## Scaling up the Anderson transition in random-regular graphs

We study the Anderson transition in lattices with the connectivity of a random-regular graph. Our results indicate that fractal dimensions are continuous across the transition, but a discontinuity occurs in their derivatives, implying the non-ergodicity of the metal near the Anderson transition. A critical exponent and critical disorder are found via a scaling approach. Our data support that the predictions of the relevant Gaussian Ensemble are only recovered at zero disorder.

## Fast High-Fidelity Quantum Nondemolition Qubit Readout via a Nonperturbative Cross-Kerr Coupling

Qubit readout is an indispensable element of any quantum information processor. In this work, we experimentally demonstrate a non-perturbative cross-Kerr coupling between a transmon and a polariton mode which enables an improved quantum non-demolition (QND) readout for superconducting qubits. The new mechanism uses the same experimental techniques as the standard QND qubit readout in the dispersive approximation, but due to its non-perturbative nature, it maximizes the speed, the single-shot fidelity and the QND properties of the readout. In addition, it minimizes the effect of unwanted decay channels such as the Purcell effect. We observed a single-shot readout fidelity of 97.4% for short 50 ns pulses, and we quantified a QND-ness of 99% for long measurement pulses with repeated single-shot readouts.

## Experimental reconstruction of the few-photon nonlinear scattering matrix from a single quantum dot in a nanophotonic waveguide

Coherent photon-emitter interfaces offer a way to mediate effcient nonlinear photon-photon interactions, much needed for quantum-information processing. Here we experimentally study the case of a two-level emitter, a quantum dot, coupled to a single optical mode in a nanophotonic waveguide. We carry out few-photon transport experiments and record the statistics of the light to reconstruct the scattering matrix elements of 1- and 2-photon components. This provides direct insight to the complex nonlinear photon interaction that contains rich many-body physics.

## Dynamics of Rydberg excitations and quantum correlations in an atomic array coupled to a photonic crystal waveguide

We study the dynamics of up to two Rydberg excitations and the correlation growth in a chain of atoms coupled to a photonic crystal waveguide. In this setup, an excitation can hop from one atom to another via exponentially decaying exchange interactions mediated by the waveguide. An initially localized excitation undergoes a continuous-time quantum walk for short-range hopping, and for long-range hopping, it experiences quasilocalization. In addition, the inverse participation ratio reveals a superballistic diffusion of the excitation in short times, whereas, at a long time, it becomes ballistic. For two initially localized excitations, intriguing and complex dynamical scenarios emerge for different initial separations due to the competition between the Rydberg-Rydberg and exchange interactions. In particular, the two-point correlation reveals a light-cone behavior even for sufficiently long-range exchange interactions. Additionally, we characterize the growth of bipartite entanglement entropy, which exhibits a global bound if only one excitation is present in the dynamics. Finally, we analyze the effect of imperfections due to spontaneous emission from the Rydberg state into photons outside the waveguide and show that all of the physical phenomena we predict are well within experimental reach.

## Seeing topological edge and bulk currents in time-of-flight images

Here we provide a general methodology to directly measure the topological currents emerging in the optical lattice implementation of the Haldane model. Alongside the edge currents supported by gapless edge states, transverse currents can emerge in the bulk of the system whenever the local potential is varied in space, even if it does not cause a phase transition. In optical lattice implementations the overall harmonic potential that traps the atoms provides the boundaries of the topological phase that supports the edge currents, as well as providing the potential gradient across the topological phase that gives rise to the bulk current. Both the edge and bulk currents are resilient to several experimental parameters such as trapping potential, temperature, and disorder. We propose to investigate the properties of these currents directly from time-of-flight images with both short-time and long-time expansions.

## Topological bulk states and their currents

We provide evidence that, alongside topologically protected edge states, two-dimensional Chern insulators also support localized bulk states deep in their valence and conduction bands. These states manifest when local potential gradients are applied to the bulk, while all parts of the system remain adiabatically connected to the same phase. In turn, the bulk states produce bulk current transverse to the potential difference. This occurs even when the potential is always below the energy gap, where one expects only edge currents to appear. Bulk currents are topologically protected and behave as edge currents under an external influence, such as temperature or local disorder. Detecting topologically resilient bulk currents offers a direct means to probe the localized bulk states.

## Qubit-photon corner states in all dimensions

A single quantum emitter coupled to a one-dimensional photon field can perfectly trap a photon when placed close to a mirror. This occurs when the interference between the emitted and reflected light is completely destructive, leading to photon confinement between the emitter and the mirror. In higher dimensions, the spread of the light field in all directions hinders interference and, consequently, photon trapping by a single emitter remains elusive so far. In this work, we show how a single emitter can indeed trap light in any dimension. We provide a constructive recipe based on judiciously coupling an emitter to a photonic crystal-like bath with properly designed open boundary conditions. The directional propagation of the photons in such baths enables perfect destructive interference, forming what we denote as qubit-photon corner states. We characterize these states in all dimensions, showing that they are robust under fluctuations of the emitter’s properties, and persist also in the ultrastrong coupling regime.

## Observing the single-photon wavefunction with frequency and time resolved spectroscopy

The quantum wavefunction, despite continuous debates on its exact physical interpretation, is a fundamental concept in quantum physics and a useful tool to describe and simulate the state of a quantum system. While wavefunctions usually are not considered to be directly observable, in this work we show how the wavefunction of a single photon can be directly visualised in frequency and time domain. Our technique relates the wavefunction of the microwave photon to measurements of the electromagnetic field quadratures. We apply this technique to studying the process of single microwave photon emission, as described theoretically by Wigner and Weisskopf in the early days of quantum physics. In our experiment the photon is emitted from a single transmon qubit or from a collective state of two coupled transmons. In both scenarios, these photon portraits agree perfectly with the predictions of Wigner-Weisskopf as well as input-output theory, exemplifying the well known energy-time Heisenberg uncertainty relation. Our work promises a new experimental analysis method in analog quantum simulation of open quantum systems and collective phenomena.

