Abstract
Remarkably, complex assemblies of superconducting wires, electrodes, and Josephson junctions are compactly described by a handful of collective phase degrees of freedom that behave like quantum particles in a potential. Almost all these circuits operate in the regime where quantum phase fluctuations are small—the associated flux is smaller than the superconducting flux quantum—although entering the regime of large fluctuations would have profound implications for metrology and qubit protection. The difficulty arises from the apparent need for circuit impedances vastly exceeding the resistance quantum. Independently, exotic circuit elements that require Cooper pairs to form pairs in order to tunnel have been developed to encode and topologically protect quantum information. In this work, we demonstrate that pairing Cooper pairs magnifies the phase fluctuations of the circuit ground state. We measure a tenfold suppression of flux sensitivity of the first transition energy only, implying a twofold increase in the vacuum phase fluctuations and showing that the ground state is delocalized over several Josephson wells.
- Received 22 February 2021
- Revised 3 December 2021
- Accepted 2 February 2022
DOI:https://doi.org/10.1103/PhysRevX.12.021002
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International 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
Physics Subject Headings (PhySH)
Popular Summary
A quantum particle, such as an electron hopping around a crystal, is not perfectly localized at a single site. Instead, its position fluctuates, and much like a wave, it may delocalize across multiple sites. Remarkably, this wave-particle duality applies to macroscopic circuits composed of superconducting plates and wires, where quantities such as magnetic flux and electric charge play the role of position and momentum. Delocalizing the wave functions of quantum bits encoded in these circuits is known to protect them against the deleterious effects of external perturbations but has remained largely out of reach. Here, we achieve wave-function delocalization by doubling the number of sites covered by the flux fluctuations of the circuit ground state.
When attempting to build a circuit with delocalized wave functions, one battles against the smallness of the fine structure constant, which sets the scale of fluctuations of flux relative to charge. In this work, we circumvent this fundamental obstacle by forcing charge carriers to group together in ensembles of four electrons, known as pairs of Cooper pairs. We demonstrate that this pairing, which results from the destructive interference of single Cooper-pair trajectories, increases the number of sites accessible to the circuit ground-state wave function, which washes out the effect of local perturbations.
In the future, we envision incorporating our Cooper-pair-pairing element into more complex circuits that robustly encode quantum information.
