Dynamics and quantum Zeno effect for a qubit in either a low- or high-frequency bath: A non-markovian approach beyond the rotating-wave approximation

摘要

We use a non-Markovian approach to study the decoherence dynamics of a qubitin either a low- or high-frequency bath modeling the qubit environment. Thisapproach is based on a unitary transformation and does not require therotating-wave approximation. We show that for low-frequency noise, the bathshifts the qubit energy towards higher energies (blue shift), while theordinary high-frequency cutoff Ohmic bath shifts the qubit energy towards lowerenergies (red shift). In order to preserve the coherence of the qubit, we alsoinvestigate the quantum Zeno effect in two cases: low- and high-frequencybaths. For very frequent projective measurements, the low-frequency bath givesrise to the quantum anti-Zeno effect on the qubit. The quantum Zeno effect onlyoccurs in the high-frequency cutoff Ohmic bath, after consideringcounter-rotating terms. For a high-frequency environment, the decay rate shouldbe faster (without frequent measurements) or slower (with frequentmeasurements, in the Zeno regime), compared to the low-frequency bath case. Theexperimental implementation of our results here could distinguish the type ofbath (either a low- or high-frequency one) and protect the coherence of thequbit by modulating the dominant frequency of its environment.