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arXiv:2312.09910

Dynamics of Quantum Coherence and Quantum Fisher Information of a V-type Atom in Isotropic Photonic Crystal

Ghafar Ahmadi, Shahpoor Saeidian, Ghasem Naeimi

Published Dec 15, 2023• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2312.09910

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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.
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.
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.
We demonstrate the coherent control of spontaneous emission for a three-level atom located within a photonic band-gap structure with one resonant frequency near the edge of the photonic band gap. Spontaneous emission from the three-level atom can be totally suppressed or strongly enhanced depending on the relative phase between the steady-state control laser coupling the two upper levels and the pump laser pulse used to create an excited state of the atom in the form of a coherent superposition of the two upper levels. Unlike the free-space case, the steady-state inversion of the atomic system is strongly dependent on the externally prescribed initial conditions. This nonzero steady-state population is achieved by virtue of the localization of light in the vicinity of the emitting atom. It is robust to decoherence effects provided that the Rabi frequency of the control laser field-atom interaction exceeds the rate of dephasing interactions. As a result, such a system may be relevant for a single-atom, phase-sensitive, optical memory device on the atomic scale. The protected electric dipole within the photonic band gap provides a basis for a qubit to encode information for quantum computations.