Decoherence induced by an ordered environment

Abstract

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.

Single spin probe of many-body localization

“…The study of the decoherence dynamics of a single spin attached to a bath has a long history [25][26][27][28][29][30][31][32] . In particular, the roles of soft modes close to second order phase transition 27,33 , or the presence of a non-vanishing order-parameter in the bath have been studied in depth.…”

Heat current characteristics in nanojunctions with superconducting baths

“…The time to achieve steady state following a reversal of temperature bias is determined by the relaxation time of the setup. Here, the BCS reservoir brings another advantage which can be argued as follows: The Markovian relaxation is described by 19,30 ln σ z (t) ∝ − ν=L,R γ ν t with the relaxation rate γ ν (ω) ∝ [k ν (ω) + k ν (−ω)]. For small splitting of the qubit levels, the BCS rate dominates because of its singular behaviour at low fields.…”

“…The accuracy of these schemes depends on the problem studied, making it difficult to assert a priori which one is more appropriate 21,22 . In the present problem, since the qubit has intrinsic dynamics H S = 0, we anticipate a Markovian time evolution of the reduced density matrix at long times 19 . This evolution is well described by the usual Born-Markov master equation derived below.…”

“…The rate for the BCS reservoir cannot be evaluated analytically for all frequencies ω and temperatures 0 < T < T C 19 . In particular, it is singular for ω → 0 due to the singularity of the DOS at E = ∆, and it shows a pseudogap due to the gap in the density of states.…”

“…In particular, it is singular for ω → 0 due to the singularity of the DOS at E = ∆, and it shows a pseudogap due to the gap in the density of states. For 0 < ω ∆ Λ 19 , (this excludes regions close to T C , where the gap ∆ is very small),…”