Higher-order exceptional lines in a non-Hermitian JaynesCummings triangle

Abstract

Higher-order exceptional points (EPs) in non-Hermitian systems showcase diverse physical phenomena but require more parameter space freedom or symmetries. It leads to a challenge for the exploration of high-order EP geometries in low-dimensional systems. Here we observe both a third-order exceptional surface and line in a Jaynes-Cummings triangle consisting of three cavities arranged in a ring. A fine-tuning artificial magnetic field dramatically enriches the emergence of the third-order exceptional lines ($3$ELs), which require only three tuning parameters in the presence of chiral symmetry and parity-time (PT) symmetry. Third-order EPs amplify the effect of perturbations through a cube-root response mechanism, displaying a greater sensitivity than second-order EPs. We develop novel fidelity and Loschmidt echo using the associated-state biorthogonal approach, which successfully characterizes EPs and quench dynamics even in PT breaking regime. Our work advances the use of higher-order EPs in quantum technology applications.

Figures (5)

• Figure 1: (a) Schematic of the JC triangle with an artificial gauge field $\phi=3\theta$, showing cavity $1$ with gain and cavity $3$ with loss. (b) Third-order exceptional surface $\theta_{3c}$ as a function of $g_1/g_2$ and $J_1/J_3$ for $\omega=1,\Delta=20$.
• Figure 2: The colored surfaces represent the eigenenergies for the real $\mathrm{Re}(E_n)$ (a) and imaginary $\mathrm{Im}(E_n)$ (b) components for $\theta_{3c}=\pi/6$, with respect to gain/loss $\gamma$ and the hopping ratio $J_1/J_3$.The red solid line represents the line of $3$EPs $\gamma_{3c}$. Distinct eigenenergies are shown for $\theta=\pi/4$ in (c) and (d). A blue dot marks a $3$EP, and a black dashed line represents the $2$ELs $\gamma_{2c}$. For fixed values of $J_1=J_3=0.01$, $\mathrm{Re}(E_n)$ and $\mathrm{Im}(E_n)$ are plotted as functions of $\gamma$, illustrating PT-symmetry breaking at $3$EPs (e)-(f) and $2$EPs (g)-(f). Here, $g_1/\omega=g_2/\omega=0.3$ and $\Delta/\omega=50$.
• Figure 3: Real (a) and imaginary (b) parts of $E_n$ as a function of $\gamma$ for the critical magnetic flux $\theta_{3c}$ of a $3$EPs when $g_1/\omega=g_3/\omega=0.1, g_2/\omega=0.3$ and $J_1=J_3=0.01$.(c) Fidelity $F_n$ for three eigenstates between $|\psi_n(\gamma+\epsilon)\rangle$ and $|\psi_n(\gamma)\rangle$ with a small amount $\epsilon=0.00005$.
• Figure 4: (a)-(f)Real and imaginary parts of $E_{n}$, and the energy difference $\mathrm{Re}(\Delta E_{12})$, $\mathrm{Re}(\Delta E_{13})$ at the $3$EP ($\theta_{3c}=\pi/6$) for the perturbation $\epsilon$ on the gain cavity $1$ (left column) and the neutral one $2$ (middle column), respectively. Right column shows $E_{n}$ and $\mathrm{Re}(\Delta E_{23})$ at the $2$EP ( $\theta=\pi/4$) for the perturbing on the gain cavity.
• Figure 5: Loschmidt echo of quenching processes across the $3$EP ($\theta=\pi/6$) (a) from $\gamma_i=0.006$ to $\gamma_f=0.018$ and its reversal dynamics (c). The quench dynamics cross the $2$EPs ($\theta=\pi/4$) (b) from $\gamma_i=0.001$ to $\gamma_f=0.01$ and its reversal process (d). The initial states are chosen three eigenstates.