Bound states and photon emission in non-Hermitian nanophotonics

Abstract

We establish a general framework for studying the bound states and the photon-emission dynamics of quantum emitters coupled to structured nanophotonic lattices with engineered dissipation (loss). In the singleexcitation sector, the system can be described exactly by a non-Hermitian formalism. We have pointed out in the accompanying letter [Gong et al., arXiv:2205.05479] that a single emitter coupled to a one-dimensional non-Hermitian lattice may already exhibit anomalous behaviors without Hermitian counterparts. Here we provide further detail on these observations. We also present several additional examples on the cases with multiple quantum emitters or in higher dimensions. Our work unveils the tip of the iceberg of the rich non-Hermitian phenomena in dissipative nanophotonic systems.

Anomalous Behaviors of Quantum Emitters in Non-Hermitian Baths

“…2(c)), the amplification governed by the poles (free-like propagation) will dominate the long-time behavior. We mention that the three dynamical regimes appear also in the general Hatano-Nelson model and a similar analysis applies [18]. Critical emitter decay.-While the emitter decay into the Hatano-Nelson bath is trivially exponential, we show that novel critical (algebraic) decay emerges for another simple NH bath with alternating on-site loss.…”

“…It turns out that the self-energy vanishes inside the loop. This result actually has a topological origin [18] and implies the existence of a bound state "hidden" in the loop, with its energy pinned at ∆. Its photon profile vanishes to the right of the emitter and decays exponentially to the left, with localization length ξ = (ln |κ/(∆ + iκ)|) −1 .…”

“…See Ref. [18] for a quantitative analysis. Recalling that the branch point has the largest imaginary part, we know that the algebraic decay dominates the long-time dynamics.…”

“…What is important is to have a branch point on the real axis while all the poles well below the real axis. For example, this can be realized by Wick rotating (i.e., multiplying by i) the Hermitian bath with nearest-neighbor hopping [18]. Note that algebraic decay is usually invisible for 1D periodic Hermitian baths [3], since there are always bound states with real energies, which dominate the long-time dynamics [29].…”

“…For example, the eigenenergies are always pinned at the (generally different) complex detunings, as if the emitters did not influence each other. Further details can be found in the companion paper [18].…”