Coexistence of directed momentum current and ballistic energy diffusion in coupled non-Hermitian kicked rotors

We numerically investigate the quantum transport in a coupled kicked rotors with the $\mathcal{PT}$-symmetric potential. We find that the spontaneous $\mathcal{PT}$-symmetry breaking of wavefunctions emerges when the amplitude of the imaginary part of the complex potential is beyond a threshold value, which can be modulated by the coupling strength effectively. In the regime of the $\mathcal{PT}$-symmetry breaking, the particles driven by the periodical kicks move unidirectionally in momentum space, indicating the emergence of a directed current. Meanwhile, with increasing the coupling strength, we find a transition from the ballistic energy diffusion to a kind of the modified ballistic energy diffusion where the width of the wavepacket also increases with time in a power law. Our findings suggest that the decoherence effect induced by the interplay between the inter-particle coupling and the non-Hermitian driving potential is responsible for these particular transport behaviors.