Abstract
A universal approach to decoherence control combined with quantum estimation theory reveals a critical behavior, akin to a phase transition, of the information obtainable by a qubit probe concerning the memory time of environmental fluctuations. This criticality emerges only when the probe is subject to dynamical control. It gives rise to a sharp transition between two dynamical phases characterized by either a short or long memory time compared to the probing time. This phase-transition of the environmental information is a fundamental feature that facilitates the attainment of the highest estimation precision of the environment memory-time and the characterization of probe dynamics.
Highlights
A universal approach to decoherence control combined with quantum estimation theory reveals a critical behavior, akin to a phase transition, of the information obtainable by a qubit probe concerning the memory time of environmental fluctuations
For the purpose of environment-noise spectroscopy it is useful to resort to the universal formula for the rate of decoherence under dynamical control [22,23,24,25], which is at the heart of the unified theory of dynamically-controlled open quantum systems [26,27,28]
This universal formula allows the design of control fields or pulse sequences that through the choice of a spectral filter function are optimally tailored to the specific environment-noise spectrum and the task at hand [25, 29]: decoherence control [22, 23, 26, 27, 30,31,32,33,34], state-transfer [35, 36] or storage [36,37,38] in a fluctuating environment
Summary
The derivative of the spectrum dG dτc exhibits a critical behavior dG dτc. The two dynamical regimes occur when the narrow filters probe frequency components of G(ω) on both sides of the critical point. (green, in linear scale) scan the spectrum on both sides of the transition πN ωctrl. (b) The attainable relative erro√r εcFtrl(τc, t τc by the qubit-probe under CW control
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