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

TL;DR

This paper investigates the decoherence and quantum Zeno effect of a qubit in different frequency baths using a non-Markovian approach that goes beyond the rotating-wave approximation, revealing how bath frequency influences qubit energy shifts and coherence preservation.

Contribution

It introduces a non-Markovian method that models qubit-bath interactions without the rotating-wave approximation, analyzing effects of low- and high-frequency environments on qubit dynamics and coherence.

Findings

Low-frequency bath causes a blue shift in qubit energy.

High-frequency Ohmic bath causes a red shift in qubit energy.

Quantum Zeno effect is observed only in high-frequency baths with counter-rotating terms.

Abstract

We use a non-Markovian approach to study the decoherence dynamics of a qubit in either a low- or high-frequency bath modeling the qubit environment. This approach is based on a unitary transformation and does not require the rotating-wave approximation. We show that for low-frequency noise, the bath shifts the qubit energy towards higher energies (blue shift), while the ordinary high-frequency cutoff Ohmic bath shifts the qubit energy towards lower energies (red shift). In order to preserve the coherence of the qubit, we also investigate the quantum Zeno effect in two cases: low- and high-frequency baths. For very frequent projective measurements, the low-frequency bath gives rise to the quantum anti-Zeno effect on the qubit. The quantum Zeno effect only occurs in the high-frequency cutoff Ohmic bath, after considering counter-rotating terms. For a high-frequency environment, the decay rate should be faster (without frequent measurements) or slower (with frequent measurements, in the Zeno regime), compared to the low-frequency bath case. The experimental implementation of our results here could distinguish the type of bath (either a low- or high-frequency one) and protect the coherence of the qubit by modulating the dominant frequency of its environment.