Time molecules with periodically driven interacting qubits

We provide numerical evidence for a temporal quantum-mechanical interference phenomenon: time molecules (TM). A variety of such stroboscopic states are observed in the dynamics of two interacting qubits subject to a periodic sequence of $pi$-pulses with the period $T$. The TMs appear periodically in time and have a large duration, $delta t_mathrm{TM} gg T$. All TMs demonstrate an almost zero value of the total polarization and a strong enhancement of the entanglement entropy $S$ up to the maximum value $S=ln 2$ of a corresponding Bell state. The TMs are generated by the commensurability of the Floquet eigenvalues and the presence of maximally entangled Floquet eigenstates. The TMs remain stable with detuned system parameters and with an increased number of qubits. The TMs can be observed in microwave experiments with an array of superconducting qubits.