arXiv subjects

Federico Roccati

Publications and source records attributed to Federico Roccati.

17 recordsLinked to original sources

arXiv2026

Atom-Photon Bound States in Fractal Photonic Lattices: Localization Length and Anomalous Diffusion

We study atom-photon bound states seeded by two-level emitters coupled to self-similar photonic lattices. By expressing the photonic Green's function through the heat kernel, we show that the far-field localization length obeys $\xi \sim \Delta^{-1/d_w}$, with the detuning $\Delta$ from the lower spectral edge and the walk dimension $d_w$ of the underlying fractal. This scaling is controlled by anomalous diffusion and does not rely on translational invariance or a band-edge effective-mass approximation. Exact diagonalization on Sierpi\'nski gaskets, pyramids, Vicsek graphs, and Sierpi\'nski carpets confirms the far-field prediction once the bath Hamiltonian is rendered Laplacian-like by compensating the local inhomogeneity in the connectivities with on-site potentials. In the near field, the bound-state amplitude exhibits an additional algebraic variation. For nested finitely ramified fractals, the corresponding exponent agrees with the classical resistance/ first-passage scaling, whereas Sierpi\'nski carpets display clear deviations from this simple law. Our results extend structured-bath waveguide QED to self-similar non-periodic geometries and connect bound-state profiles to transport exponents of the underlying fractal lattice.

quant-ph↗

arXiv2026

Perspective: Interactions and Nonlinearity in Non-Hermitian Physics

For decades, Hermiticity was considered an immutable axiom of quantum mechanics, essential for ensuring real energies and unitary evolution. This perspective has shifted radically, driven by the realization that non-Hermitian Hamiltonians provide a powerful effective description of open quantum systems, granting access to unique phenomena such as Exceptional Points and the Non-Hermitian Skin Effect. In this Perspective, we chart the trajectory of this field, moving from its established foundations in single-particle, linear models to the emerging frontier of interacting many-body systems. We first clarify the physical origins of non-Hermitian dynamics, distinguishing between mean-field approximations, conditional "no-click" evolution, and exact Liouvillian dynamics. We then focus on the rich phenomenology arising from the interplay of non-Hermiticity and interactions. We discuss interaction-induced topological phases, the generalization of skin effects to the many-body Hilbert space, and the distinct signatures of dissipative quantum chaos and complexity. Finally, we highlight collective phenomena in nonlinear regimes, including skin solitons and dissipative phase transitions. We also comment on measurement-induced entanglement transitions and their relation to non-Hermitian spectra and topology. By synthesizing these diverse developments, we provide a roadmap for the future of non-Hermitian physics.

quant-ph↗

arXiv2025

Fibonacci Waveguide Quantum Electrodynamics

Waveguide quantum electrodynamics (QED) provides a powerful framework for engineering quantum interactions, traditionally relying on periodic photonic arrays with continuous energy bands. Here, we investigate waveguide QED in a fundamentally different environment: A one-dimensional photonic array whose hopping strengths are structured aperiodically according to the deterministic Fibonacci-Lucas substitution rule. These "Fibonacci waveguides" lack translational invariance and are characterized by a singular continuous energy spectrum and critical eigenstates, representing a deterministic intermediate between ordered and disordered systems. We demonstrate how to achieve decoherence-free, coherent interactions in this unique setting. We analyze two paradigmatic cases: (i) Giant emitters resonantly coupled to the simplest aperiodic version of a standard waveguide. For these, we show that atom photon bound states form only for specific coupling configurations dictated by the aperiodic sequence, leading to an effective atomic Hamiltonian, which itself inherits the Fibonacci structure; and (ii) emitters locally and off-resonantly coupled to the aperiodic version of the Su-Schrieffer-Heeger waveguide. In this case the mediating bound states feature aperiodically modulated profiles, resulting in an effective Hamiltonian with multifractal properties. Our work establishes Fibonacci waveguides as a versatile platform, which is experimentally feasible, demonstrating that the deterministic complexity of aperiodic structures can be directly engineered into the interactions between quantum emitters.

