Revealing the non-classicality of a molecular nanomagnet

TL;DR

This work investigates whether molecular nanomagnets, specifically single-molecule magnets (SMMs) like Fe$_8$ and Mn$_{12}$, exhibit genuine non-classical behavior. By placing an SMM inside a multi-mode cavity and applying a non-classicality criterion that entanglement between two non-interacting probes mediated by an inaccessible object implies quantum correlations in the mediator, the authors analyze three modeling levels: a zeroth-order Gaussian (Holstein–Primakoff) approximation, inclusion of a nuclear-spin bath, and a second-order nonlinear (Kerr-like) correction, complemented by a density-matrix master equation approach. Across Fe$_8$ and Mn$_{12}$ and for various bath strengths and anisotropy values, they consistently observe entanglement between cavity modes induced by the SMM mediator, indicating the SMMs’ intrinsic quantum nature and their viability as resources for quantum information processing. The results demonstrate robust non-classicality under realistic conditions, and point to future extensions to ensembles, multi-molecule architectures, and chemically engineered SMMs for scalable quantum technologies, including memory, spintronics, and sensing applications.

Abstract

Molecular nanomagnets are compounds characterized by a high-spin magnetic core that is protected by organic ligands. They have recently gained attention as potential quantum information carriers in solid-state quantum computing platforms, simultaneously exhibiting classical macroscopic properties and quantum features in light of their complex nature and configuration. Addressing the condition when they manifest unquestionable quantum behavior is key to guarantee their effectiveness as resources for quantum information processing. We address the quantumness of molecular nanomagnets using a recently formulated criterion [cf. Krisnanda et al., Phys. Rev. Lett. 119, 120402 (2017)] demonstrating that these systems exhibit an intrinsic quantum nature, as evidenced by their ability to generate and enhance quantum correlations between two non-interacting probes. Our analysis, which is performed addressing various dynamical regimes, paves the way to the design of experimentally viable tests of non-classicality in multipartite registers consisting of ensembles of molecular nanomagnets.

Figures (7)

• Figure 1: (Top panel) Probes A and B individually interact with a mediator object C, but not with each other. Each system is open to its own environment, represented by the colored shadows. (Bottom panel) Schematic representation of the working setup: an SMM is placed inside a multi-mode cavity. The straight black arrow indicates the presence of a magnetic field $B$, while the straight red arrow represents the external drive. The wavy red and orange arrows represent, respectively, the energy decay rates for the $m^{\text{th}}$-cavity mode and for the nanomagnet. Each cavity mode has a different frequency and they do not interact with each other.
• Figure 2: A. A. Bipartite entanglement in the zeroth-order case, without the effect of the bath, and in the first-order case, including the bath. The introduction of the environment leads to a reduction in entanglement without significantly altering its shape, as expected; B. B. Bipartite entanglement in the zeroth-order case, without the effect of the bath; in the first-order case, including the bath and in the second-order case, adding the non-linear terms with $K_1 = 3.6 \cdot 10^{10}~\mathrm{Hz}$ and $K_2 = 1420 \cdot 10^6~\mathrm{Hz}$; C. C. First-order bipartite entanglement (time-averaged over the interval [$0$, $0.8]~\mathrm{ns}$) varying the hyperfine coupling strength: the environmental effect remains negligible until a certain value of $\alpha$ is reached; once this threshold is exceeded, the entanglement is rapidly destroyed. The 3D inset explicitly illustrates three representative cases of entanglement dynamics, the yellow curve corresponds to the zeroth-order case, which remains unaffected by variation in the hyperfine coupling strength; D. D. First-order bipartite entanglement (time-averaged over the interval [$0$, $0.8]~\mathrm{ns}$) varying the number of spins in the bath. A higher number of spins in the bath increases the impact of the environment on the SMM, as expected. For all figures, without explicitly saying different, the parameters used are: $B = 0.01~\mathrm{T}\text{,}\ E = 6.02\cdot 10^9~\mathrm{Hz}\text{,}\ D = 3.6 \cdot 10^{10}~\mathrm{Hz}\text{,}\ S = 10 \text{,} \ \omega=6.75\cdot10^{11}~\mathrm{Hz} \text{,} \ J= 25 \ \text{and} \ \alpha=\gamma=1420 \cdot 10^6~\mathrm{Hz}.$
• Figure 3: Comparison between the entanglement for $\text{Fe}_{8}$ obtained using the two different approaches. The columns show (from left to right) DM vs. zeroth-order CM, DM vs. first-order CM, and DM vs. second-order CM. The rows correspond to different axial anisotropy constants: first row $D$, second row $3D$. For the simulations: $B = 0.01\ \mathrm{T} \text{,} \ E = 6.02\cdot 10^9 ~\mathrm{Hz} \text{,} \ D = 3.6 \cdot 10^{10} ~\mathrm{Hz} \text{,} \ S = 3 \text{,}\ \omega = 6.75\cdot10^{11} ~\mathrm{Hz} \text{,} \ \kappa_s = 10^9~\mathrm{Hz} \text{,} \ \kappa = 7.5 \cdot 10^9~\mathrm{Hz} \ \ \text{and} \ P = 0.01 \ \mathrm{pW}$. The dashed lines indicate the entanglement averaged over the considered time interval.
• Figure 4: Bipartite entanglement for $\text{Mn}_{12}$ in the zeroth-order case (without the effect of the bath), in the first-order case (including the bath), and in the second-order case (adding the non-linear terms). The parameters used are: $B = 0.01~\mathrm{T}\text{,} \ D=K_1= 8.64 \cdot 10^{10}~\mathrm{Hz}\text{,} \ E = 0 \text{,} \ \omega= 1.64 \cdot 10^{12}~\mathrm{Hz} \text{,} \ S = 10 \text{,} \ \alpha=\gamma=K_2=1420 \cdot 10^6~\mathrm{Hz} \ \text{and} \ J=25.$
• Figure 5: Comparison between the entanglement for $\text{Mn}_{12}$ obtained using the two different approaches. The columns show (from left to right) DM vs. zeroth-order CM, DM vs. first-order CM, and DM vs. second-order CM. The rows correspond to different axial anisotropy constants: first row $D$, second row $3D$. For the simulations: $B = 0.01\ \mathrm{T} \text{,}\ D = 8.64 \cdot 10^{10} ~\mathrm{Hz} \text{,}\ E = 0 \text{,} \ S = 3 \text{,}\ \omega = 1.64\cdot10^{12} ~\mathrm{Hz}\text{,} \ \kappa_s = 10^9~\mathrm{Hz} \text{,} \ \kappa = 7.5 \cdot 10^9~\mathrm{Hz} \ \text{and} \ P = 0.01 \ \mathrm{pW}$. The dashed lines indicate the entanglement averaged over the considered time interval.