Few quantum walkers for the generation of vortex creep on bosonic flux ladders

Abstract We investigate the quantum–classical correspondence of vortex creep within the framework of quantum ladder lattice with artificial gauge. By introducing operators to characterize microscopic vortices in the bosonic flux ladder, we focus on quantum walks initiated from states with one, two and four particles localized at the central sites of the ladder. In the single-particle systems, we observe an asymmetric spreading of vortices stemming from the specific construction of the initial states and the gauge choice. In the two- and four-particle systems, comparisons across different conditions reveal that the individual application of flux and interactions slows down particle propagation due to pairing and vortex formation. Notably, when both flux and interaction are present concurrently, our results demonstrate that the mean square displacement (MSD) of the vortices grows significantly slower than the typical <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi>MSD</mml:mi> </mml:mrow> <mml:mo>∼</mml:mo> <mml:msup> <mml:mi>t</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> for quantum walk, instead approaching the characteristic behavior of classical walk <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi>MSD</mml:mi> </mml:mrow> <mml:mo>∼</mml:mo> <mml:mi>t</mml:mi> </mml:mrow> </mml:math> . This indicates that the observed spreading process is consistent with the classical walk of vortices formed by circulating particles, i.e. vortex creep in superconductors.