  In the long-time limit, an open quantum system coupled to a dissipative
environment is believed to lose its coherence without driving or measurement.
Counterintuitively, we provide a necessary condition on trapping the coherence
of a two-level system entirely with a thermal bath. Based on a time-local
master equation, it is found that the residue coherence survives even under a
high-temperature bath as long as the long-time Lamb shift is exactly negative
to the system transition frequency. This condition is generally met in the
strong and even ultrastrong coupling regime that could be relaxed by increasing
the environmental temperature. The counter-rotating interactions between system
and bath is indispensable to the residue coherence, whose magnitude is affected
by the system initial state and the bath structure.
