  In the classical world, physical events always happen in a fixed causal
order. However, it was recently revealed that quantum mechanics allows events
to occur with indefinite causal order (ICO). In this study, we use an optical
quantum switch to experimentally investigate the application of ICO in
thermodynamic tasks. Specifically, we simulate the working system interacting
with two identical thermal reservoirs in an ICO, observing the quantum heat
extraction even though they are in thermal equilibrium where heat extraction is
unaccessible by traditional thermal contact. Using such a process, we simulate
an ICO refrigeration cycle and investigate its properties. We also show that by
passing through the ICO channel multiple times, one can extract more heat per
cycle and thus obtain a higher refrigeration performance. Our results suggest
that the causal nonseparability can be a powerful resource for quantum
thermodynamic tasks.
