Entropy and Variance Squeezing of V-type Atom in Dissipative Cavity

TL;DR

This work addresses quantum fluctuations in a three-level V-type atom coupled to a dissipative cavity by employing entropic uncertainty relations to define entropy squeezing and comparing it to variance squeezing. The authors solve the atom–cavity dynamics using Fano theory, derive reduced density matrices, and compute $E(S_j)$ and $V(S_j)$ as functions of time, SGI $θ$, detuning $Δ$, and coupling $γ_0/κ$ for two representative initial states. Key findings show that only entropy squeezing in $S_x$ appears (with no $S_y$ squeezing) at resonance, while detuning can induce variance squeezing in $S_x$ and prolong squeezing in both entropy and variance measures; strong coupling enhances entropy squeezing more than weak coupling, and the impact of $θ$ depends on the initial state. These results demonstrate that entropy squeezing provides a more precise quantification of quantum fluctuations than variance squeezing and suggest its usefulness as an ultra-low-noise resource for quantum information processing in open quantum systems.

Abstract

Based on Ref.\cite{Riccardi A}, we investigate the entropy and variance squeezing of a V-type atom in a dissipative cavity, and discuss the influences of parameters including the spontaneously generated interference (SGI) ($θ$), the cavity-environment coupling ($γ_0/κ$) and the atom-cavity detuning ($Δ$) on the atomic squeezing by using different initial states. The results show that no squeezing of $S_y$ occurs under any condition and that variance squeezing of $S_x$ appears only when $Δ>0$. Entropy squeezing quantifies quantum fluctuations more precisely than variance squeezing. Moreover, the atomic squeezing of $S_x$ clearly depends on $θ$, $γ_0/κ$, $Δ$ and the initial state. These findings are meaningful for quantum information processing as an ultra-low-noise resource.

Figures (8)

• Figure 1: Time evolution of atomic squeezing factors $E(S_x)$, $E(S_y)$, $V(S_x)$, $V(S_y)$, and atomic inversion $\langle S_{z}\rangle$ for the V-type three-level atom with $\gamma_0= 0.1$ (green dot dashed line), $\gamma_0 = 10$ (red solid line). The other parameters are $\theta = 0.5$, $\Delta = 0$, $\kappa = 1$. (a) entropy squeezing factor $E(S_x)$; (b) entropy squeezing factor $E(S_y)$; (c) variance squeezing factor $V(S_x)$; (d) variance squeezing factor $V(S_y)$; (e) atomic inversion $\langle S_{z}\rangle$.
• Figure 2: Time evolution of squeezing factors $E(S_x)$, $E(S_y)$, $V(S_x)$, $V(S_y)$, and atomic inversion $\langle S_{z}\rangle$ for the V-type three-level atom with $\theta=0$ (green dot dashed line), $\theta=0.5$ (blue dashed line), $\theta=1$ (red solid line). The atom is initially in the superposition state of $|A\rangle$ and $|C\rangle$, with $\alpha = \frac{\pi}{4}$, $\beta = 0$. The other parameters are $\Delta = 0$, $\gamma_0= 10$ and $\kappa = 1$. (a) entropy squeezing factor $E(S_x)$; (b) entropy squeezing factor $E(S_y)$; (c) variance squeezing factor $V(S_x)$; (d) variance squeezing factor $V(S_y)$; (e) atomic inversion $\langle S_{z}\rangle$.
• Figure 3: Time evolution of squeezing factors $E(S_x)$, $E(S_y)$, $V(S_x)$, $V(S_y)$, and atomic inversion $\langle S_{z}\rangle$ for the V-type three-level atom with $\gamma_0=0.1$ (green dot dashed line), $\gamma_0=10$ (red solid line). And the other parameters are $\theta = 1$, $\Delta = 0$, $\kappa = 1$. (a) entropy squeezing factor $E(S_x)$; (b) entropy squeezing factor $E(S_y)$; (c) variance squeezing factor $V(S_x)$; (d) variance squeezing factor $V(S_y)$; (e) atomic inversion $\langle S_{z}\rangle$.
• Figure 4: Time evolution of squeezing factors $E(S_x)$, $E(S_y)$, $V(S_x)$, $V(S_y)$, and atomic inversion $\langle S_{z}\rangle$ for the V-type three-level atom with $\theta=0$ (green dot dashed line), $\theta=0.5$ (blue dashed line), $\theta=1$ (red solid line). The other parameters are $\gamma_0 = 10$, $\Delta = 0$, $\kappa = 1$. Subplots: (a) entropy squeezing factor $E(S_x)$; (b) entropy squeezing factor $E(S_y)$; (c) variance squeezing factor $V(S_x)$; (d) variance squeezing factor $V(S_y)$; (e) atomic inversion $\langle S_{z}\rangle$.
• Figure 5: Time evolution of squeezing factors $E(S_x)$, $E(S_y)$, $V(S_x)$, $V(S_y)$, and atomic inversion $\langle S_{z}\rangle$ for the V-type three-level atom with $\gamma_0=0.1$ (green dot dashed line), $\gamma_0=10$ (red solid line). The other parameters are $\theta = 1$, $\Delta = 5$, $\kappa = 1$. Subplots: (a) entropy squeezing factor $E(S_x)$; (b) entropy squeezing factor $E(S_y)$; (c) variance squeezing factor $V(S_x)$; (d) variance squeezing factor $V(S_y)$; (e) atomic inversion $\langle S_{z}\rangle$