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1. Noise-resilient phase transitions and limit-cycles in coupled Kerr oscillators

   https://doi.org/10.1088/1367-2630/ad2414  

   Alaeian, H; Soriente, M; Najafi, K; Yelin, S F (February 2024, New Journal of Physics)

   Abstract In recent years, there has been considerable focus on exploring driven-dissipative quantum systems, as they exhibit distinctive dissipation-stabilized phases. Among themdissipative time crystalis a unique phase emerging as a shift from disorder or stationary states to periodic behaviors. However, understanding the resilience of these non-equilibrium phases against quantum fluctuations remains unclear. This study addresses this query within a canonical parametric quantum optical system, specifically, a multi-mode cavity with self- and cross-Kerr non-linearity. Using mean-field (MF) theory we obtain the phase diagram and delimit the parameter ranges that stabilize a non-stationary limit-cycle phase. Leveraging the Keldysh formalism, we study the unique spectral features of each phase. Further, we extend our analyses beyond the MF theory by explicitly accounting for higher-order correlations through cumulant expansions. Our findings unveil insights into the modifications of the open quantum systems phases, underscoring the significance of quantum correlations in non-equilibrium steady states. Importantly, our results conclusively demonstrate the resilience of the non-stationary phase against quantum fluctuations, rendering it a dissipation-induced genuine quantum synchronous phase. 

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2. Observation of a prethermal discrete time crystal

   https://doi.org/10.1126/science.abg8102  

   Kyprianidis, A.; Machado, F.; Morong, W.; Becker, P.; Collins, K. S.; Else, D. V.; Feng, L.; Hess, P. W.; Nayak, C.; Pagano, G.; et al (June 2021, Science)

   null (Ed.)

   Extending the framework of statistical physics to the nonequilibrium setting has led to the discovery of previously unidentified phases of matter, often catalyzed by periodic driving. However, preventing the runaway heating that is associated with driving a strongly interacting quantum system remains a challenge in the investigation of these newly discovered phases. In this work, we utilize a trapped-ion quantum simulator to observe the signatures of a nonequilibrium driven phase without disorder—the prethermal discrete time crystal. Here, the heating problem is circumvented not by disorder-induced many-body localization, but rather by high-frequency driving, which leads to an expansive time window where nonequilibrium phases can emerge. Floquet prethermalization is thus presented as a general strategy for creating, stabilizing, and studying intrinsically out-of-equilibrium phases of matter. 

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3. Topological Phases with Average Symmetries: The Decohered, the Disordered, and the Intrinsic

   https://doi.org/10.1103/PhysRevX.15.021062  

   Ma, Ruochen; Zhang, Jian-Hao; Bi, Zhen; Cheng, Meng; Wang, Chong (May 2025, Physical Review X)

   Global symmetries greatly enrich the landscape of topological quantum phases, playing an essential role from topological insulators to fractional quantum Hall effect. Topological phases in mixed quantum states, originating from decoherence in open quantum systems or disorders in imperfect crystalline solids, have recently garnered significant interest. Unlike pure states, mixed quantum states can exhibit average symmetries—symmetries that keep the total ensemble invariant but not on each individual state. In this work, we present a systematic classification and characterization of average symmetry-protected topological (ASPT) phases applicable to generic symmetry groups, encompassing both average and exact symmetries, for bosonic and fermionic systems. Moreover, we formulate the theory of average symmetry-enriched topological (ASET) orders in disordered bosonic systems. Our systematic approach helps clarify nuanced issues in previous literature and uncovers compelling new physics. Notably, we discover that (1) the definition and classification of ASPT phases in decohered and disordered systems exhibit subtle differences, (2) despite these differences, ASPT phases in both settings can be classified and characterized under a unified framework of defect decoration and spectral sequence, (3) this systematic classification uncovers a plethora of ASPT phases that are intrinsically mixed, implying they can exclusively manifest in decohered or disordered systems where part of the symmetry is average, and (4) similarly for ASET, we find intrinsically disordered phases exhibiting exotic anyon behaviors—the ground states of such phases necessarily contain localized anyons, with gapless (yet still localized) excitation blue spectra. 

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4. Quantum Composites with Charge‐Density‐Wave Fillers

   https://doi.org/10.1002/adma.202209708  

   Barani, Zahra; Geremew, Tekwam; Stokey, Megan; Sesing, Nicholas; Taheri, Maedeh; Hilfiker, Matthew J.; Kargar, Fariborz; Schubert, Mathias; Salguero, Tina T.; Balandin, Alexander A. (May 2023, Advanced Materials)

   Abstract A unique class of advanced materials—quantum composites based on polymers with fillers composed of a van der Waals quantum material that reveals multiple charge‐density‐wave quantum condensate phases—is demonstrated. Materials that exhibit quantum phenomena are typically crystalline, pure, and have few defects because disorder destroys the coherence of the electrons and phonons, leading to collapse of the quantum states. The macroscopic charge‐density‐wave phases of filler particles after multiple composite processing steps are successfully preserved in this work. The prepared composites display strong charge‐density‐wave phenomena even above room temperature. The dielectric constant experiences more than two orders of magnitude enhancement while the material maintains its electrically insulating properties, opening a venue for advanced applications in energy storage and electronics. The results present a conceptually different approach for engineering the properties of materials, extending the application domain for van der Waals materials. 

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5. Topological prethermal strong zero modes on superconducting processors

   https://doi.org/10.1038/s41586-025-09476-z  

   Jin, Feitong; Jiang, Si; Zhu, Xuhao; Bao, Zehang; Shen, Fanhao; Wang, Ke; Zhu, Zitian; Xu, Shibo; Song, Zixuan; Chen, Jiachen; et al (September 2025, Nature)

   Abstract Symmetry-protected topological phases^1–4cannot be described by any local order parameter and are beyond the conventional symmetry-breaking model⁵. They are characterized by topological boundary modes that remain stable under symmetry respecting perturbations^1–4,6–8. In clean, gapped systems without disorder, the stability of these edge modes is restricted to the zero-temperature manifold; at finite temperatures, interactions with mobile thermal excitations lead to their decay^9–11. Here we report the observation of a distinct type of topological edge mode^12–14, which is protected by emergent symmetries and persists across the entire spectrum, in an array of 100 programmable superconducting qubits. Through digital quantum simulation of a one-dimensional disorder-free stabilizer Hamiltonian, we observe robust long-lived topological edge modes over up to 30 cycles for a wide range of initial states. We show that the interaction between these edge modes and bulk excitations can be suppressed by dimerizing the stabilizer strength, leading to an emergent U(1) × U(1) symmetry in the prethermal regime of the system. Furthermore, we exploit these topological edge modes as logical qubits and prepare a logical Bell state, which exhibits persistent coherence, despite the system being disorder-free and at finite temperature. Our results establish a viable digital simulation approach^15–18to experimentally study topological matter at finite temperature and demonstrate a potential route to construct long-lived, robust boundary qubits in disorder-free systems. 

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