quant-ph↗

arXiv2025

Many-body quantum optics in a Bose-Hubbard waveguide

Waveguide quantum electrodynamics (QED) studies the interaction between quantum emitters and guided photons in one-dimension. When the waveguide hosts interacting photons, it becomes a platform to explore many-body quantum optics. However, the influence of photonic correlations on emitter dynamics remains poorly understood. In this work, we study the collective decay and coherent interactions of quantum emitters coupled to a one-dimensional Bose-Hubbard waveguide, an array of coupled photonic modes with repulsive on-site interactions that supports superfluid and Mott insulating phases. We show that photon-photon interactions alone can trigger a superradiant burst, independent of emitter spacing and transition frequency. In the off-resonant regime, emitters exhibit two distinct types of mediated interactions. Delocalized superfluid excitations yield persistent, long-range couplings, challenging the noninteracting paradigm, where long-range (dissipative) couplings occur in-band, whereas short-range and coherent interactions occur in a bandgap. In the Mott limit, quasiparticles generate short-range interactions mediated by doublons and holons. Our work bridges many-body physics and waveguide QED, revealing how photonic many-body states shape emitter dynamics.

quant-ph↗

arXiv2025

Finite steady-state current defies non-Hermitian many-body localization

Non-Hermitian many-body localization (NH MBL) has emerged as a possible scenario for stable localization in open systems, as suggested by spectral indicators identifying a putative transition for finite system sizes. In this work, we shift the focus to dynamical probes, specifically the steady-state spin current, to investigate transport properties in a disordered, non-Hermitian XXZ spin chain. Through exact diagonalization for small systems and tensor-network methods for larger chains, we demonstrate that the steady-state current remains finite and decays exponentially with disorder strength, showing no evidence of a transition up to disorder values far beyond the previously claimed critical point. Our results reveal a stark discrepancy between spectral indicators, which suggest localization, and transport behavior, which indicates delocalization. This highlights the importance of dynamical observables in characterizing NH MBL and suggests that traditional spectral measures may not fully capture the physics of non-Hermitian systems. Additionally, we observe a non-commutativity of limits in system size and time, further complicating the interpretation of finite-size studies. These findings challenge the existence of NH MBL in the studied model and underscore the need for alternative approaches to understand localization in non-Hermitian settings.

cond-mat.dis-nn↗

arXiv2024

Controlling Markovianity with Chiral Giant Atoms

Giant artificial atoms are promising and flexible building blocks for the implementation of analog quantum simulators. They are realized via a multi-local pattern of couplings of two-level systems to a waveguide, or to a two-dimensional photonic bath. A hallmark of giant-atom physics is their non-Markovian character in the form of self-coherent feedback, leading, e.g., to non-exponential atomic decay. The timescale of their non-Markovianity is essentially given by the time delay proportional to the distance between the various coupling points. In parallel, with the state-of-the-art experimental setups, it is possible to engineer complex phases in the atom-light couplings. Such phases simulate an artificial magnetic field, yielding a chiral behavior of the atom-light system. Here, we report a surprising connection between these two seemingly unrelated features of giant atoms, showing that the chirality of a giant atom controls its Markovianity. In particular, by adjusting the couplings' phases, a giant atom can, counterintuitively, enter an exact Markovian regime irrespectively of any inherent time delay. We illustrate this mechanism as an interference process and via a collision model picture. Our findings significantly advance the understanding of giant atom physics, and open new avenues for the control of quantum nanophotonic networks.

quant-ph↗

arXiv2024

Diagnosing non-Hermitian Many-Body Localization and Quantum Chaos via Singular Value Decomposition

Strong local disorder in interacting quantum spin chains can turn delocalized eigenmodes into localized eigenstates, giving rise to many-body localized (MBL) phases. This is accompanied by distinct spectral statistics: chaotic for the delocalized phase and integrable for the localized phase. In isolated systems, localization and chaos are defined through a web of relations among eigenvalues, eigenvectors, and real-time dynamics. These may change as the system is made open. We ask whether random dissipation (without random disorder) can induce chaotic or localized behavior in an otherwise integrable system. The dissipation is described using non-Hermitian Hamiltonians, which can effectively be obtained from Markovian dynamics conditioned on null measurement. Through the use of the singular value decomposition and the introduction of new diagnostic tools complementing the singular-value statistics, namely, the singular form factor, the inverse participation ratio, and entanglement entropy for singular vectors, we provide a positive answer. Our method is illustrated in an XXZ Hamiltonian with random local dissipation.

