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Entropy

Quantum Interference Effects on Information Phase Space and Entropy Squeezing

Abdel‐Baset A. Mohamed, Shoukry S. Hassan, Rania A. Alharbey

Published Feb 5, 2019• 2 citations
Publisher

Abstract

Wehrl entropy and its density are used to investigate the dynamics of loss of coherence and information in a phase space for an atomic model of two-photon two-level atom coupled to different radiation reservoirs (namely, normal vacuum (NV), thermal field (TF) and squeezed vacuum (SV) reservoirs). Particularly, quantum interference (QI) effect, due to the 2-photon transition decay channels, has a paramount role in: (i) the atomic inversion decay in the NV case, which behaves as quantum Zeno and anti-Zeno decay effect; (ii) the coherence and information loss in the phase space; and (iii) identifying temporal information entropy squeezing. Results are also sensitive to the initial atomic state.

DOI
10.3390/e21020147

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Wehrl entropy and its density are used to investigate the dynamics of loss of coherence and information in a phase space for an atomic model of two-photon two-level atom coupled to different radiation reservoirs (namely, normal vacuum (NV), thermal field (TF) and squeezed vacuum (SV) reservoirs). Particularly, quantum interference (QI) effect, due to the 2-photon transition decay channels, has a paramount role in: (i) the atomic inversion decay in the NV case, which behaves as quantum Zeno and anti-Zeno decay effect; (ii) the coherence and information loss in the phase space; and (iii) identifying temporal information entropy squeezing. Results are also sensitive to the initial atomic state.
This work explores the dynamics of quantum Fisher information (QFI) in open quantum systems coupled to squeezed reservoirs, providing a mathematical framework for analyzing parameter estimation precision under decoherence. We analyze QFI in two-qubit systems undergoing pure dephasing, considering the effects of squeezing parameter, phase difference, and coupling strength within an Ohmic spectral density model. The decoherence factor shows how reservoir engineering influences coherence loss. Numerical results demonstrate that optimal squeezing and local bath configurations enhance QFI preservation, while collective couplings accelerate decay. We also examine the interplay with von Neumann entropy, highlighting their inverse correlation, where increased mixedness reduces metrological sensitivity.
From a quantum information point of view we investigate the entropy squeezing properties for a two-level atom interacting with the two-mode coherent fields via the two-photon transition. We discuss the influences of the initial state of the system on the atomic information entropy squeezing. Our results show that the squeezed component number,squeezed direction, and time of the information entropy squeezing can be controlled by choosing atomic distribution angle,the relative phase between the atom and the two-mode field, and the difference of the average photon number of the two field modes, respectively. Quantum information entropy is a remarkable precision measure for the atomic squeezing.
From a quantum information point of view we investigate the entropy squeezing properties for a two-level atom interacting with the two-mode coherent fields via the two-photon transition. We discuss the influences of the initial state of the system on the atomic information entropy squeezing. Our results show that the squeezed component number, squeezed direction, and time of the information entropy squeezing can be controlled by choosing atomic distribution angle, the relative phase between the atom and the two-mode field, and the difference of the average photon number of the two field modes, respectively. Quantum information entropy is a remarkable precision measure for the atomic squeezing.
Abstract The c-number atomic Bloch equations modelling the coupling of a 2-photon 2-level single atom with a non-resonant ( Δ ≠ 0 ) squeezed vacuum (SV) radiation reservoir show that: (i) The quantum interference (QI) process, of parameter f ≠ 0 , between the 2-photon transition channels causes coupling of the atomic variables (inversion and polarisation), and, (ii) The SV reservoir parameters ( N , M ) induce periodic coefficients and hence inhibited oscillatory behaviour in the atomic variables. Perturbative analytical solutions of these non-autonomous Bloch equations are derived and used to calculate the absorption spectrum of a weak field probing the system. Of particular, the zero-absorption isolines in the relevant ( N , f )- and ( Δ , f )-planes of the system parameters are identified computationally. It is found that, the largest set of points, where absorption is zero, in the ( Δ , f ) -plane depends on the choice of the degree of squeezing parameter ( M ) of the SV reservoir .
The interaction of an atomic two-level system and a squeezed vacuum leads to interesting effects in atomic dynamics, including line narrowing in resonance fluorescence and absorption spectra, and a suppressed (enhanced) decay of the in-phase and out-of-phase components of the atomic polarization. On the experimental side these predictions have so far eluded observation, essentially due to the difficulty of embedding atoms in a $4\ensuremath{\pi}$ squeezed vacuum. In this paper we show how to ``engineer'' a squeezed-bath-type interaction for an effective two-level system. In the simplest example, our two-level atom is represented by the two ground levels of an atom with an angular momentum $J=1/\stackrel{\ensuremath{\rightarrow}}{2}J=1/2$ transition (a four-level system), which is driven by (weak) laser fields and coupled to the vacuum reservoir of radiation modes. Interference between the spontaneous emission channels in optical pumping leads to a squeezed-bath-type coupling and thus to symmetry breaking of decay on the Bloch sphere. With this system it should be possible to observe the effects predicted in the context of squeezed-bath--atom interactions. The laser parameters allow one to choose properties of the squeezed-bath interaction, such as the (effective) photon-number expectation number NNN and the squeezing phase $\ensuremath{\varphi}$. We present results of a detailed analytical and numerical study.
The Jaynes–Cummings interaction of a two-level atom with the radiation field is studied when the radiation is initially in a strongly squeezed coherent state. The dynamic response of the atomic inversion shows echoes after each revival when the squeezed coherent state exhibits an oscillatory photon-counting distribution due to the phase-space interference effect. The sensitivity of the dynamic behavior to approximations used in computing the atomic inversion is discussed. Comparison is made with the intensity-dependent interaction model of Buck and Sukumar [ Phys. Lett.81A, 132 ( 1981)]; this model does not exhibit echoes. The mean, variance, and entropy for the photon-number distribution are calculated and found to show behavior similar to that of the atomic inversion.