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Journal of the Optical Society of America B

Protecting the precision of estimation in a photonic crystal

K. Berrada

Published Mar 10, 2015• 31 citations
Publisher

Abstract

The quantum Fisher information (QFI) of a two-level atom in an anisotropic and isotropic photonic band-gap (PBG) crystal has been studied without Born or Markovian approximation. We show that the precision of the parameter estimation for the two-level atom in the photonic crystal is greatly different from that of a two-level atom in vacuum or that subjected to the usual non-Markovian reservoir. The phenomenon shows that the QFI, namely, the precision of estimation, changes dramatically with the environment structure. The results also show that, for PBG materials, environmentally high values of QFI trapping can be achieved and thus prevention of QFI sudden drop occurs, which greatly enhances the coherence and increases the precision of estimation. Moreover, the QFI in the isotropic PBG is more easily preserved than that of the anisotropic PBG under the same condition. These features make the atom system in PBG materials a good candidate for implementation of different schemes of quantum optics and information with high precision.

DOI
10.1364/josab.32.000571

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The quantum Fisher information (QFI) of a two-level atom in an anisotropic and isotropic photonic band-gap (PBG) crystal has been studied without Born or Markovian approximation. We show that the precision of the parameter estimation for the two-level atom in the photonic crystal is greatly different from that of a two-level atom in vacuum or that subjected to the usual non-Markovian reservoir. The phenomenon shows that the QFI, namely, the precision of estimation, changes dramatically with the environment structure. The results also show that, for PBG materials, environmentally high values of QFI trapping can be achieved and thus prevention of QFI sudden drop occurs, which greatly enhances the coherence and increases the precision of estimation. Moreover, the QFI in the isotropic PBG is more easily preserved than that of the anisotropic PBG under the same condition. These features make the atom system in PBG materials a good candidate for implementation of different schemes of quantum optics and information with high precision.
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.
The time evolution of quantum Fisher information, quantum coherence, and non-Markovianity of a V-type three-level atom embedded in free space or a photonic band gap crystal have been investigated. It has been demonstrated that the photonic band gap crystal, as a structured environment, significantly influences the preservation and enhancement of these quantum features. Additionally, we observe that by manipulating the initial relative phase values encoded in the atomic state and the relative positions of the upper levels within the forbidden gap, control over the dynamics of quantum features can be achieved. These findings highlight the potential benefits of utilizing photonic band gap crystals in quantum systems, offering improved preservation and manipulation of quantum information. The ability to control quantum features opens new avenues for applications in quantum information processing and related technologies.
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.
The spontaneous emission spectrum from a four-level atom in a double-band photonic crystal has been investigated. We use the model which assumes three atomic transitions. One of the transitions interacts with the free vacuum modes and the other two transitions couple to the modes of the isotropic photonic band gap (PBG), the anisotropic PBG and another free vacuum. The effects of the fine structure of the lower levels on the spontaneous emission spectrum of an atom are investigated in detail in the three cases. New features of four (two) transparencies with two (one) spontaneous emission peaks, resulting from the fine structure of the lower levels of an atom, are predicted in the case of isotropic PBG modes.
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.
In this paper, the time evolution of quantum coherence and Hilbert-Schmidt speed, as a criterion to measure the memory of the quantum system, of a V-type three-level atom embedded in an anisotropic photonic crystal are investigated. The effect of the different relative positions of the upper levels from the forbidden gap and the initial relative phase values on the mentioned quantum features are studied. We show that the photonic band gap crystal, as a structured environment, significantly influences the preservation and enhancement of these quantum features. The photonic gap band materials have non-Markovian properties and offer a new approach as a basic solution in overcoming the decoherence problem and subsequently in problems related to quantum information.