Quantum entanglement and Einstein-Podolsky-Rosen steering in ultrastrongly light-matter coupled system

TL;DR

The paper addresses how to generate and control quantum entanglement and EPR steering in a two-mode Hopfield-type light–matter system coupled to a common reservoir. It employs Gaussian-state formalism, covariance matrices, and PPT/steering criteria to analyze ground-state and thermal correlations, highlighting the distinct roles of squeezing, mode-mixing, and the diamagnetic term. Key findings show that ground-state entanglement is enhanced by ultrastrong/deep-strong coupling via a combination of squeezing and mixing, with two-way steering possible in resonant regimes and one-way steering induced by diamagnetic asymmetry; these effects persist under moderate temperatures and across a range of frequencies. The work offers a route to robust quantum correlations for quantum information tasks and outlines experimental avenues using cavity optomagnonics and superconducting platforms, as well as extensions to multi-mode cavities.

Abstract

This work presents a scheme for engineering quantum entanglement and Einstein-Podolsky-Rosen (EPR) steering with Gaussian measurements based on the quantum Hopfield model that incorporates a common thermal reservoir. We begin by examining quantum correlations, specifically quantum entanglement and EPR steering, in the ground state. These quantum correlations primarily stem from squeezing interactions in weak and normal strong coupling regimes. As the coupling strength increases, especially upon entering the ultrastrong coupling regime, the correlations emerge from the combined effect of squeezing and mix-mode interactions. Importantly, this scenario enables the realization of two-way EPR steering. Moreover, lower optical frequencies enhance both quantum entanglement and EPR steering. Further, when considering thermal effects, the ultrastrong and deep strong coupling regimes, paired with lower optical frequencies, lead to improved entanglement. The one-way EPR steering for resonant case can be effectively controlled in the ultrastrong and deep strong coupling regimes which originates from the asymmetry of subsystem and reservoir coupling induced by the diamagnetic term. Additionally, one-way EPR steering can also be produced for nonresonant case. In this case, the asymmetry of the subsystem and reservoir originates from the combined effect of nonresonant frequencies and diamagnetic term. Our findings have the potential to inspire further research into quantum information processing that leverages light-matter entanglement and EPR steering.

Figures (8)

• Figure 1: (a) A diagram of two ultrastrongly coupled oscillators consisting of a cavity photon mode and a matter mode; (b) The two coupled oscillators with modes $a$ and $b$, sharing a common thermal reservoir at temperature $T$.
• Figure 2: The quantum entanglement is analyzed along with $\mathcal{G}^{a \rightarrow b}$, $\mathcal{G}^{b \rightarrow a}$ about the coupling strength $\lambda$ for different frequencies $\omega_{a}$. In panels (a) and (b), the internal coupling is considered full coupling, incorporating mode-mixing and mode-squeezing interactions. In contrast, panels (c) and (d) examine mode-squeezing ($\lambda=\lambda_2$, $\lambda_1=0$) and mode-mixing ($\lambda=\lambda_1$, $\lambda_2=0$) interactions separately, comparing them to the effect of full coupling. It is important to note that the square lines in (b) represent the reverse EPR steering $\mathcal{G}^{b \rightarrow a}$. The parameters in panels (c) and (d) can be set such that $\omega_{a} = \omega_{b}$.
• Figure 3: (a) Plot of quantum entanglement as a function of optical frequency $\omega_{a}$ and coupling strength $\lambda$; (b) Plot of quantum entanglement as a function of temperature $T$ and coupling strength $\lambda$. The parameter values are specified as follows: (a) $T = 0.15\omega_{b}$; (b) $\omega_{a} = \omega_{b}$.
• Figure 4: The polaritons frequencies $\omega_{j}$ with $j=U, L$ are plotted against the coupling strength $\lambda$ for various optical frequencies $\omega_{a}$. The red, blue, green, and black lines represent the ratios $\omega_{a}/\omega_{b} = 0.01, 0.1, 1, 5$, respectively. Solid lines indicate upper polaritons, whereas other lines represent lower polaritons.
• Figure 5: Quantum steering $\mathcal{G}^{a \rightarrow b}$ (a) and $\mathcal{G}^{b \rightarrow a}$ (b) are analyzed in relation to the frequency $\omega_{a}$ and the coupling strength $\lambda$; for panels (c) and (d), $\mathcal{G}^{a \rightarrow b}$ and $\mathcal{G}^{b \rightarrow a}$ are examined as functions of temperature $T$ and $\lambda$. The parameters are set as follows: for panels (a) and (b), $T=0.15\omega_{b}$; and for panels (c) and (d), $\omega_{a}=\omega_{b}$.