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arXiv:2101.01645 · Physical Review Research

Many-body localization in waveguide quantum electrodynamics

N. Fayard, Loïc Henriet, Ana Asenjo-Garcı́a, D. E. Chang

Published Sep 10, 2021• 68 citations
arXivHTMLPDF

Abstract

At the quantum many-body level, atom-light interfaces generally remain challenging to solve for or understand in a nonperturbative fashion. Here we consider a waveguide quantum electrodynamics model, where two-level atoms interact with and via propagating photons in a one-dimensional waveguide, and specifically investigate the interplay of atomic position disorder, multiple scattering of light, quantum nonlinear interactions, and dissipation. We develop qualitative arguments and present numerical evidence that such a system exhibits a many-body localized (MBL) phase, provided that atoms are less than half excited. Interestingly, while MBL is originally formulated with respect to closed systems, this system is intrinsically open. However, as dissipation originates from transport of energy to the system boundaries and the subsequent radiative loss, the lack of transport in the MBL phase makes the waveguide QED system look essentially closed and makes applicable the notions of MBL. Conversely, we show that if the system is initially in a delocalized phase due to a large excitation density, then rapid initial dissipation can leave the system unable to efficiently transport energy at later times, resulting in a dynamical transition to an MBL phase. These phenomena can be feasibly realized in state-of-the-art experimental setups.

