Abstract
The possibility of engineering artificial Kitaev chains in arrays of quantum dots coupled via narrow superconducting regions has emerged as an attractive way to overcome the disorder issues that complicate the realization and detection of topological superconducting phases in other platforms. Although a true topological phase would require long chains, a two-site chain realized in a double quantum dot can already be tuned to points in parameter space where it hosts zero-energy states that seem identical to the Majorana bound states that characterize a topological phase. These states have been named “poor man’s Majorana bound states” (PMMs) because they lack formal topological protection. In this work, we propose a pathway for next-generation experiments on PMMs. The pathway starts with experiments to characterize a single pair of PMMs by measuring the Majorana quality and then moves on to initialization and readout of the parity of a PMM pair, which allows the measurement of quasiparticle poisoning times. The next step is to couple two PMM systems to form a qubit. We discuss measurements of the coherence time of such a qubit, as well as a test of Majorana fusion rules in the same setup. Finally, we propose and analyze three different types of braidinglike experiments that require more complex device geometries. Our conclusions are supported by calculations based on a realistic model with interacting and spinful quantum dots, as well as by simpler models to gain physical insight. Our calculations show that it is indeed possible to demonstrate non-Abelian physics in minimal two-site Kitaev chains despite the lack of a true topological phase. However, our findings also reveal that doing so requires some extra care, appropriately modified protocols, and awareness of the details of this particular platform.
- Received 30 June 2023
- Revised 29 November 2023
- Accepted 22 December 2023
DOI:https://doi.org/10.1103/PRXQuantum.5.010323
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. Funded by Bibsam.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Majoranas are quantum particles with the spectacular property that exchanging the positions of two Majoranas will nontrivially change their joint quantum state. One more exchange restores the original particle positions but not the original quantum state. This so-called non-Abelian statistics set them apart from bosons and fermions and might be used in quantum computers, but despite intense efforts it has never been experimentally demonstrated. We show how to demonstrate non-Abelian statistics with a new type of Majorana-like particle, called a poor man’s Majorana.
Poor man's Majoranas are easier to realize than regular Majoranas because they do not rely on defect-free materials and interfaces but can exist in two confined regions of a semiconductor (quantum dots) coupled via a superconductor. However, because they are more fragile than regular Majoranas, it has not been clear whether they can be used to demonstrate non-Abelian statistics and, if so, what the best experiment would be for doing so. Here, we answer these questions. We show that yes, it is indeed possible to demonstrate non-Abelian statistics with poor man’s Majoranas. We also provide detailed guidelines for experimentalists aiming to do so. These directions start from relatively simple experiments to measure the “quality” of poor man’s Majoranas, then gradually builds toward more complicated experiments, and end with three different tests of non-Abelian statistics.
Our work can inspire further experimental and theoretical exploration, leading to empirical evidence of non-Abelian particles, deeper understanding of their properties, and their potential application in quantum technologies.
