Rosario Fazio

Measurement-induced phases exhibit unconventional dynamics as emergent collective phenomena, yet their behavior in tailored interacting systems -- crucial for quantum technologies -- remains less understood. We develop a systematic toolbox to analyze monitored dynamics in long-range interacting systems, relevant to platforms like trapped ions and Rydberg atoms. Our method extends spin-wave theory to general dynamical generators at the quantum trajectory level, enabling access to a broader class of states than approaches based on density matrices. This allows efficient simulation of large-scale interacting spins and captures nonlinear dynamical features such as entanglement and trajectory correlations. We showcase the versatility of our framework by exploring entanglement phase transitions in a monitored spin system with power-law interactions in one and two dimensions, where the entanglement scaling changes from logarithm to volume law as the interaction range shortens, and by dwelling on how our method mitigates experimental post-selection challenges in detecting monitored quantum phases.

Quantum systems evolving unitarily and subject to quantum measurements exhibit various types of non-equilibrium phase transitions, arising from the competition between unitary evolution and measurements. Dissipative phase transitions in steady states of time-independent Liouvillians and measurement induced phase transitions at the level of quantum trajectories are two primary examples of such transitions. Investigating a many-body spin system subject to periodic resetting measurements, we argue that many-body dissipative Floquet dynamics provides a natural framework to analyze both types of transitions. We show that a dissipative phase transition between a ferromagnetic ordered phase and a paramagnetic disordered phase emerges for long-range systems as a function of measurement probabilities. A measurement induced transition of the entanglement entropy between volume law scaling and sub-volume law scaling is also present, and is distinct from the ordering transition. The two phases correspond to an error-correcting and a quantum-Zeno regimes, respectively. The ferromagnetic phase is lost for short range interactions, while the volume law phase of the entanglement is enhanced. An analysis of multifractal properties of wave function in Hilbert space provides a common perspective on both types of transitions in the system. Our findings are immediately relevant to trapped ion experiments, for which we detail a blueprint proposal based on currently available platforms.

In this work we discuss the existence of time-translation symmetry breaking in a kicked infinite-range-interacting clean spin system described by the Lipkin-Meshkov-Glick model. This Floquet time crystal is robust under perturbations of the kicking protocol, its existence being intimately linked to the underlying $\mathbb{Z}_2$ symmetry breaking of the time-independent model. We show that the model being infinite-range and having an extensive amount of symmetry breaking eigenstates is essential for having the time-crystal behaviour. In particular we discuss the properties of the Floquet spectrum, and show the existence of doublets of Floquet states which are respectively even and odd superposition of symmetry broken states and have quasi-energies differing of half the driving frequencies, a key essence of Floquet time crystals. Remarkably, the stability of the time-crystal phase can be directly analysed in the limit of infinite size, discussing the properties of the corresponding classical phase space. Through a detailed analysis of the robustness of the time crystal to various perturbations we are able to map the corresponding phase diagram. We finally discuss the possibility of an experimental implementation by means of trapped ions.

From the steam engine to current nano-devices, the design of efficient thermal machines has been instrumental in modern societies. In its essence a thermal engine can be thought as a working substance, in contact with two or more baths, undergoing a cyclic transformation. What happens if the working substance is on the verge of a phase transition? Already in 1902 the latent heat was identified as a key to improve the efficiency of steam engines Despite this early observation, the impact of phase transitions on the performance of thermal machines has not been addressed. By combining the tools of non-equilibrium and quantum thermodynamics with finite-size-scaling and information theory, we unveil an unnoticed mechanism, triggered by the vicinity to a phase transition, to boost the performance of an engine. This result sheds new light on the so called power-efficiency dilemma and could be used to realise powerful and, at the same time, efficient engines. Specific implementations with trapped ions and superconducting nano-circuits will be discussed.