## Remote Sub-Wavelength Addressing of Quantum Emitters with Chirped Pulses

We propose to use chirped pulses propagating near a bandgap to remotely address quantum emitters with sub-wavelength resolution. We introduce a particular family of chirped pulses that dynamically self-focus during their evolution in a medium with a quadratic dispersion relation. We analytically describe how the focusing distance and width of the pulse can be tuned through its initial parameters. We show that the interaction of such pulses with a quantum emitter is highly sensitive to its position due to effective Landau-Zener processes induced by the pulse chirping. Our results propose pulse engineering as a powerful control and probing tool in the field of quantum emitters coupled to structured reservoirs.

## Theory of waveguide QED with moving emitters

We theoretically study a system composed of a waveguide and a quantum emitter moving in a one-dimensional potential along the waveguide axis. We focus on the single-excitation subspace and treat the emitter motional degrees of freedom fully quantum mechanically. We first characterize single-photon scattering off a single moving quantum emitter, showing both direction-dependent transmission and recoil-induced reduction of the quantum emitter motional energy. We then characterize the bound states within the band gap, which display a motion-induced asymmetric phase in real space. We also demonstrate how these bound states form a continuous band with exotic dispersion relations. Finally, we study the spontaneous emission of an initially excited quantum emitter with various initial momentum distributions, finding strong deviations with respect to the static emitter counterpart both in the occupation dynamics and in the spatial distribution of the emitted photons. Our work extends the waveguide-QED toolbox by including the quantum motional degrees of freedom of emitters, whose impact on the few-photon dynamics could be harnessed for quantum technologies.

## Chiral quantum optics in photonic sawtooth lattices

Chiral quantum optics has become a burgeoning field due to its potential applications in quantum networks or quantum simulation of many-body physics. Current implementations are based on the interplay between local polarization and propagation direction of light in nanophotonic structures. In this manuscript, we propose an alternative platform based on coupling quantum emitters to a photonic sawtooth lattice, a one-dimensional model with an effective flux per plaquette introduced by complex tunnelings. We study the dynamics emerging from such structured photonic bath and find the conditions to obtain quasiperfect directional emission when the emitters are resonant with the band. In addition, we find that the photons in this bath can also mediate complex emitter-emitter interactions tunable in range and phase when the emitters transition frequencies lie within a band gap. Since these effects do not rely on polarization, we propose an implementation based on circuit QED to observe this physics.

## Limits of photon-mediated interactions in one-dimensional photonic baths

The exchange of off-resonant propagating photons between distant quantum emitters induces coherent interactions among them. The range of such interactions, and whether they are accompanied by dissipation, depends on the photonic energy dispersion, its dimensionality, and/or the light-matter couplings. In this manuscript, we characterize the limits of photon-mediated interactions for the case of generic one-dimensional photonic baths under the typical assumptions, that are, having finite range hoppings for the photonic bath plus local and rotating-wave light-matter couplings. In that case, we show how, irrespective of the system’s parameter, the coherent photon-mediated interactions can always be written as a finite sum of exponentials, and thus can not display a power-law asymptotic scaling. As an outlook, we show how by relaxing some of these conditions, e.g., going beyond local light-matter couplings (e.g., giant atoms) or with longer-range photon hopping models, power-law interactions can be obtained within certain distance windows, or even in the asymptotic regime for the latter case

## Multimode Fock states with large photon number: effective descriptions and applications in quantum metrology

We develop general tools to characterise and efficiently compute relevant observables of multimode N-photon states generated in nonlinear decays in one-dimensional waveguides. We then consider optical interferometry in a Mach–Zender interferometer where a d-mode photonic state enters in each arm of the interferometer. We derive a simple expression for the quantum Fisher information in terms of the average photon number in each mode, and show that it can be saturated by number-resolved photon measurements that do not distinguish between the different d modes.

## Taking snapshots of a quantum thermalization process: emergent classicality in quantum jump trajectories.

We theoretically investigate the emergence of classical statistical physics in a finite quantum system that is subjected to a quantum measurement process. A random matrix theory approach to non-integrable quantum systems predicts that the set of outcomes of the measurement of a macroscopic observable evolve in time like stochastic variables, whose variance satisfies the celebrated Einstein relation for Brownian diffusion. Our results show how to extend the framework of eigenstate thermalization to the prediction of properties of quantum measurements on an otherwise closed quantum system. We show numerically the validity of the random matrix approach in quantum chain models.

## Scalable multiphoton generation from cavity-synchronized single-photon sources

We propose an efficient, scalable and deterministic scheme to generate up to hundreds of indistinguishable photons over multiple channels, on demand. Our design relies on multiple single-photon sources, each coupled to a waveguide, and all of them interacting with a common cavity mode. The cavity synchronizes and triggers the simultaneous emission of one photon by each source, which are collected by the waveguides. For a state-of-the-art circuit QED implementation, this scheme supports the creation of single photons with purity, indistinguishability, and efficiency of 99% at rates of ∼MHz. We also discuss conditions to create a device to produce 30-photon simultaneously with efficiency above 70% at a rate of hundreds of kHz. This is several orders of magnitude more efficient than previous demultiplexed sources for boson sampling, and enables the realization of deterministic multi-photon sources and scalable quantum information processing with photons.