Directing entanglement spreading by means of a quantum East/West heterojunction structure

We extend the translationally invariant quantum East model to an inhomogeneous chain with East/West heterojunction structure. In analogy to the quantum diffusion of substantial particles, we observe a cyclic entanglement entropy spreading in the heterojunction during time evolution, which can be regarded as continuous cycles in a quantum heat engine. In order to figure out the possibility of manipulating the entanglement entropy as a quantum resource, the entropy growth is shown to be determined by the initial occupation and the site-dependent chemical potential, and the former is equivalent to an effective temperature. Through fine adjustment of these parameters, we discover the entanglement flow is simply superposed with those from two sources of the chain. An intriguing relation between our model and the traditional heat engines is subsequently established.