  This Letter deals with the time evolution of a qubit weakly coupled to a
reservoir which has a symmetry broken state with long range order at finite
temperatures. In particular, we model the ordered reservoir by a standard BCS
superconductor with s-wave pairing. We study the reduced density matrix of a
qubit using both the time-convolutionless and Nakajima-Zwanzig approximations.
We study different kinds of couplings between the qubit and the superconducting
bath. We find that ordering in the superconducting bath generically leads to an
unfavorable non- Markovian faster-than-exponential decay of the qubit
coherence. On the other hand, a coupling of the qubit to the non-ordered sector
of the bath can result in a Markovian decoherence of the qubit with a drastic
reduction of the decoherence rate. Since these behaviors are endemic to the
ordered phase, qubits can serve as useful probes of continuous phase
transitions in their environment. We also briefly discuss the validity of our
main result, faster than exponential decay of the qubit coherences, for a qubit
coupled to a generic ordered bath with a spontaneously broken continuous
symmetry at finite temperatures.
