Two-dimensional topological effect in a transmon qubit array with tunable couplings

  1. Yan-Jun Zhao,
  2. Yu-Qi Wang,
  3. Yang Xue,
  4. Xun-Wei Xu,
  5. Yan-Yang Zhang,
  6. Wu-Ming Liu,
  7. and Yu-xi Liu
We investigate a square-lattice architecture of superconducting transmon qubits with inter-qubit interactions mediated by inductive couplers. Therein, the inductive couling between
the qubit and couplers is suggested to be designed into the gradiometer form to intigimate the flux noise orginating from the environment. Via periodically modulating the couplers,the Abelian gauge potential, termed effective magnetic flux, can be synthesized artificially, making the system an excellent platform for simulating two-dimensional topological physics. In the simplest two-dimensional model, the double (or three-leg) ladder, the staggered vortex-Meissner phase transition different from that in the two-leg ladder can be found in the single-particle ground state as the effective magnetic flux varies. Besides, the large coupling ratio between the interleg and intraleg coupling strengths also makes the chiral current resemble squeezed sinusoidal functions. If the row number is further increased, the topological band structure anticipated at massive rows begins to occur even for a relatively small number of rows (ten or so for the considered parameters). This heralds a small circuit scale to observe the topological band. The edge state in the band gap is determined by the topological Chern number and can be calculated through integrating the Berry curvature with respect to the first Brillouin zone. Besides, we present a systematic method on how to measure the topological band structure based on time- and space-domain Frourier transformation of the wave function after properly excited. The result offers an avenue for simulating two-dimensional topological physics on the state-of-the-art superconducting quantum chips.

Vortex-Meissner phase transition induced by two-tone-drive-engineered artificial gauge potential in the fermionic ladder constructed by superconducting qubit circuits

  1. Yan-Jun Zhao,
  2. Xun-Wei Xu,
  3. Hui Wang,
  4. Yu-xi Liu,
  5. and Wu-Ming Liu
We propose to periodically modulate the onsite energy via two-tone drives, which can be furthermore used to engineer artificial gauge potential. As an example, we show that the fermionic
ladder model penetrated with effective magnetic flux can be constructed by superconducting flux qubits using such two-tone-drive-engineered artificial gauge potential. In this superconducting system, the single-particle ground state can range from vortex phase to Meissner phase due to the competition between the interleg coupling strength and the effective magnetic flux. We also present the method to experimentally measure the chiral currents by the single-particle Rabi oscillations between adjacent qubits. In contrast to previous methods of generating artifical gauge potential, our proposal does not need the aid of auxiliary couplers and in principle remains valid only if the qubit circuit maintains enough anharmonicity. The fermionic ladder model with effective magnetic flux can also be interpreted as one-dimensional spin-orbit-coupled model, which thus lay a foundation towards the realization of quantum spin Hall effect.