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Annalen der Physik

Non‐Markovian Dynamics of Quantum Resources in an Anisotropic Photonic Bandgap Crystal: Metrology and Entanglement

S. Nafise Mousavi, Shahpoor Saeidian, Ghasem Naeimi

Published May 1, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1002/andp.202500528

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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.
Entanglement evolution for a classically pumped three-level atom interacting with an anisotropic structured reservoir is studied. We demonstrate that entanglement decay is much slower in the reservoir with the memory effects. This point is beneficial for the implementation of quantum computation in the non-Markovian environments. Unlike the free-space case, the unusual reservoir stimulates stationary entanglement with amplitude depends strongly on the relative phase between the control laser coupling the two upper levels and the pump laser pulse used to create an excited state of the atom in a coherent superposition of the two upper levels. An optimal stationary degree of entanglement is achieved for negative relative phase, where both detunings - from the upper band gap and driving laser - are the same. Moreover, a significant stationary degre e of entanglement is reached, for high detuned upper levels with the pump laser pulse, on resonant frequency near the edge of the PBG. For entanglement in stationary regime, the Rabi frequency of the control laser field exceeds the rate of entanglement degradation or e nhancement for tuned or detuned frequency from the band gap, depending on the relative phase value.
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.
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.
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.
The entanglement dynamics of a V-type three-level atom and its radiation field near the band edge of a photonic crystal is investigated. It is shown that the entanglement dynamics experiences periodic oscillation behavior with a constant amplitude, and can be enhanced or reduced by the quantum interference between the two atomic transitions. These properties depend strongly on the relative position between the upper levels and the band edge, and on the initial state of the atom. There is a special position at which the time evolution of the entanglement changes from oscillating to constant in long time limits.
By means of Von Neumann entropy and Schmidt number K, we study the time evolution properties of the entanglement between a two-level atom and spontaneous emission field in anisotropic photonic crystal. The evolution properties of the atom-field entanglement are directly related to the relative position of the upper level from the band edge. The atom-field entanglement can keep steady when the atomic upper level is within the band gap. The atom-field entanglement increases to the maximum value firstly and then decay to zero when the atomic upper level is within the transmitting band. The atom-field entanglement also depends on the initial state of the atom. We can control the time evolution properties of the atom-field entanglement by choosing special atomic initial state and the relative position of the upper level from the band edge.