Towards quantum simulation of topological superconductors with a Penning trap*

The p+ip superconductor is an unconventional superconductor in which Cooper pairs form with angular momentum in two dimensions. These chiral systems exhibit protected dynamical phases that hold potential for topological quantum computing [1]. In this work, we present preliminary results in generating the initial Bardeen-Cooper-Schrieffer (BCS) phase of a p+ip superconductor using a Penning trap, which naturally confines over a hundred ion qubits in a two-dimensional ion Coulomb crystal. The ions' spin states encode the presence or absence of a Cooper pair while the ion positions take the role of the momentum of the Andersen pseudospins. We initialize the radially symmetric BCS spin configuration by leveraging the natural rotation of the crystal. To achieve this, we generate a radially dependent AC Stark shift across the crystal plane by precisely controlling the tilt angle of a spin-dependent force with respect to the crystal plane [2]. Finally, with individual spin-state readout [3], we perform a full tomographic reconstruction of the individual spins of all the ions to confirm the state initialization protocol.

References:

[1] A. Shankar, E. A. Yuzbashyan, V. Gurarie, P. Zoller, J. J. Bollinger and A. M. Rey, Simulating dynamical phases of chiral p+ip superconductors with a trapped ion magnet, PRX Quantum 3, 040324 (2022).

[2] J. H. Pham, J. Y. Z. Jee, A. Rischka, M. J. Biercuk and R. N. Wolf, In-situ-tunable spin-spin interactions in a Penning trap with in-bore optomechanics, Adv. Quantum Technol. 2024, 2400086

[3] R. N. Wolf, J. H. Pham, J. Y. Z. Jee, A. Rischka, and M. J. Biercuk, Efficient site-resolved imaging and spin-state detection in dynamic two-dimension ion crystals, Phys. Rev. Applied 21, 054067