quant-ph↗

arXiv2023

Hermitian and Non-Hermitian Topology from Photon-Mediated Interactions

Light can mediate effective dipole-dipole interactions between atoms or quantum emitters coupled to a common environment. Exploiting them to tailor a desired effective Hamiltonian can have major applications and advance the search for many-body phases. Quantum technologies are mature enough to engineer large photonic lattices with sophisticated structures coupled to quantum emitters. In this context, a fundamental problem is to find general criteria to tailor a photonic environment that mediates a desired effective Hamiltonian of the atoms. Among these criteria, topological properties are of utmost importance since an effective atomic Hamiltonian endowed with a non-trivial topology can be protected against disorder and imperfections. Here, we find general theorems that govern the topological properties (if any) of photon-mediated Hamiltonians in terms of both Hermitian and non-Hermitian topological invariants, thus unveiling a system-bath topological correspondence. The results depend on the number of emitters relative to the number of resonators. For a photonic lattice where each mode is coupled to a single quantum emitter, the Altland-Zirnbauer classification of topological insulators allows us to link the topology of the atoms to that of the photonic bath: we unveil the phenomena of topological preservation and reversal to the effect that the atomic topology can be the same or opposite to the photonic one, depending on Hermiticity of the photonic system and on the parity of the spatial dimension. As a consequence, the bulk-edge correspondence implies the existence of atomic boundary modes with the group velocity opposite to the photonic ones in a 2D Hermitian topological system. If there are fewer emitters than photonic modes, the atomic system is less constrained and no general photon-atom topological correspondence can be found. We show this with two counterexamples.

quant-ph↗

arXiv2023

Non-Hermitian Hamiltonian Deformations in Quantum Mechanics

The construction of exactly-solvable models has recently been advanced by considering integrable $T\bar{T}$ deformations and related Hamiltonian deformations in quantum mechanics. We introduce a broader class of non-Hermitian Hamiltonian deformations in a nonrelativistic setting, to account for the description of a large class of open quantum systems, which includes, e.g., arbitrary Markovian evolutions conditioned to the absence of quantum jumps. We relate the time evolution operator and the time-evolving density matrix in the undeformed and deformed theories in terms of integral transforms with a specific kernel. Non-Hermitian Hamiltonian deformations naturally arise in the description of energy diffusion that emerges in quantum systems from time-keeping errors in a real clock used to track time evolution. We show that the latter can be related to an inverse $T\bar{T}$ deformation with a purely imaginary deformation parameter. In this case, the integral transforms take a particularly simple form when the initial state is a coherent Gibbs state or a thermofield double state, as we illustrate by characterizing the purity, Rényi entropies, logarithmic negativity, and the spectral form factor. As the dissipative evolution of a quantum system can be conveniently described in Liouville space, we further discuss the spectral properties of the Liouvillians, i.e., the dynamical generators associated with the deformed theories. As an application, we discuss the interplay between decoherence and quantum chaos in non-Hermitian deformations of random matrix Hamiltonians and the Sachdev-Ye-Kitaev model.

hep-th↗

arXiv2022

Quantum correlations in dissipative gain-loss systems across exceptional points

We investigate the behavior of correlations dynamics in a dissipative gain-loss system. First, we consider a setup made of two coupled lossy oscillators, with one of them subject to a local gain. This provides a more realistic platform to implement parity-time (PT) symmetry circumventing the implementation of a pure gain. We show how the qualitative dynamics of correlations resembles that for a pure-gain-loss setup. The major quantitative effect is that quantum correlations are reduced, while total ones are enhanced. Second, we study the behavior of these correlations across an exceptional point (EP) outside of the PT-symmetric regime of parameters, observing how different behaviors across the EP occur only in the transient dynamics. This shows how PT symmetry plays a relevant role at large times.

quant-ph↗

arXiv2022

Quantum correlations beyond entanglement in a classical-channel model of gravity

A direct quantization of the Newtonian interaction between two masses is known to establish entanglement, which if detected would witness the quantum nature of the gravitational field. Gravitational interaction is yet compatible also with gravitational decoherence models relying on classical channels, hence unable to create entanglement. Here, we show in paradigmatic cases that, despite the absence of entanglement, a classical-channel model of gravity can still establish quantum correlations in the form of quantum discord between two masses. This is demonstrated for the Kafri-Taylor-Milburn (KTM) model and a recently proposed dissipative extension of this. In both cases, starting from an uncorrelated state, a significant amount of discord is generally created. This eventually decays in the KTM model, while it converges to a small stationary value in its dissipative extension. We also find that initial local squeezing on the state of the masses can significanlty enhance the generated discord.

