig. 4 (a) -using pure Cu underlayer. We also tested other metals and just a single layer Nb film. All of them work in a similar manner and results do not depend on a specific material. Variable-thickness-bridge type JJ's are made by cutting a narrow (∼ 20 nm) grove in the top Nb layer by focused ion beam (FIB) etching, as sketched in Fig. 2 (b). Details of junction fabrication can be found elsewhere [18,23,27]. Planar junction properties were described in Ref. [52]. SQUID device, Fig. 4, was made by FIB milling of a rectangular loop in the middle of a junction.
Supplementary Figure 1 shows a sketch of the device from Fig. 2 with corresponding junction lengths and distances to the traps counted from the bottom junction-2.
Experimental Measurements are performed in a cryogen-free cryostat using a four-probe configuration. Magnetic field is applied perpendicular to the films. Vortex states are prepared in the following way. We start from the Meissner state by zero-field cooling of a device without bias current. Vortices are intro-duced either by applying current pulses, magnetic fields, or both, as described in Ref. [18]. Depending on the amplitude and the sign of current pulses, we can introduce either vortices, or antivortices as shown in Fig. 2 (c).
MFM imaging Low-temperature MFM imaging is carried out on AttoCube scanning probe system (AttoDry 1000/SU) with a standard Co/Cr-coated cantilever (MESP, Bruker, 2.8 N/m spring constant). MFM images, shown in Figs. 1 (e) and (f) are made in a tapping mode at a fixed resonance frequency, 87 kHz. The color scale represents the phase of tip oscillations: the black color corresponds to zero phase, brighter areas to a positive phase with the brightest level +10 • . The positive phase shift indicates a repulsive force on the tip, which is caused by Meissner screening of the tip field by the superconductor. To trap a vortex, the tip was approached close enough to the hole so that inhomogeneous magnetic field of the tip locally introduced a vortex. The sign of the vortex depends on the direction of tip magnetization. Because the vortex is introduced by the tip field, the tip-vortex interaction is attractive, resulting in the dark contrast of the trapped vortex in a subsequent MFM phase map, shown in Fig. 1 (f). I c (H) measurements, presented in Figs. 1 (h) and (i) are performed in the same MFM system with a retracted tip, in order not to induce extra distortion from the tip itself [29].
Numerical simulations We use numerical fitting for extraction of JPS. Simulations presented by red lines in Figs. 1 (g), 2 (d-g) and 3 are done taking ϕ v (x) from Eq. (1) with actual trap geometries (x vi /L x , z vi /L x , Θ vi ) and using V i as a fitting parameter. The critical current is calculated by maximization of integrated Josephson current, I = (I c0 /L) L 0 sin[ϕ(H) + ϕ v ]dx, where ϕ(H) represents the linear field-dependent phase gradient in the absence of vortices. Details of the formalism can be found in Ref. [29]. In all demonstrated cases such fitting allows unambiguous estimation of JPS, ∆ϕ v = − i V i Θ vi .