Formation of Quantum Phase Slip Pairs in Superconducting Nanowires

Open Access

Formation of Quantum Phase Slip Pairs in Superconducting Nanowires

A. Belkin, M. Belkin, V. Vakaryuk, S. Khlebnikov, and A. Bezryadin

Phys. Rev. X 5, 021023 – Published 10 June 2015

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 $2 π$ , there are quantum transitions that change the phase by $4 π$ . 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.

Received 30 July 2014

DOI:https://doi.org/10.1103/PhysRevX.5.021023

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Authors & Affiliations

A. Belkin¹, M. Belkin¹, V. Vakaryuk^2,3, S. Khlebnikov⁴, and A. Bezryadin^1,*

¹Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
²Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
³American Physical Society, 1 Research Road, Ridge, New York 11961, USA
⁴Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA

^*bezryadi@illinois.edu

Popular Summary

In a quasi-one-dimensional system, phase slips are fluctuations in the superconducting order parameter that drive a system’s segments into a normal state for a short period of time. Phase slips, which were first proposed by Little in 1967, play a crucial role in the physics of thin nanowires where their proliferation leads to the destruction of superconductivity. Phase slips also change the winding number, i.e., the net number of vortices that have entered into a closed superconducting loop. Phase slips are stochastic in nature because they are induced by thermal fluctuations or by quantum tunneling. A quantum phase slip constitutes a prominent example of macroscopic quantum tunneling since it involves a large number of microscopic degrees of freedom. Here, we experimentally demonstrate the pairing of quantum phase slips, a process that preserves the parity of the number of vortices that have entered our superconducting loop. The difference between quantum and classical in our context is that quantum phase slip pairs represent a simultaneous and quantum-coherent entrance of two fluxons; classical pairs represent a sequential entrance of two fluxons where the first phase slip causes the second one.

It has been recently suggested that paired phase slips can be used to build topologically protected qubits, which show increased resistance to decoherence and may play key roles in the quantum computers of the future. We use microwave measurement techniques at 0.06–3 K to study the fluxoid states of a device composed of a superconducting loop that includes two homogeneous nanowires. We focus on transitions between different fluxoid states that occur through phase slips in the nanowires. We identify a regime for which paired phase slips are exponentially more likely than single unpaired phase slips. In this regime our thin-wire superconducting loop acts as a parity-conserving element that can be utilized for the topological protection of qubits, provided that the overall rate of quantum phase slips can be made sufficiently high. We argue that in the quantum tunneling regime the paired phase slips are not composed of sequential single phase slips but rather they occur via macroscopic quantum tunneling events that proceed in pairs, i.e., by means of “quantum cotunneling.”

We anticipate that our approach will stimulate new experiments on building parity-protected qubits based on superconducting nanowires.

Key Image

Article Text

Click to Expand

Supplemental Material

Click to Expand

References

Click to Expand

Issue

Vol. 5, Iss. 2 — April - June 2015

Subject Areas

Reuse & Permissions

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Schematic representation of the samples (not to scale). (a) The superconducting coplanar resonator has two nanowires in the middle of the center conductor, which are suspended over a trench in the substrate (see Ref. [27], SM-1). MoGe film is shown in gray; regions where it is removed are shown in white. The superconducting loop is threaded by an external magnetic field $B$ . Yellow stripes depict gold coating. QPPS is shown as a pair of fluxoids simultaneously crossing both nanowires. Each fluxoid changes the phase accumulated on the loop by $2 π$ and generates voltage on each wire, $V = ℏ (d ϕ_{wire} / d t) / 2 e$ . Plus and minus signs indicate the quadrupole charge distribution during QPPS. (b) Scanning electron microscope images of the nanowires in sample A. The spacing between nanowires is $13 μ m$ .
Reuse & Permissions
Figure 2
Dependence of the transmission phase on the current in the solenoid. The bath temperature is 350 mK. Periodically spaced “parabolas,” each corresponding to a particular vorticity or the quantum winding number $n$ , are clearly observed. SPS result in jumps of $θ_{S 21}$ to the next parabola (single-line red arrow) and $n \to (n \pm 1)$ change in the vorticity. PPS result in jumps of $θ_{S 21}$ to the next-nearest parabolas (double-line red arrow) and $n \to (n \pm 2)$ change in the vorticity. The Little-Parks period is marked as $J_{LP}$ . Regions where switching events form clusters correspond to magnetic fields and vorticity values at which the current in the wires is near the critical current.
Reuse & Permissions
Figure 3
Probability densities of SPS and PPS as functions of normalized current in solenoid. Blue squares correspond to SPS; red ovals correspond to PPS transitions. These measurements have been performed at $T = 60 mK$ .
Reuse & Permissions
Figure 4
Dependence of the standard deviation of SPS switching current distribution on the reduced input power of the microwave signal. The measurements are made at 60 mK. $P_{c}$ corresponds to a power that induces in the wires a current equal to their critical current.
Reuse & Permissions
Figure 5
Temperature dependence of standard deviations of SPS and PPS switching current distributions. The temperature $T_{q}$ (black arrow) marks a crossover from thermal activation to quantum tunneling of SPS. The solid red line is the best fit of $σ_{SPS} (T)$ in the thermally activated regime: $σ_{SPS} (T > T_{q}) = 0.136 T^{0.54} rad$ . The dashed black line shows the best fit in the quantum tunneling regime: $σ_{PPS} (T < T_{q}) = 0.130 rad$ . In the inset, the average switching current versus temperature, $J_{sw} (T)$ , is shown. The switching current continues to increase with cooling down to temperatures much lower than $T_{q}$ .
Reuse & Permissions
Figure 6
Rates of SPS (blue squares) and PPS (red ovals) as functions of the normalized current in the solenoid. The bath temperature is 60 mK. Single (blue squares) and paired (red ovals) phase slip rates are obtained from the switching current distributions shown in Fig. 3. The solid black line is the Kurkijärvi-Garg fit for the rate of SPS. The dashed red line is the QPPS fit, generated according to Korshunov’s theory of QPPS [14]. Rates of SPS and PPS are equal at the current $j_{x}$ . The inset shows the schematic difference between CPPS (red solid line) and QPPS (red dashed line).
Reuse & Permissions

Physical Review X