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Thanks to their high quality factor, combined to the smallest modal volume, defect-cavities in photonic crystal slabs represent a promising, versatile tool for fundamental studies and applications in photonics. In paricular, the L3, H0 and H1 defects are the most popular and widespread cavity designs, due to their compactness, simplicity and small mode volume. For these cavities, the current best optimal designs still result in Q -values of a few times 10 5 only, namely one order of magnitude below the bound set by fabrication imperfections and material absorption in silicon. Here, we use a genetic algorithm to find a global maximum of the quality factor of these designs, by varying the positions of few neighbouring holes. We consistently find Q -values above one million – one order of magnitude higher than previous designs. Furthermore, we study the effect of disorder on the optimal designs and conclude that a similar improvement is also expected experimentally in state-of-the-art systems.

In open quantum systems, dissipative phase transitions (DPTs) emerge from the interplay between unitary evolution, drive, and dissipation. While second-order DPTs have been predominantly investigated theoretically, first-order DPTs have been observed in single-photon-driven Kerr resonators. We present here an experimental and theoretical analysis of both first and second-order DPTs in a two-photon-driven superconducting Kerr resonator. We characterize the steady state at the critical points, showing squeezing below vacuum and the coexistence of phases with different photon numbers. Through time resolved measurements, we study the dynamics across the critical points and observe hysteresis cycles at the first-order DPT and spontaneous symmetry breaking at the second-order DPT. Extracting the timescales of the critical phenomena reveals slowing down across five orders of magnitude when scaling towards the thermodynamic limit. Our results showcase the engineering of criticality in superconducting circuits, advancing the use of parametric resonators for critically-enhanced quantum information applications. Dissipative quantum phase transitions in open quantum systems have been extensively studied, but experiments have been mostly limited to first-order transitions. Here, the authors report the observation of first- and second-order dissipative quantum phase transitions in a superconducting Kerr resonator under two-photon pumping.

We characterize photonic transport in a boundary driven array of nonlinear optical cavities. We find that the output field suddenly drops when the chain length is increased beyond a threshold. After this threshold a highly chaotic and unstable regime emerges, which marks the onset of a super-diffusive photonic transport. We show the scaling of the threshold with pump intensity and nonlinearity. Finally, we address the competition of disorder and nonlinearity presenting a diffusive-insulator phase transition.

From fundamental sciences to economics and industry, discrete optimization problems are ubiquitous. Yet, their complexity often renders exact solutions intractable, necessitating the use of approximate methods. Heuristics inspired by classical physics have long played a central role in this domain. More recently, quantum annealing has emerged as a promising alternative, with hardware implementations realized on both analog and digital quantum devices. Here, we develop a heuristic inspired by quantum annealing, using Generalized Coherent States as a parameterized variational Ansatz to represent the quantum state. This framework allows for the analytical computation of energy and gradients with low-degree polynomial complexity, enabling the study of large problems with thousands of spins. Concurrently, these states capture non-trivial entanglement, crucial for the effectiveness of quantum annealing. We benchmark the heuristic on the three-dimensional Edwards-Anderson model and compare the solution quality and runtime of our method to other popular heuristics. Our findings suggest that it offers a scalable way to leverage quantum effects for complex optimization problems, with the potential to complement or improve upon conventional alternatives in large-scale applications. Optimization problems are everywhere in science and industry, but their complexity often makes them hard to solve exactly. The authors introduce a quantum-inspired heuristic based on generalized coherent states that captures quantum effects, while scaling to thousands of spins and achieving competitive performance against alternative methods.

Thermalization in quantum many-body systems typically unfolds over timescales governed by intrinsic relaxation mechanisms. Yet, its spatial aspect is less understood. We investigate this phenomenon in the nonequilibrium steady state (NESS) of a Bose-Hubbard chain subject to coherent driving and dissipation at its boundaries, a setup inspired by current designs in circuit quantum electrodynamics. The dynamical fingerprints of chaos in this NESS are probed using semiclassical out-of-time-order correlators within the truncated Wigner approximation. At intermediate drive strengths, we uncover a two-stage thermalization along the spatial dimension: phase coherence is rapidly lost near the drive, while amplitude relaxation occurs over much longer distances. This separation of scales gives rise to an extended hydrodynamic regime exhibiting anomalous temperature profiles, which we designate as a “prethermal” domain. At stronger drives, the system enters a nonthermal, non-chaotic finite-momentum condensate characterized by sub-Poissonian photon statistics and a spatially modulated phase profile, whose stability is undermined by quantum fluctuations. We explore the conditions underlying this protracted thermalization in space and argue that similar mechanisms are likely to emerge in a broad class of extended driven-dissipative systems. Thermalization in quantum many-body systems can unfold across space in surprising ways. The authors reveal nonequilibrium regimes in a driven-dissipative quantum chain, including a spatially emergent prethermal domain and a nonthermal condensate destabilized by quantum fluctuations, with broad implications for driven quantum platforms

