Quantum control in open and periodically driven systems

Quantum technology resorts to efficient utilization of quantum resources realize technique innovation. The systems are controlled such that their states follow the desired manners different protocols. However, decoherence caused by system-environment interactions causes deviating from manners. How protect under coexistence active control and passive is significance. Recent studies have revealed determined feature energy spectrum: Accompanying formation bound in spectrum, can be suppressed. It supplies a guideline decoherence. Such idea generalized periodic driving. By virtue manipulating Floquet quasienergy coherent via driving dubbed as engineering has become versatile tool not only controlling decoherence, but also artificially synthesizing exotic topological phases. We will review progress on open periodically driven systems. Special attention paid distinguished role played controllability suppressing generating novel