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Annalen der Physik

Coherent Control of the Dynamics of Quantum Fisher Information and Geometric Phase in a 1D Photonic Crystal Waveguide

Negar Nikdel Yousefi, Ali Mortezapour

Published Jan 22, 2024• 2 citations
Publisher

Abstract

Abstract It is aimed to study a hybrid quantum‐classical system in which a qubit as a quantum system coupled to a semi‐infinite 1D photonic crystal (PC) waveguide, and is controlled by a classical driving field. PC waveguides with engineering capability serve as engineered reservoirs where various manifestations of quantum mechanics can be studied. Here, the main purpose of the study is to evaluate the effect of coherent control on the dynamics of quantum Fisher information (QFI) and geometric phase (GP). It is revealed that the intensity (the Rabi frequency) of the classical field, memory time, and geometric length of the waveguide are key variables whose judicious choice aids in optimizing the estimation of the quantum parameters that are initially encoded in the qubit state. It is observed that the optical length of the waveguide and the Rabi frequency of the classical field have an interplay effect on the dynamic of the QFI and geometric phase. As an interesting finding, it is disclosed that as the Rabi frequency increases, the effect of the optical length of the waveguide fades away, and the Rabi frequency solely controls the geometric phase. Moreover, it is demonstrated that the estimation accuracy increases as the memory time decreases. On the other hand, lengthening the memory time lessens the dependency of the geometric phase on the length of the waveguide.

