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Abstract Topologically ordered phases of matter elude Landau’s symmetry-breaking theory, featuring a variety of intriguing properties such as long-range entanglement and intrinsic robustness against local perturbations. Their extension to periodically driven systems gives rise to exotic new phenomena that are forbidden in thermal equilibrium. Here, we report the observation of signatures of such a phenomenon—a prethermal topologically ordered time crystal—with programmable superconducting qubits arranged on a square lattice. By periodically driving the superconducting qubits with a surface code Hamiltonian, we observe discrete time-translation symmetry breaking dynamics that is only manifested in the subharmonic temporal response of nonlocal logical operators. We further connect the observed dynamics to the underlying topological order by measuring a nonzero topological entanglement entropy and studying its subsequent dynamics. Our results demonstrate the potential to explore exotic topologically ordered nonequilibrium phases of matter with noisy intermediate-scale quantum processors. 

Abstract. Mixed-layer depth (MLD) exhibits significant variability, which is important for atmosphere–ocean exchanges of heat and atmospheric gases. The origins of the mesoscale MLD variability in the Southern Ocean are studied here in an idealised regional ocean–atmosphere model (ROAM). The main conclusion from the analysis of the upper-ocean buoyancy budget is that, while the atmospheric forcing and oceanic vertical mixing, on average, induce the mesoscale variability of MLD, the three-dimensional oceanic advection of buoyancy counteracts and partially balances these atmosphere-induced vertical processes. The relative importance of advection changes with both season and average MLD. From January to May, when the mixed layer is shallow, the atmospheric forcing and oceanic mixing are the most important processes, with the advection playing a secondary role. From June to December, when the mixed layer is deep, both atmospheric forcing and oceanic advection are equally important in driving the MLD variability. Importantly, buoyancy advection by mesoscale ocean current anomalies can lead to both local shoaling and deepening of the mixed layer. The role of the atmospheric forcing is then directly addressed by two sensitivity experiments in which the mesoscale variability is removed from the atmosphere–ocean heat and momentum fluxes. The findings confirm that mesoscale atmospheric forcing predominantly controls MLD variability in summer and that intrinsic oceanic variability and surface forcing are equally important in winter. As a result, MLD variance increases when mesoscale anomalies in atmospheric fluxes are removed in winter, and oceanic advection becomes a dominant player in the buoyancy budget. This study highlights the importance of oceanic advection and intrinsic ocean dynamics in driving mesoscale MLD variability and underscores the importance of MLD in modulating the effects of advection on upper-ocean dynamics. 

Understanding the nature of high-redshift dusty galaxies requires a comprehensive view of their interstellar medium (ISM) and molecular complexity. However, the molecular ISM at high redshifts is commonly studied using only a few species beyond¹²C¹⁶O, limiting our understanding. In this paper, we present the results of deep 3 mm spectral line surveys using the NOrthern Extended Millimeter Array (NOEMA) targeting two strongly lensed dusty galaxies observed when the Universe was less than 1.8 Gyr old: APM 08279+5255, a quasar at redshiftz= 3.911, and NCv1.143 (H-ATLAS J125632.7+233625), az= 3.565 starburst galaxy. The spectral line surveys cover rest-frame frequencies from about 330 to 550 GHz for both galaxies. We report the detection of 38 and 25 emission lines in APM 08279+5255 and NCv1.143, respectively. These lines originate from 17 species, namely CO,¹³CO, C¹⁸O, CN, CCH, HCN, HCO⁺, HNC, CS, C³⁴S, H₂O, H₃O⁺, NO, N₂H⁺, CH, c-C₃H₂, and the vibrationally excited HCN and neutral carbon. The spectra reveal the chemical richness and the complexity of the physical properties of the ISM. By comparing the spectra of the two sources and combining the analysis of the molecular gas excitation, we find that the physical properties and the chemical imprints of the ISM are different: the molecular gas is more excited in APM 08279+5255, which exhibits higher molecular gas temperatures and densities compared to NCv1.143; the molecular abundances in APM 08279+5255 are akin to the values of local active galactic nuclei (AGN), showing boosted relative abundances of the dense gas tracers that might be related to high-temperature chemistry and/or the X-ray-dominated regions, while NCv1.143 more closely resembles local starburst galaxies. The most significant differences between the two sources are found in H₂O: the 448 GHz ortho-H₂O(4₂₃ − 3₃₀) line is significantly brighter in APM 08279+5255, which is likely linked to the intense far-infrared radiation from the dust powered by AGN. Our astrochemical model suggests that, at such high column densities, far-ultraviolet radiation is less important in regulating the ISM, while cosmic rays (and/or X-rays and shocks) are the key players in shaping the molecular abundances and the initial conditions of star formation. Both our observed CO isotopologs line ratios and the derived extreme ISM conditions (high gas temperatures, densities, and cosmic-ray ionization rates) suggest the presence of a top-heavy stellar initial mass function. From the ∼330–550 GHz continuum, we also find evidence of nonthermal millimeter flux excess in APM 08279+5255 that might be related to the central supermassive black hole. Such deep spectral line surveys open a new window into the physics and chemistry of the ISM and the radiation field of galaxies in the early Universe. 

Abstract We analyze the role of mesoscale heat advection in a mixed layer (ML) heat budget, using a regional high-resolution coupled model with realistic atmospheric forcing and an idealized ocean component. The model represents two regions in the Southern Ocean, one with strong ocean currents and the other with weak ocean currents. We conclude that heat advection by oceanic currents creates mesoscale anomalies in sea surface temperature (SST), while the atmospheric turbulent heat fluxes dampen these SST anomalies. This relationship depends on the spatial scale, the strength of the currents, and the mixed layer depth (MLD). At the oceanic mesoscale, there is a positive correlation between the advection and SST anomalies, especially when the currents are strong overall. For large-scale zonal anomalies, the ML-integrated advection determines the heating/cooling of the ML, while the SST anomalies tend to be larger in size than the advection and the spatial correlation between these two fields is weak. The effects of atmospheric forcing on the ocean are modulated by the MLD variability. The significance of Ekman advection and diabatic heating is secondary to geostrophic advection except in summer when the MLD is shallow. This study links heat advection, SST anomalies, and air–sea heat fluxes at ocean mesoscales, and emphasizes the overall dominance of intrinsic oceanic variability in mesoscale air–sea heat exchange in the Southern Ocean. 

North Atlantic cooling during Heinrich Stadial 1 triggered an east-west precipitation dipole over the tropical Indian Ocean. 

Topologically ordered phases of matter elude Landau's symmetry-breaking theory, featuring a variety of intriguing properties such as long-range entanglement and intrinsic robustness against local perturbations. Their extension to periodically driven systems gives rise to exotic new phenomena that are forbidden in thermal equilibrium. Here, we report the observation of signatures of such a phenomenon -- a prethermal topologically ordered time crystal -- with programmable superconducting qubits arranged on a square lattice. By periodically driving the superconducting qubits with a surface-code Hamiltonian, we observe discrete time-translation symmetry breaking dynamics that is only manifested in the subharmonic temporal response of nonlocal logical operators. We further connect the observed dynamics to the underlying topological order by measuring a nonzero topological entanglement entropy and studying its subsequent dynamics. Our results demonstrate the potential to explore exotic topologically ordered nonequilibrium phases of matter with noisy intermediate-scale quantum processors.