Formation of Quantum Phase Slip Pairs in Superconducting Nanowires

Abstract

Macroscopic quantum tunneling is a fundamental phenomenon of quantum mechanics related to the actively debated topic of quantum-to-classical transition. The ability to realize macroscopic quantum tunneling affects implementation of qubit-based quantum computing schemes and their protection against decoherence. Decoherence in qubits can be reduced by means of topological protection, e.g., by exploiting various parity effects. In particular, paired phase slips can provide such protection for superconducting qubits. Here, we report on the direct observation of quantum paired phase slips in thin-wire superconducting loops. We show that in addition to conventional single phase slips that change the superconducting order parameter phase by 2π, there are quantum transitions that change the phase by 4π. Quantum paired phase slips represent a synchronized occurrence of two macroscopic quantum tunneling events, i.e., cotunneling. We demonstrate the existence of a remarkable regime in which paired phase slips are exponentially more probable than single ones. DOI: 10.1103/PhysRevX.5.021023 Subject Areas: Mesoscopics, Quantum Information, SuperconductivityDecoherence and quantum noise are primary roadblocks for large-scale implementation of quantum computing that in many cases relies on the phenomenon of macroscopic quantum tunneling [1][2][3][4][5]. Decoherence is inherently related to the collapse of macroscopic wave functions caused by various environment-induced interactions. In quantum computers, detrimental effects of decoherence can be eliminated by means of quantum error correction as originally proposed by Shor [6]. An alternative approach was suggested by Kitaev [7], who argued that the use of topologically ordered quantum systems can eliminate the burden of quantum error correction. In such systems, qubits are implemented by topologically distinct states connected by a global operation (such as braiding, in the case of anyons) that cannot be mixed by a local perturbation.Less exotic schemes of topological protection based on various parity effects in superconducting circuits have also been presented [8][9][10][11]. The crucial component of these proposals is a device that discriminates between parity-conserving and parity-violating transitions. Ideally, such a device fully suppresses the latter, thus creating well-separated parity-based sectors in the Hilbert space, which are used as a "grid" for qubit operations.Here, we focus on a multiply-connected device formed by a superconducting loop containing homogeneous superconducting nanowires. Flux states of the loop are described by the winding number (vorticity) of the superconducting phase on a path encircling the loop. Transitions between different winding number states occur through phase slips taking place in the nanowires. Realization of a parityprotected qubit requires suppression of 2π phase slips, which change the winding number by 1, and a significant amplitude of 4π phase slips, which are parity-conserving [12][13][14] events. We term them single phase s...

Decay of near-critical currents in superconducting nanowires

“…It seems reasonable to assume that this configuration is the "critical droplet"-the saddle point whose energy determines the height of the activation barrier. Since, compared to the ground state, the phase difference changes on only one link, that height is exactly the same as for a single junction and, in particular, scales according to (1). A potential difficulty with this explanation becomes apparent if we observe that the activation process envisioned above requires a change in the total phase difference between the ends of the wire: if there is a total of better-have lower values of Tc than their amorphous counterparts.…”

“…In [1], such a description has been found to provide good fits to the experimental data. Moreover, in that work, as well as in some of the earlier experiments [2,3], some of the behavior characteristic of a JJ has been identified in nanowires also for the classical, thermally activated variety of phase slips.…”

“…The recent observation in [1] of double phase slips in superconducting nanowires and the interpretation of these there as paired quantum phase slips have brought to the fore the question of to what extent a nanowire can be modeled as a lumped superconducting element, i.e., described by a single phase variable, similarly to a Josephson junction (JJ). In [1], such a description has been found to provide good fits to the experimental data.…”

“…In that case, the barrier is determined by the energy of the Langer-Ambegaokar (LA) [5] saddle-point and scales as (1 − i b ) 5/4 [6]. Somewhat surprisingly, as a description of the experimental data on nanowires, the power-3/2 scaling characteristic of a JJ typically works quite well [1][2][3], although there is one type of wires (the crystalline wires of Ref. [3]) where the power-5/4 scaling has been found to work better.…”

Maximizing switching current of superconductor nanowires via improved impedance matching

“…13,14 Generally, phase slips include the thermal-activated phase slip (TAPS), 15 thermal barrier-crossing by the order-parameter field at high temperatures, and the quantum phase slip (QPS), 3 a quantum tunneling event occurring at low temperatures. Recently, more complex phenomena such as quantum phase slip pairs 16 and coherent quantum phase slips 17 have been reported in superconductor nanowires. The phase slip transition is unfortunately difficult to measure as it is random, weak, and fast.…”