Floquet engineering of quantum state control by exceptional-point proximity in a single dissipative qubit

Open quantum systems interacting with an environment can be described by Lindblad density matrix equation that encodes their approach to a steady state. When the quantum trajectories of this decoherence-inducing dynamics are restricted to those with no quantum jumps, the resulting evolution is described by effective non-Hermitian Hamiltonians. The presence of a special kind of degeneracy known as an exceptional point (EP) plays an important role in the unique topology of these non-Hermitian systems. Such an EP occurs when both the eigenvalues and eigenstates of the system coalesce. We demonstrate real-time control over a single dissipative qubit described by an effective non-Hermitian Hamiltonian. We reveal how quasistatic tuning of the system parameters results in coherent quantum gates enabled by the complex energy topology. Leaving the quasistatic limit, an effective Floquet Hamiltonian enables rapid quantum gates. Finally, we characterize the geometric phases accumulated from quantum state transport around the EP, revealing the chirality of the transport. Our work demonstrates a new method for control over quantum state, highlighting new facets of quantum bath engineering enabled through time-periodic non-Hermitian control.