Quantum metamaterial without local control

A quantum metamaterial can be implemented as a quantum coherent one-dimensional array of qubits placed in a transmission line. The properties of quantum metamaterials are determined by the local quantum state of the system. Here we show that a spatially periodic quantum state of such a system can be realized without direct control of the constituent qubits, by their interaction with the initializing (“priming”) pulses sent through the system in opposite directions. The properties of the resulting quantum photonic crystal are determined by the choice of the priming pulses. This proposal can be readily generalized to other implementations of quantum metamaterials