  The principle of microscopic reversibility lies at the core of fluctuation
theorems, which have extended our understanding of the second law of
thermodynamics to the statistical level. In the quantum regime, however, this
elementary principle should be amended as the system energy cannot be sharply
determined at a given quantum phase space point. In this Letter, we propose and
experimentally test a quantum generalization of the microscopic reversibility
when a quantum system interacts with a heat bath through energy-preserving
unitary dynamics. Quantum effects can be identified by noting that the backward
process is less likely to happen in the existence of quantum coherence between
the system's energy eigenstates. The experimental demonstration has been
realized by mixing coherent and thermal states in a beam-splitter, followed by
heterodyne detection in an optical setup. We verify that the quantum
modification for the principle of microscopic reversibility is critical in the
low-temperature limit, while the quantum-to-classical transition is observed as
the temperature of the thermal field gets higher.
