Quantum Control of Atoms in Collective Decoherence-Free Subspaces*

In this theoretical presentation, we propose methods for modelling and controlling a stable, time-dependent decoherence-free subspace (DFS) in a dissipative atom-cavity system. The atoms considered have many internal energy levels, which allows for the creation of multi-dimensional DFSs. Storing and manipulating quantum information in these subspaces has applications in quantum sensing, simulation, and computation. Our system exhibits collective behavior, where the number of internal states determines the underlying SU(n) group structure of the system. We use tunable external laser drives to transfer the system from a coherent spin state to a DFS of predominantly highly entangled states. A crucial property is that the state remains in an instantaneous DFS throughout evolution, thereby making the system robust to dissipation and decoherence and allowing pure states to be prepared. We show that adiabatic shortcuts can carry out the evolution with high purity and fidelity on reduced timescales.