quant-ph↗

arXiv2022

Exotic interactions mediated by a non-Hermitian photonic bath

Photon-mediated interactions 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 the 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-neighbour, implementing a dissipative, fully non-reciprocal, Hatano-Nelson model. Counter-intuitively, this occurs irrespective of the lattice boundary conditions. Thus photons can mediate an effective emitters' 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 new paradigm of light-mediated interactions with unprecedented features such as non-reciprocity, non-trivial dependence on the field boundary conditions and range tunability via a loss rate.

quant-ph↗

arXiv2022

Non-Hermitian physics and master equations

A longstanding tool to characterize the evolution of open Markovian quantum systems is the GKSL (Gorini-Kossakowski-Sudarshan-Lindblad) master equation. However, in some cases, open quantum systems can be effectively described with non-Hermitian Hamiltonians, which have attracted great interest in the last twenty years due to a number of unconventional properties, such as the appearance of exceptional points. Here, we present a short review of these two different approaches aiming in particular to highlight their relation and illustrate different ways of connecting non-Hermitian Hamiltonian to a GKSL master equation for the full density matrix.

quant-ph↗

arXiv2021

Non-Hermitian skin effect as an impurity problem

A striking feature of non-Hermitian tight-binding Hamiltonians is the high sensitivity of both spectrum and eigenstates to boundary conditions. Indeed, if the spectrum under periodic boundary conditions is point gapped, by opening the lattice the non-Hermitian skin effect will necessarily occur. Finding the exact skin eigenstates may be demanding in general, and many methods in the literature are based on ansatzes and on recurrence equations for the eigenstates' components. Here we devise a general procedure based on the Green's function method to calculate the eigenstates of non-Hermitian tight-binding Hamiltonians under open boundary conditions. We apply it to the Hatano-Nelson and non-Hermitian SSH models and finally we contrast the edge states localization with that of bulk states.

quant-ph↗

arXiv2020

Quantum correlations in $\mathcal{PT}$-symmetric systems

We study the dynamics of correlations in a paradigmatic setup to observe $\mathcal{PT}$-symmetric physics: a pair of coupled oscillators, one subject to a gain one to a loss. Starting from a coherent state, quantum correlations (QCs) are created, despite the system being driven only incoherently, and can survive indefinitely. $\mathcal{PT}$ symmetry breaking is accompanied by non-zero stationary QCs. We link $\mathcal{PT}$ symmetry breaking to the long-time behavior of both total and QCs, which display different scalings in the $\mathcal{PT}$-broken/unbroken phase and at the exceptional point (EP). This is analytically shown and quantitatively explained in terms of entropy balance. The EP in particular stands out as the most classical configuration.

quant-ph↗

arXiv2019

Stationary quantum correlations in a system with mean-field PT symmetry

A pair of coupled quantum harmonic oscillators, one subject to a gain one to a loss, is a paradigmatic setup to implement PT-symmetric, non-Hermitian Hamiltonians in that one such Hamiltonian governs the mean-field dynamics for equal gain and loss strengths. Through a full quantum description (so as to account for quantum noise) here is shown that when the system starts in any two-mode coherent state, including vacuum, there appear quantum correlations (QCs) without entanglement, as measured by the Gaussian discord. When the loss rate is above a threshold, once generated QCs no more decay. This occurs in a wide region of parameters, significantly larger than that where the full quantum dynamics is stable. For equal gain and loss rates, in particular, QCs decay in the exact phase (including the exceptional point) and are stable in the broken phase.

quant-ph↗

arXiv2019

A no-go result for the quantum damped harmonic oscillator

In this letter we show that it is not possible to set up a canonical quantization for the damped harmonic oscillator using the Bateman lagrangian. In particular, we prove that no square integrable vacuum exists for the {\em natural} ladder operators of the system, and that the only vacua can be found as distributions. This implies that the procedure proposed by some authors is only formally correct, and requires a much deeper analysis to be made rigorous.

quant-ph↗