  We propose a quantum heat engine based on a quadratically coupled
optomechanical system. The optical component of the system is driven
periodically with an incoherent thermal drive, which induces periodic
oscillations in the mechanical component. Under the action of the quadratic
optomechanical interaction, the mechanical mode evolves from an initial thermal
state to a thermal-squeezed steady state, as verified by calculating the Wigner
functions. The dynamics of the system is identified as an effective four-stroke
Otto cycle. We investigated the performance of the engine by evaluating the
dissipated power, the maximum power under a load, and the maximum extractable
work. It is found that the engine operating with quadratic optomechanics is
more powerful than the one operating with linear optomechanics. The effect is
explained by the presence of squeezing in the quantum state of the mechanical
mode.