DOI
10.1002/andp.202300361

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Abstract It is aimed to study a hybrid quantum‐classical system in which a qubit as a quantum system coupled to a semi‐infinite 1D photonic crystal (PC) waveguide, and is controlled by a classical driving field. PC waveguides with engineering capability serve as engineered reservoirs where various manifestations of quantum mechanics can be studied. Here, the main purpose of the study is to evaluate the effect of coherent control on the dynamics of quantum Fisher information (QFI) and geometric phase (GP). It is revealed that the intensity (the Rabi frequency) of the classical field, memory time, and geometric length of the waveguide are key variables whose judicious choice aids in optimizing the estimation of the quantum parameters that are initially encoded in the qubit state. It is observed that the optical length of the waveguide and the Rabi frequency of the classical field have an interplay effect on the dynamic of the QFI and geometric phase. As an interesting finding, it is disclosed that as the Rabi frequency increases, the effect of the optical length of the waveguide fades away, and the Rabi frequency solely controls the geometric phase. Moreover, it is demonstrated that the estimation accuracy increases as the memory time decreases. On the other hand, lengthening the memory time lessens the dependency of the geometric phase on the length of the waveguide.
ABSTRACT We study the time evolution of quantum Fisher information and atom–field entanglement for a V‐type three‐level atom embedded in an anisotropic photonic bandgap crystal. The structured reservoir strongly modifies the atomic decay near the photonic bandgap, giving rise to non‐Markovian memory effects. By employing the quantum Fisher information matrix, we determine the quantum Cramér‐Rao bound for both single‐parameter estimation and simultaneous two‐parameter estimation encoded in the atomic initial state. In parallel, we investigate the dynamics of atom‐field entanglement, quantified through the Von Neumann entropy, to characterize the correlations resulting from the interaction with the photonic bandgap. Our results show that both the detuning of the atomic transition frequency from the upper band edge frequency and the initial relative phase play a crucial role in the attainable precision and long‐lived entanglement. These findings demonstrate the potential of photonic bandgap materials as structured reservoirs for protecting quantum information, sustaining long‐time entanglement, and enhancing multiparameter quantum metrology.
We investigate the simultaneous control of quantum parameter-estimation precision and non-Markovian memory effects in a driven two-qubit system that is collectively coupled to a leaky cavity. Using a dressed-state formalism, we derive analytical solutions for identical and non-identical qubits and analyze how classical driving and detuning affect metrological performance. Classical driving enhances the quantum Fisher information (QFI) by sustaining coherence and shifting effective transitions away from cavity resonance, thereby suppressing decoherence in both weak- and strong-coupling regimes. The steady-state QFI is further improved by positive classical-field detuning, which reduces spectral overlap with the lossy reservoir. To characterize memory effects, we examine the QFI-flow and the Breuer–Laine–Piilo (BLP) trace-distance measure. Our results reveal a nontrivial control trade-off: increasing the Rabi frequency suppresses non-Markovian information backflow, whereas increasing qubit detuning enhances memory effects by promoting system–environment correlations. Despite their different definitions, the QFI-flow and BLP measures yield consistent qualitative behavior in this system. These findings demonstrate that classical-field parameter tuning empowers researchers to optimize estimation precision and non-Markovianity in dissipative cavity-QED, with direct applicability to superconducting circuit platforms.
Quantum Fisher information (QFI) and geometric phase have recently performed different tasks in quantum information technology. We investigate the statistical quantities as the QFI and entanglement of a three‐level atom in Λ configuration interacting with a quantized field mode by using linear entropy. We study the dynamical behavior of the geometric phase based on the engineering of a three‐level atomic configuration. We analyze the effect of energy dissipation of the dynamical properties of the geometric phase and the QFI as an entanglement quantifier between the three‐level atom and field. We explore the correlation between the engineering geometric phase and QFI in the absence and presence of energy dissipation effect. We have found that the QFI is very sensitive to the effect of the time‐dependent coupling and energy dissipation.
A comparative study of a qutrit (three-level atomic system) coupled to a classical field in a typical Markovian reservoir (free space) and in a photonic-band-gap (PBG) crystal is carried out. The aim of the study is to assess the collective impact of a structured environment and classical control of the system on the dynamics of quantum coherence, non-Markovianity, and estimation of parameters that are initially encoded in the atomic state. We show that the constructive interplay of PBG material as a medium and a classical driving field as a part of the system results in a significant enhancement of all the quantum traits of interest, compared to the case when the driven qutrit is in a Markovian environment. Our results supply insights for preserving and enhancing quantum features in qutrit systems, which are promising alternative candidates to be used in quantum processors instead of qubits.
We study the non-Markovian effect on the dynamics of the quantum Fisher information (QFI) by exactly solving a model consisting of a qubit system subjects to a zero-temperature reservoir for two different non-Markovian conditions: a high-QQQ cavity slightly off-resonant with the qubit transition frequency and a nonperfect photonic band gap, respectively. The phenomenon that the QFI, namely, the precision of estimation, changes dramatically with the environment structure and is affected by the environment memory effects. We find that revivals and retardation of QFI loss may occur by adjusting the cavity-qubit detuning, in the first case, while partial QFI trapping occurs in nonideal photonic band gaps and the decreasing gap width seriously destroys coherence, thus reducing the precision of estimation. These features make the qubit system in non-Markovian environments a good candidate for implementation of quantum optics schemes and information with high precision.
Quantum speedup of an open quantum system can be induced by the non-Markovian effect of the environment. Although an environment with a higher degree of non-Markovianity may seem like it should cause a faster speed of quantum evolution, this seemingly intuitive thinking may not always be correct. To clarify this point, we give a mechanism for controlling speedup of a single qubit that is coupled to a hierarchical photonic-crystal (PC) environment, which contains a defect single-mode cavity and a semi-infinite one-dimensional (1D) waveguide. Via studying the dynamics of the qubit, we reveal that with a judicious choice of the qubit-cavity coupling strength and the memory time of the waveguide environment, a speed-up evolution can be achieved. In particular, we found that the quantum speedup is not entirely attributed to the non-Markovianity, but to the increase of the total amount of flow information. That is the intrinsic physical reason that the hierarchical environment may induce the speed-up process. Our results may open new perspectives for detecting quantum speedup in realistic environments.