  We propose a theoretical scheme to realize nonreciprocal transition between
two energy levels that can not coupled directly. Suppose they are coupled
indirectly by two auxiliary levels with a cyclic four-level configuration, and
the four transitions in the cyclic configuration are controlled by external
fields. The indirectly transition become nonreciprocal when the time reversal
symmetry of the system is broken by the synthetic magnetic flux, i.e., the
total phase of the external driving fields through the cyclic four-level
configuration. The nonreciprocal transition can be identified by the
elimination of a spectral line in the spontaneous emission spectrum. Our work
introduces a feasible way to observe nonreciprocal transition in a wide range
of multi-level systems, including natural atoms or ions with parity symmetry.
