The assumption that quantum systems relax to a stationary state in the long-time limit underpins statistical physics and much of our intuitive understanding of scientific phenomena. For isolated systems this follows from the eigenstate thermalization hypothesis. When an environment is present the expectation is that all of phase space is explored, eventually leading to stationarity. Notable exceptions are decoherence-free subspaces that have important implications for quantum technologies and have so far only been studied for systems with a few degrees of freedom. Here we identify simple and generic conditions for dissipation to prevent a quantum many-body system from ever reaching a stationary state. We go beyond dissipative quantum state engineering approaches towards controllable long-time non-stationarity typically associated with macroscopic complex systems. This coherent and oscillatory evolution constitutes a dissipative version of a quantum time crystal. We discuss the possibility of engineering such complex dynamics with fermionic ultracold atoms in optical lattices.

The properties of organic conductors are often tuned by the application of chemical or external pressure, which change orbital overlaps and electronic bandwidths while leaving the molecular building blocks virtually unperturbed. Here, we show that, unlike any other method, light can be used to manipulate the local electronic properties at the molecular sites, giving rise to new emergent properties. Targeted molecular excitations in the charge-transfer salt κ-ðBEDTÀTTFÞ 2 Cu½NðCNÞ 2 Br induce a colossal increase in carrier mobility and the opening of a superconducting optical gap. Both features track the density of quasiparticles of the equilibrium metal and can be observed up to a characteristic coherence temperature T Ã ≃ 50 K, far higher than the equilibrium transition temperature T C ¼ 12.5 K. Notably, the large optical gap achieved by photoexcitation is not observed in the equilibrium superconductor, pointing to a light-induced state that is different from that obtained by cooling. First-principles calculations and model Hamiltonian dynamics predict a transient state with long-range pairing correlations, providing a possible physical scenario for photomolecular superconductivity.

We show how, upon heating the spin degrees of freedom of the Hubbard model to infinite temperature, the symmetries of the system allow the creation of steady states with long-range correlations between η-pairs. We induce this heating with either dissipation or periodic driving and evolve the system towards a non-equilibrium steady state, a process which melts all spin order in the system. The steady state is identical in both cases and displays distance-invariant off-diagonal η correlations. These correlations were first recognised in the superconducting eigenstates described in C. N. Yang's seminal paper {Physical Review Letters, 63, 2144 (1989)}, which are a subset of our steady states. We show that our results are a consequence of symmetry properties and entirely independent of the microscopic details of the model and the heating mechanism. arXiv:1902.05012v2 [quant-ph]

In nature, instances of synchronisation abound across a diverse range of environments. In the quantum regime, however, synchronisation is typically observed by identifying an appropriate parameter regime in a specific system. In this work we show that this need not be the case, identifying conditions which, when satisfied, guarantee that the individual constituents of a generic open quantum system will undergo completely synchronous limit cycles which are, to first order, robust to symmetry-breaking perturbations. We then describe how these conditions can be satisfied by the interplay between several elements: interactions, local dephasing and the presence of a strong dynamical symmetry-an operator which guarantees long-time non-stationary dynamics. These elements cause the formation of entanglement and off-diagonal long-range order which drive the synchronised response of the system. To illustrate these ideas we present two central examples: a chain of quadratically dephased spin-1s and the many-body charge-dephased Hubbard model. In both cases perfect phase-locking occurs throughout the system, regardless of the specific microscopic parameters or initial states. Furthermore, when these systems are perturbed, their nonlinear responses elicit longlived signatures of both phase and frequency-locking.

In driven-dissipative systems, the presence of a strong symmetry guarantees the existence of several steady states belonging to different symmetry sectors. Here we show that, when a system with a strong symmetry is initialized in a quantum superposition involving several of these sectors, each individual stochastic trajectory will randomly select a single one of them and remain there for the rest of the evolution. Since a strong symmetry implies a conservation law for the corresponding symmetry operator on the ensemble level, this selection of a single sector from an initial superposition entails a breakdown of this conservation law at the level of individual realizations. Given that such a superposition is impossible in a classical, stochastic trajectory, this is a a purely quantum effect with no classical analogue. Our results show that a system with a closed Liouvillian gap may exhibit, when monitored over a single run of an experiment, a behaviour completely opposite to the usual notion of dynamical phase coexistence and intermittency, which are typically considered hallmarks of a dissipative phase transition. We discuss our results with a simple, realistic model of squeezed superradiance.Driven dissipative systems are ubiquitous in many body physics and cavity QED [1][2][3][4][5][6][7][8][9][10][11][12]. These systems are typically gapped and feature a unique, non-equilibrium steady state. In the regime of a dissipative phase transition (DPT), however, this gap vanishes and the null-space of the Liouvillian is spanned by several compatible steady-states. [13][14][15][16][17][18][19][20][21][22]. Due to their fundamental interest and practical applications, such as enhanced metrological properties [23,24], DPTs have attracted a significant amount of attention, with much work being devoted to study the associated phenomena of bistability [3-5, 22, 25-28], hysteresis [2,29], intermittency [6,26,[29][30][31][32], multimodality [25,31], metastability [33] and symmetry breaking [34][35][36]. All these effects are understood as different manifestations of the coexistence of several non-equilibrium phases. In particular, many experiments will look for intermittency as the hallmark of such phase coexistence [6,26,[29][30][31][32]. Intermittency is a phenomenon defined by a random switching between periods of high and low dynamical activity (for instance in the rate of photon emission). This behaviour, which is observed during a single run of the experiment, is conveniently described using the formalism of quantum jumps in which the system is characterized in terms of a pure wavefunction that undergoes stochastic evolution [37][38][39].The timescale τ of this intermittency is given by the inverse of the Liouvillian gap or asymptotic decay rate (ADR), i.e. the eigenvalue λ 2 of the Liouvillian operator L with the second largest real part [23,40,41]. Since a DPT is defined by a vanishing Liouvillian gap [13,14], it will necessarily imply that τ diverges. In most typical situations, this closing is reached in the thermod...