Control-assisted decoherence-free manifolds

Quantum coherence of open quantum systems is usually compromised because of the interaction with the ambient environment. A ¿decoherence-free subspace¿ (DFS) of the system Hilbert space is defined where the evolution remains unitary. In the absence of a priori existence of such subspaces, it seems natural that utilizing quantum control may help generate and/or retain a DFS. Here, we introduce a time-varying DFS wherein the system´s density matrix has a unitarily evolving sub-density corresponding to some given set of its eigenvalues (which we aim to preserve). This subspace is characterized from both topological and algebraic perspectives. In particular, we show that this DFS admits a complex vector bundle structure over a real-analytic manifold (the decoherence-free manifold).