Dynamical non-Hermitian control of a superconducting qubit
Kater Murch, Washington University in St. Louis
A system described by a non-Hermitian Hamiltonian will, in general, have complex energies and non-orthogonal eigenstates. The degeneracies of such a system are known as exceptional points. Near these degeneracies, the complex energies are described by Riemann manifolds whose topology enables new methods of control over the system. Using a superconducting circuit QED platform we employ dynamical control over an effective non-Hermitian Hamiltonian to utilize the topology of its complex energy surfaces to control quantum state vectors. If a quantum system is initialized in one eigenstate, and the Hamiltonian parameters are varied slowly such as to encircle an EP, returning to the initial parameters, the topology of the Riemann manifold predicts that adiabatic evolution will switch the state to a different eigenstate. We observe this state mapping behavior and further characterize the chiral geometric phases associated with quantum coherent evolution on the Riemann manifolds.