Landau–Zener–Stückelberg–Majorana (LZSM) interference occurs when qubit parameters are periodically modulated across avoided level crossings. We explore this phenomenon in nonlinear multilevel bosonic systems, where interference is influenced by multiple energy levels. We fabricate two superconducting resonators with flux-tunable Josephson junction arrays. The first device, exhibiting weak nonlinearity, behaves like a linear resonator under weak driving but shows LZSM interference akin to two-level systems. With stronger driving, nonlinear effects alter the interference pattern. We theoretically demonstrate that merging LZSM peaks can lead to dissipative quantum chaos. In the second device, where nonlinearity exceeds photon-loss rates, we observe additional LZSM peaks from Kerr multiphoton resonances. Under Floquet theory, these resonances represent synthetic modes of coupled nonlinear cavities, revealing effective coupling as modulation parameters vary. Our findings advance the understanding of LZSM physics and emphasize the control of nonlinear Floquet states and the emergence of chaos in engineered systems, with significant implications for novel applications in quantum dynamics and quantum control.

The quantum Rabi model (QRM) is a cornerstone in the study of light-matter interactions within cavity and circuit quantum electrodynamics (QED). It effectively captures the dynamics of a two-level system coupled to a single-mode resonator, serving as a foundation for understanding quantum optical phenomena in a great variety of systems. However, this model may produce inaccurate results for large coupling strengths, even in systems with high anharmonicity. Moreover, issues of gauge invariance further undermine its reliability. In this work, we introduce a renormalized QRM that incorporates the effective influence of higher atomic energy levels, providing a significantly more accurate representation of the system while still maintaining a two-level description. To demonstrate the versatility of this approach, we present two different examples: an atom in a double-well potential and a superconducting artificial atom (fluxonium qubit). This procedure opens new possibilities for precisely engineering and understanding cavity and circuit QED systems, which are highly sought-after, especially for quantum information processing. The quantum Rabi model is widely used to describe how light interacts with atoms or artificial atoms in cavities and circuits, but it often becomes inaccurate in modern strong-coupling experiments. The authors introduce a renormalized version that accounts for higher atomic levels while keeping a simple two-level picture, greatly improving accuracy.

The lack of suitable quantum emitters in silicon and silicon-based materials has prevented the realization of room temperature, compact, stable and integrated sources of single photons in a scalable on-chip architecture, so far. Current approaches rely on exploiting the enhanced optical nonlinearity of silicon through light confinement or slow-light propagation and are based on parametric processes that typically require substantial input energy and spatial footprint to reach a reasonable output yield. Here we propose an alternative all-silicon device that employs a different paradigm, namely the interplay between quantum interference and the third-order intrinsic nonlinearity in a system of two coupled optical cavities. This unconventional photon blockade allows to produce antibunched radiation at extremely low input powers. We demonstrate a reliable protocol to operate this mechanism under pulsed optical excitation, as required for device applications, thus implementing a true single-photon source. We finally propose a state-of-art implementation in a standard silicon-based photonic crystal integrated circuit that outperforms existing parametric devices either in input power or footprint area.

Thermalization in quantum many-body systems, the process by which they naturally evolve toward thermal equilibrium, typically unfolds over timescales set by the underlying relaxation mechanisms. Yet, the spatial aspect of thermalization in these systems is less understood. We investigate this phenomenon within the nonequilibrium steady state (NESS) of a Bose-Hubbard chain subject at its boundaries to coherent driving and dissipation, a setup inspired by current designs in circuit quantum electrodynamics. We uncover a two-stage thermalization process along the spatial dimension. Close to the coherent drive, the U(1) symmetry of the phase of the photonic field is restored over a short length scale, while its amplitude relaxes over a much larger scale. This opens up an extensive region of the chain characterized by a chaotic yet nonthermal phase. Dynamical fingerprints of chaos in this NESS are probed using semiclassical out-of-time-order correlators (OTOCs) within the truncated Wigner approximation (TWA). We explore the conditions underlying this protracted thermalization in space and argue that similar prethermal chaotic phases are likely to occur in a broad range of extended driven-dissipative systems.

The lack of suitable quantum emitters in silicon and silicon-based materials has prevented the realization of room temperature, compact, stable, and integrated sources of single photons in a scalable on-chip architecture, so far. Current approaches rely on exploiting the enhanced optical nonlinearity of silicon through light confinement or slow-light propagation, and are based on parametric processes that typically require substantial input energy and spatial footprint to reach a reasonable output yield. Here we propose an alternative all-silicon device that employs a different paradigm, namely the interplay between quantum interference and the third-order intrinsic nonlinearity in a system of two coupled optical cavities. This unconventional photon blockade allows to produce antibunched radiation at extremely low input powers. We demonstrate a reliable protocol to operate this mechanism under pulsed optical excitation, as required for device applications, thus implementing a true single-photon source. We finally propose a state-of-art implementation in a standard silicon-based photonic crystal integrated circuit that outperforms existing parametric devices either in input power or footprint area.