Anomalous Behaviors of Quantum Emitters in Non-Hermitian Baths

Both non-Hermitian systems and the behavior of emitters coupled to structured baths have been studied intensely in recent years. Here, we study the interplay of these paradigmatic settings. In a series of examples, we show that a single quantum emitter coupled to a non-Hermitian bath displays a number of unconventional behaviors, many without Hermitian counterpart. We first consider a unidirectional hopping lattice whose complex dispersion forms a loop. We identify peculiar bound states inside the loop as a manifestation of the non-Hermitian skin effect. In the same setting, emitted photons may display spatial amplification markedly distinct from free propagation, which can be understood with the help of the generalized Brillouin zone. We then consider a nearest-neighbor lattice with alternating loss. We find that the long-time emitter decay always follows a power law, which is usually invisible for Hermitian baths. Our Letter points toward a rich landscape of anomalous quantum emitter dynamics induced by non-Hermitian baths.

Figure 1

(a) Two-level quantum emitter coupled to a Hatano-Nelson lattice with unidirectional right hopping and background loss. The detuning of the emitter is complex, $\mathrm{\Delta }=(0.3-0.5i)\kappa$. (b) Single-excitation spectrum under periodic boundary conditions (BCs) for three different coupling strengths. The schematic drawings on top show the profiles of the bound states inside and outside the loop, which are skin-mode- and Hermitian-like (denoted by red and blue markers, respectively). We dub the former “hidden” bound states, as we will see that they do not apparently affect the emitter decay. Unlike Hermitian-like bound states, the energy of the hidden bound state stays pinned at the emitter detuning, irrespective of the value of $g$. (c) Dependence of the localization length $\xi$ and atomic weight $|c_e{|}^2$ of the hidden (red) and Hermitian-like (blue) bound states on coupling strength $g$. Dashed vertical lines indicate the onset of the Hermitian-like bound state.

Figure 2

Real-space dynamics of the emitted photon for $\mathrm{\Delta }=-2i\kappa$, $g=0.6\kappa$ (a),(b), $\mathrm{\Delta }=0$, $g=0.6\kappa$ (c),(d) and $\mathrm{\Delta }=0$, $g=1.6\kappa$ (e),(f). Insets in (a),(c),(e) show the original (dashed) and generalized (solid) Brillouin zone as well as the poles (red crosses) of Eq. (8) in terms of $\beta \equiv e^{-ik}$. In (b),(d),(f), the photon profiles have been normalized by multiplying $\sqrt{\kappa t}$ to retrieve probability conservation asymptotically.

Figure 3

(a) Two-level quantum emitter coupled to a dissipative (upper) or nondissipative (lower) site of a 1D lattice with symmetric hopping and alternating on-site loss. (b) Asymptotic algebraic decay of the atomic excitation. The power-law behavior is $t^{-1}$ and $t^{-3}$ for the dissipative and nondissipative coupling, respectively. Here, $\mathrm{\Delta }=0$, $J=\kappa$, and $g=1.5\kappa$. (c) (left) Band structure and the (right) density of states (DOS) for the alternatively lossy lattice. Dashed vertical lines indicate the exceptional points. Dotted curves in (b) and (c) correspond to a perturbation that explicitly breaks the passive $PT$ symmetry and destroys the EPs.