Nonlinear electron–phonon interactions in a quantum dot phonon cavity

Controlling electron transport and statistical properties in a quantum dot phonon cavity has been extensively studied, yet most are focused on the linear electron–phonon interactions. By introducing a nonlinear version in which the quantum dot couples to the cavity mode through a k-phonon interaction, we show that it is possible to switch the transport channels from opening to blocking by simply adjusting k-phonon-mediated inelastic processes, and also reveal the resultant nonthermal phonon transition from antibunching to superbunching. In the lasing transitions, a bistable phonon emission for $k\ge 2$ is generated, and its applications in work extraction can go beyond those of traditional coherent states. Our results pave the way for designing current switches and generating nonthermal phonon statistics in quantum dot devices.