Entanglement dynamics of Multi-Level Atoms embedded in Photonic Crystals: Leveraging Resonant Dipole-Dipole Interactions and Quantum Interference

TL;DR

The paper tackles entanglement dynamics of two multi-level V-type atoms embedded in photonic crystals, focusing on the cooperative roles of resonant dipole-dipole interactions (RDDI) and vacuum-induced quantum interference near band edges. An analytical model in the single-photon manifold, solved via Schrödinger dynamics and Laplace transforms, yields the time evolution of probability amplitudes and a reduced density matrix from which the logarithmic negativity $E_N$ is computed. Key findings show that anti-parallel dipoles ($\eta=\pi$) significantly prolong entanglement lifetimes near the band edge due to strong RDDI, while orthogonal dipoles ($\eta=\pi/2$) induce oscillatory, non-Markovian entanglement dynamics governed by bound states and interference; the initial state (entangled vs. unentangled) further shapes these effects. The depth of the band-gap placement modulates entanglement: deeper placement suppresses resonant energy exchange via evanescent modes and accelerates decoherence, whereas near-band-edge configurations sustain longer-lived quantum correlations. Overall, the work demonstrates tunable entanglement control in PC platforms and offers design principles for quantum devices leveraging structured photonic environments.

Abstract

We present a comprehensive investigation of entanglement dynamics in multi-level V-type atomic systems embedded within photonic crystals. We mainly focus on the synergistic roles of resonant dipole-dipole interactions and quantum interference through analytical modeling and numerical simulations using the Schrodinger equation. Key findings reveal that resonant interaction dominates when the interatomic distance is comparable to the localization length of photon-atom bound states lying in the bandgap region. For atoms with anti-parallel dipole orientations, both initially entangled and separable states exhibit robust entanglement preservation due to strong collective interactions. Conversely, when dipoles are oriented orthogonally, initially entangled states exhibit unique oscillatory patterns in their entanglement dynamics. This effect arises from the formation of dark states due to destructive interference within the structured photonic environment, with resonant dipole-dipole interactions sustaining non-Markovian dynamics. We further demonstrate that positioning the atomic excited states deeper within the photonic bandgap accelerates the decay of entanglement oscillations due to the exponential suppression of resonant energy exchange mediated by evanescent modes. Our analysis establishes resonant dipole-dipole interactions and quantum interference as potential tools for tailoring entanglement dynamics, paving the way for controlled quantum coherence in photonic crystal platforms.

Figures (8)

• Figure 1: Schematic of two V-type three-level atoms.
• Figure 2: Negativity dynamics as a function of $\beta t$, for unentangled initial state as $\psi(0)=\ket{a_1,a_6}$, for position of dipole transitions to be anti-parallel, $\eta=\pi$ such that $\omega_{1c}=0.6\beta$, $\omega_{2c}=0.2\beta$, and $\omega_{12}=0.4\beta$ for RDDI strengths, (a) $\gamma_1=\gamma_2=1.5\beta$, (b) $\gamma_1=\gamma_2=6\beta$, (c) $\gamma_1=\gamma_2=10\beta$.
• Figure 3: Schematic of atomic splitting for unentangled state as initial state for the position of $\omega_{1c}=0.6\beta$, $\omega_{2c}=0.2\beta$ relative to $\omega_c$, where $\omega_c$ lie below $\ket{a_1}(\ket{a_4})$ and $\ket{a_2}(\ket{a_5})$, and $\omega_{12}=0.4\beta$, when dipole transitions of excited levels $\ket{a_1}(\ket{a_4})$ and $\ket{a_2}(\ket{a_5})$ are, (a) orthogonal, $\eta=\pi/2$, (b) anti-parallel, $\eta=\pi$.
• Figure 4: Negativity dynamics as a function of $\beta t$, for position of dipoles, $\omega_{1c}=-0.6\beta$, $\omega_{2c}=-1\beta$, and $\omega_{12}=0.4\beta$ for anti-parallel, $\eta=\pi$ dipole alignments for different RDDI strengths, (a) $\gamma_1=\gamma_2=1.5\beta$, (b) $\gamma_1=\gamma_2=6\beta$, (c) $\gamma_1=\gamma_2=10\beta$.
• Figure 5: Negativity dynamics as a function of $\beta t$, for position of dipoles, $\omega_{1c}=-0.6\beta$, $\omega_{2c}=-1\beta$, and $\omega_{12}=0.4\beta$ for orthogonal dipole transitions, $\eta=\pi/2$ for different RDDI strengths, (a) $\gamma_1=\gamma_2=1.5\beta$, (b) $\gamma_1=\gamma_2=6\beta$, (c) $\gamma_1=\gamma_2=10\beta$.