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arXiv:2205.05479 · Physical Review Letters

Anomalous Behaviors of Quantum Emitters in Non-Hermitian Baths

Zongping Gong, Miguel Bello, Daniel Malz, Flore K. Kunst

Published Nov 23, 2022• 40 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.129.223601

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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.
A single quantum emitter coupled to a structured non-Hermitian environment shows anomalous bound states and real-time dynamics without Hermitian counterparts, as shown in Gong []. In this work, we establish a general approach for studying the scattering states of a single quantum emitter coupled to one-dimensional non-Hermitian single-band baths. We formally solve the exact eigenvalue equation for all the scattering states defined on finite periodic lattices. In the thermodynamic limit, the formal solution reduces to the celebrated Lippmann-Schwinger equation for generic baths. In this case, we find that the scattering states are no longer linear superpositions of plane waves in general, unlike those in Hermitian systems; instead, the wave functions exhibit a large, yet finite localization length proportional to the lattice size. Furthermore, we show and discuss the cases where the Lippmann-Schwinger equation breaks down. We find the analytical solutions for the Hatano-Nelson and unidirectional next-to-nearest-neighbor baths in the thermodynamic limit.
Photon-mediated interaction between quantum emitters in engineered photonic baths is an emerging area of quantum optics. At the same time, non-Hermitian (NH) physics is currently thriving, spurred by the exciting possibility to access new physics in systems ruled by non-trivial NH Hamiltonians—in particular, photonic lattices—which can challenge longstanding tenets such as the Bloch theory of bands. Here, we combine these two fields and study the exotic interaction between emitters mediated by the photonic modes of a lossy photonic lattice described by a NH Hamiltonian. We show in a paradigmatic case study that structured losses in the field can seed exotic emission properties. Photons can mediate dissipative, fully non-reciprocal interactions between emitters with range critically dependent on the loss rate. When this loss rate corresponds to a bare-lattice exceptional point, the effective couplings are exactly nearest neighbor, implementing a dissipative, fully non-reciprocal Hatano–Nelson model. Counterintuitively, this can occur irrespective of the lattice boundary conditions. Thus photons can mediate an effective emitter’s Hamiltonian which is translationally invariant despite the fact that the field is not. We interpret these effects in terms of metastable atom–photon dressed states, which can be exactly localized on only two lattice cells or extended across the entire lattice. These findings introduce a paradigm of light-mediated interactions with unprecedented features such as non-reciprocity, non-trivial dependence on field boundary conditions, and range tunability via a loss rate.
To achieve translational symmetry for the computation of the band structure of a lattice model, one can either consider an infinite lattice or impose periodic boundary conditions (PBC). While in systems with short-range couplings these two approaches are equivalent, we show that for long-range couplings one can obtain considerably different results. We compare the two methods on the basis of one-dimensional quantum emitter chains both in free space and when coupled to a waveguide. The latter system allows for asymmetric couplings enabling the non-Hermitian skin effect, which we analyze using the two different band-structure calculation methods. We find that only PBC lead to physically and mathematically robust results, while the infinite-chain approach entails convergence issues and is unable to satisfyingly explain the emergence of the non-Hermitian skin effect in the waveguide system. Using PBC reveals unusual findings like a non-star shaped generalized Brillouin zone and strongly localized eigenstates with zero winding number.
Abstract The non-Hermitian skin effect and edge burst reflect the vital role of spatial boundaries in non-Hermitian systems from both static and dynamic perspectives. In this study, we investigate a non-Hermitian dissipative lattice with nonlocal coupling and demonstrate many interesting static and dynamic phenomena. In the case of global coupling with all sites coupled with each other, we observe anomalous hopping resonance, where a quantum walker initially placed at a single site almost completely escapes from the boundary of the system regardless of its initial position. In the case of non-global coupling, which is infinite-range coupling, the interplay between nonlocal hopping and the non-Hermitian skin effect results in the emergence of local bulk modes exhibiting a multipartite density distribution. The presence of local bulk modes induces the nontrivial dynamics of a quantum walker, which features multiple peaks of lost probability in spatially separated domains. Our findings demonstrate unique properties induced by nonlocal coupling in non-Hermitian systems.
The non-Hermitian skin effect is nonreciprocity-induced localization phenomena in which a macroscopic number of eigenstates accumulate anomalously at the boundary, accompanied by the extreme sensitivity to boundary conditions. Here, we develop a geometric characterization of the non-Hermitian skin effect. We demonstrate that the localization length scale associated with the skin effect is encoded in the quantum metric defined solely from right eigenstates, but not in the biorthogonal quantum metric. Moreover, we show that the quantum metrics can exhibit the power-law divergences at gapless points that depend on the different boundary conditions. We also reveal that cusps of the generalized Brillouin zone in non-Bloch band theory are signaled by discontinuities in the quantum metrics. We illustrate these behavior using prototypical non-Hermitian models, such as the Hatano-Nelson model and the non-Hermitian, nonreciprocal Su-Schrieffer-Heeger model.
Quantum emitters coupled to structured photonic reservoirs experience unconventional individual and collective dynamics emerging from the interplay between dimensionality and non-trivial photon energy dispersions. In this work, we systematically study several paradigmatic three dimensional structured baths with qualitative differences in their bath spectral density. We discover non-Markovian individual and collective effects absent in simplified descriptions, such as perfect subradiant states or long-range anisotropic interactions. Furthermore, we show how to implement these models using only cold atoms in state-dependent optical lattices and show how this unconventional dynamics can be observed with these systems.