DOI
10.1103/physrevresearch.3.033233

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At the quantum many-body level, atom-light interfaces generally remain challenging to solve for or understand in a nonperturbative fashion. Here we consider a waveguide quantum electrodynamics model, where two-level atoms interact with and via propagating photons in a one-dimensional waveguide, and specifically investigate the interplay of atomic position disorder, multiple scattering of light, quantum nonlinear interactions, and dissipation. We develop qualitative arguments and present numerical evidence that such a system exhibits a many-body localized (MBL) phase, provided that atoms are less than half excited. Interestingly, while MBL is originally formulated with respect to closed systems, this system is intrinsically open. However, as dissipation originates from transport of energy to the system boundaries and the subsequent radiative loss, the lack of transport in the MBL phase makes the waveguide QED system look essentially closed and makes applicable the notions of MBL. Conversely, we show that if the system is initially in a delocalized phase due to a large excitation density, then rapid initial dissipation can leave the system unable to efficiently transport energy at later times, resulting in a dynamical transition to an MBL phase. These phenomena can be feasibly realized in state-of-the-art experimental setups.
Photons are elementary particles of light, and their interactions in vacuum are extremely weak. The seclusion of photons makes them perfect carriers of classical and quantum information, but also poses difficulties for employing them in quantum information technologies. Recent years have seen tremendous experimental progress in the development of synthetic quantum systems where strong and controllable coupling between single photons is achieved. In a variety of solid-state and optical platforms, propagating photons are coupled with local emitters such as atoms, quantum dots, NV centers, or superconducting qubits. Despite the different nature of the platforms, many of these systems can be described using the same theoretical framework called waveguide quantum electrodynamics (WQED). Dissipation is an inevitable ingredient of many synthetic quantum systems and is a source of error in quantum information applications. Despite its important role in experimental systems, the implications of dissipation in scattering theory havenot been fully explored. Chapter 2 discusses our discovery of the dissipation-induced bound states in WQED systems. The appearance of these bound states is in a one-to-one correspondence with zeros in the single-photon transmission. We also formulate a dissipative version of Levinson's theorem by looking at the relation between the number of bound states and the winding number of the transmission phases. In Chapter 3, we study three-body loss in Rydberg polaritons. Despite past theoretical and experimental studies of the regime with dispersive interaction, the dissipative regime is still mostly unexplored. Using a renormalization group technique to solve the quantum three-body problem, we show how the shape and strength of dissipative three-body forces can be universally enhanced for Rydberg polaritons. We demonstrate how these interactions relate to the transmission through a single-mode cavity, which can be used as a probe of the three-body physics in current experiments. The high level of control of the synthetic quantum systems behind WQED offers many inspirations for theoretical studies. In Chapter 4 of this dissertation, we explore a new direction of scattering theory motivated by the controllability of dispersion relations in synthetic quantum systems. We study single-particle scattering in one dimension when the dispersion relation is E(k)=k^m, where m>= 2 is an integer. For a large class of interactions, we discover that the S-matrix evaluated at an energy E->0 converges to a universal limit that is only dependent on m. We also give a generalization of Levinson's theorem for these more general dispersion relations in WQED systems.
Engineering strong photon–photon interactions at the quantum level have been crucial in various areas of research, notably in quantum information processing and quantum simulation. It is often done by coupling matter strongly to light. A promising way to achieve this is via waveguide quantum electrodynamics (QED). Motivated by these advancements, we study few-photon transport in waveguide QED setups. First, we present a diagrammatic technique to systematically study multiphoton scattering based on the scattering formalism and Green’s function approach. We demonstrate our proposal through physically relevant examples involving scattering of few-photon states from two-level emitters as well as from arrays of correlated Kerr nonlinear resonators described by the Bose–Hubbard model. In the second part, we apply the diagrammatic technique that was developed to perform a comprehensive study on a Bose–Hubbard lattice with a quasi-periodic potential. This model exhibits many-body localisation. We compute the two-photon transmission probability and show that it carries signatures of the underlying localisation transition with close agreement to the participation ratio of the eigenstates. The systematic scattering approach provided in this paper provides a foundation for future works at the interface between quantum optics and condensed matter.
In one-dimensional waveguide quantum electrodynamics systems, quantum emitters interact through infinite-range, dispersive, and dissipative dipole-dipole interactions mediated by guided photonic modes. These long-range periodic interactions give rise to rich many-body physics absent in free space. In this work, we construct a set of symmetrized multiexcitation dark states and derive analytic expressions for their time-evolution projections. This framework captures the essential dynamics of excitation transport and storage while significantly reducing computational complexity compared to full master equation simulations. Our analysis reveals a fundamental bound on energy redistribution governed by the structure of dark states and collective dissipation and discovers that optimal excitation transfer between emitter ensembles converges toward an initial pumped fraction of ${N}_{\text{p}}/N\ensuremath{\approx}0.55$ for large system sizes. We further examine the robustness of this mechanism under realistic imperfections, including positional disorder, nonradiative decay, and dephasing. These results highlight the role of many-body dark states in enabling efficient and controllable energy transfer, offering new insights into dissipative many-body dynamics in integrated quantum platforms.
Controlling light photon-by-photon is central to quantum optics. At a fundamental level, photon interactions are mediated by their coupling to atoms, and ultimate control requires deterministic light-matter interfacing of single photons to single atoms. Extending this paradigm to radiatively couple multiple individual atoms in a deterministic and scalable manner opens the arena of many-body quantum optics. Here, we realize such a setting by coherently coupling solid-state artificial atoms to a nanophotonic waveguide and demonstrate higher-order photon correlations that are controlled by the number of quantum emitters. We study the scaling of nonlinear photonic transport induced by emitter-photon scattering and demonstrate that adding a quantum emitter generates higher-order photon correlations. Specifically, we experimentally observe genuine three-photon correlations from a pair of collectively coupled emitters, while contributions from lower photon numbers are suppressed. In addition, we scale to three resonant quantum emitters coupled to the waveguide. These advancements demonstrate the onset of many-body quantum optics in waveguide quantum electrodynamics, enabling new photonic quantum simulators, the creation of many-body entangled states, and the exploration of novel quantum phase transitions.
Understanding physical properties of quantum emitters strongly interacting with quantized electromagnetic modes is one of the primary goals in the emergent field of waveguide quantum electrodynamics (QED). When the light-matter coupling strength is comparable to or even exceeds energies of elementary excitations, conventional approaches based on perturbative treatment of light-matter interactions, two-level description of matter excitations, and photon-number truncation are no longer sufficient. Here we study in and out of equilibrium properties of waveguide QED in such nonperturbative regimes on the basis of a comprehensive and rigorous theoretical approach using an asymptotic decoupling unitary transformation. We uncover several surprising features ranging from symmetry-protected many-body bound states in the continuum to strong renormalization of the effective mass and potential; the latter may explain recent experiments demonstrating cavity-induced changes in chemical reactivity as well as enhancements of ferromagnetism or superconductivity. To illustrate our general results with concrete examples, we use our formalism to study a model of coupled cavity arrays, which is relevant to experiments in superconducting qubits interacting with microwave resonators or atoms coupled to photonic crystals. We examine the relation between our results and delocalization-localization transition in the spin-boson model; notably, we point out that a reentrant transition can occur in the regimes where the coupling strength becomes the dominant energy scale. We also discuss applications of our results to other problems in different fields, including quantum optics, condensed matter physics, and quantum chemistry.
Many-body localization for a system of bosons trapped in a one-dimensional lattice is discussed. Two models that may be realized for cold atoms in optical lattices are considered. The model with a random on-site potential is compared with previously introduced random interactions model. While the origin and character of the disorder in both systems is different they show interesting similar properties. In particular, many-body localization appears for a sufficiently large disorder as verified by a time evolution of initial density wave states as well as using statistical properties of energy levels for small system sizes. Starting with different initial states, we observe that the localization properties are energy-dependent which reveals an inverted many-body localization edge in both systems (that finding is also verified by statistical analysis of energy spectrum). Moreover, we consider computationally challenging regime of transition between many body localized and extended phases where we observe a characteristic algebraic decay of density correlations which may be attributed to subdiffusion (and Griffiths-like regions) in the studied systems. Ergodicity breaking in the disordered Bose–Hubbard models is compared with the slowing-down of the time evolution of the clean system at large interactions.