Decoherence-free Behaviors of Quantum Emitters in Dissipative Photonic Graphene

Abstract

Achieving decoherence-free quantum state manipulation is a paramount goal in modern quantum technologies. To this end, we demonstrate its implementation in a two-dimensional dissipative photonic graphene featuring exceptional rings. Employing the resolvent method, we analytically explore the quantum dynamics of emitters coupled to photonic graphene. In the thermodynamic limit, our analysis predicts a dissipation-dependent logarithmic relaxation for a single quantum emitter, alongside a pronounced quantum Zeno effect that slows the decay with increased dissipation. Notably, within a finite lattice, the excitation of single quantum emitter stabilizes in a decoherence-protected quantum state, which is identified as a dissipation-robust quasilocalized state. Interestingly, this state, together with a dark state, facilitates decoherence-free interactions between quantum emitters. This capability can be extended to topological graphenic platforms, where edge states mediate analogous protected interactions among giant atoms. Our findings highlight a promising path toward protecting quantum coherence in practical, high-dimensional photonic environment through dissipation engineering.

Figures (18)

• Figure 1: (a) Schematic of QEs coupled to a photonic graphene. The dissipative photonic environment is composed of two interspersed triangular sublattices, denoted as A (dark blue) and B (dark red). (b) Real and (c) imaginary components of the complex energy spectrum, $\mathrm{Re}[\omega_{\pm}(\boldsymbol{k})]/J$ and $\mathrm{Im}[\omega_{\pm}(\boldsymbol{k})]/J$, for the bath with single-sublattice dissipation, i.e., $\kappa_{a}=2J,\kappa_{b}=0$. The insets in (b) and (c) show the spectra $\mathrm{Re}[\omega_{+}(\boldsymbol{k})]/J$ and $\mathrm{Im}[\omega_{+}(\boldsymbol{k})]/J$ for the upper band. The dissipation-free photon modes are marked by pentagrams.
• Figure 2: The Markovian decay rates $\Gamma_{e}$ (blue lines) and frequency shifts $\delta_{e}$ (red lines) for a single QE coupled to sublattice A (a) and B (b), plotted against the detuning $\Delta_e/J$ with $\kappa_a=J,\kappa_b=0$. (c) Excited-state population $|C_e(t)|^2$ of a resonant QE ($\Delta_e=0$) located at the center of sublattice A in a photonic graphene of size $N=512$, plotted as a function of scaled time $Jt$ with $\mathrm{g}=0.5J$. The inset of (c) depicts the photonic spatial density distribution $|C_{n_x,n_y}^{\text{A}/\text{B}}|^2$ corresponding to the QLS.
• Figure 3: (a) Time evolution of $|e_1(t)|^2$ (red) and $|e_2(t)|^2$ (green) with coupling strength $\mathrm{g} = 0.01J$. Solid lines and markers denote numerical and analytical results, respectively. (b) and (c) are the spatial photonic wave function profiles $|C_{n_x,n_y}^{\text{A}}|$ (blue) and $|C_{n_x,n_y}^{\text{B}}|$ (red) corresponding to off-diagonal and diagonal disorder with a strength of $W=0.5$. (d) Maximum transferred population, $\max(|e_2(\infty)|^2)$, versus disorder strength $W$ for both disorder types with $\mathrm{g} = 0.1J$. The red (blue) dots and shaded region denote the average and standard deviation over $10^3$ realizations for off-diagonal (diagonal) disorder. Other parameters implemented here are $\Delta_{e} = -\Omega = 0.1J$, $N = 2^6$, $\kappa_a = 10J$, and $\kappa_b = 0$.
• Figure 4: (a) Schematic of a $6\times6$ photonic graphene with SSH-like hoppings $t_{\mathrm{intra}}$ (black links) and $t_{\mathrm{inter}}$ (green links). The unit cell comprises six optical cavities, with three from sublattice A (orange) and three from sublattice B (blue) assigned dissipation strengths $\kappa_a$ and $\kappa_b$, respectively. (b) and (c) are the real and imaginary components of the complex energy spectrum for a lattice of size $L=10$. (d) Spatial profiles of the photonic wavefunctions $|C^{\mathrm{A}}_{n_x,n_y}|$ (blue) and $|C^{\mathrm{B}}_{n_x,n_y}|$ (red) of the edge state for $L=8$ and $t_{\mathrm{inter}}/t_{\mathrm{intra}}=15$. (e) Excited-state population $|e_{1,2}(t)|^2$ of giant atoms coupled to the edge state, where the performed parameters are $L=8$, $\Delta_e=0$, $\Omega=0.02J$, $t_{\mathrm{inter}}/t_{\mathrm{intra}}=15$, and ${\rm{g}}=0.2J$. All panels share the same dissipation strengths $\kappa_a=J$ and $\kappa_b=0$.
• Figure S1: Schematic of the quantum emitters coupled to a photonic tight-binding lattice featuring Dirac cones. The photonic environment consists of two interspersed triangular lattices (marked by dark blue and dark red balls for sites A and B, respectively), where each site represents a bosonic or cavity mode. The primitive vectors $\boldsymbol{v}_{1},\boldsymbol{v}_{2}$ defining the Bravais lattice are plotted in cyan. Each A (B) site is coupled to its three nearest-neighbor B (A) sites via the hopping interactions indicated by brown double-headed arrow. The optical environment features engineered dissipation, manifesting as independently controlled loss rates $\kappa_a$ and $\kappa_b$ for sublattices A and B, respectively. In this scheme, a pair of qubits (represented by the red and blue balls) couples to a single cavity mode of the A sublattice, with a direct coupling $\Omega$ between them. Each quantum emitter is modeled as a two-level system with ground ($|g\rangle$) and excited ($|e\rangle$) states.