'Sudden' quantum quench and prethermalization have become a cross-cutting theme for discovering emergent states of matter. Yet this remains challenging in electron matter, especially superconductors. The grand question of what is hidden underneath superconductivity (SC) appears universal, but poorly understood. Here we reveal a long-lived gapless quantum phase of prethermalized quasiparticles (QPs) after a single-cycle terahertz (THz) quench of a NbSn SC gap. Its conductivity spectra is characterized by a sharp coherent peak and a vanishing scattering rate that decreases almost linearly towards zero frequency, which is most pronounced around the full depletion of the condensate and absent for a high-frequency pump. Above a critical pump threshold, such a QP phase with coherent transport and memory persists as an unusual prethermalization plateau, without relaxation to normal and SC thermal states for an order of magnitude longer than the QP recombination and thermalization times. Switching to this metastable 'quantum QP fluid' signals non-thermal quench of coupled SC and charge-density-wave (CDW)-like orders and hints quantum control beneath the SC.

We consider an open system near a quantum critical point that is suddenly moved towards the critical point. The bath-dominated diffusive non-equilibrium dynamics after the quench is shown to follow scaling behavior, governed by a critical exponent that emerges in addition to the known equilibrium critical exponents. We determine this exponent and show that it describes universal prethermalized coarsening dynamics of the order parameter in an intermediate time regime. Implications of this quantum critical prethermalization are a powerlaw rise of order and correlations after an initial collapse of the equilibrium state and a crossover to thermalization that occurs arbitrarily late for sufficiently shallow quenches.Predicting the out-of-equilibrium dynamics of quantum many-body systems is a challenge of fundamental and practical importance. This research area has been boosted by recent experiments in cold-atom gases [1] and scaled-up quantum-circuits [2], by ultra-fast pump-probe measurements in correlated materials [3][4][5], and by performing heavy-ion collisions that explore the quark-gluon plasma [6]. In this context, the universality near a quantum critical point (QCP), well established in and near equilibrium, comes with the potential to make quantitative predictions for strongly interacting systems far from equilibrium. For example, the quantum version [7][8][9][10][11] of the Kibble-Zurek mechanism of defect formation [12,13] was developed for systems driven through a symmetry breaking QCP at a small, but finite rate. Similarly, near a QCP the long-time dynamics after a sudden change of Hamiltonian parameters, is governed by equilibrium exponents [14]. These phenomena occur in the regime of longest time scales.Recently, however, many physical systems away from equilibrium were identified which display novel dynamical behavior on intermediate time scales, a behavior often referred to as prethermalization [15][16][17][18][19][20][21][22][23][24][25]. The question arises whether one can expect universality during prethermalization if one drives a system towards a QCP. Even if this is done at a finite rate 1/τ , a system will fall out of equilibrium at some point, a behavior owed to the critical slowing down near the QCP. Then a scaling theory with characteristic time scale τ can be developed [10], where regions of the size of the freeze-out length ∝ τ 1/z emerge that behave like in equilibrium. z is the dynamic critical exponent. In case of a quantum quench, the time scale τ and the freeze-out length become comparable to microscopic time and length scales, respectively and the system instantly falls out of equilibrium. The detailed recovery of this out-of-equilibrium dynamics, along with the time dependence of length scales, order-parameter correlations, and the potential for outof-equilibrium universality are major theoretical and experimental challenges.In this Letter, we show that the time evolution of observables in an open system that is suddenly moved to a QCP displays universal behavior (see Fig. 1(a-b)...

The non-equilibrium dynamics of a system that is located in the vicinity of a quantum critical point is affected by the critical slowing down of order-parameter correlations with the potential for novel out-of-equilibrium universality. After a quantum quench, i.e. a sudden change of a parameter in the Hamiltonian such a system is expected to almost instantly fall out of equilibrium and undergo aging dynamics, i.e. dynamics that depends on the time passed since the quench. Investigating the quantum dynamics of a N -component ϕ 4 -model coupled to an external bath, we determine this universal aging and demonstrate that the system undergoes a coarsening, governed by a critical exponent that is unrelated to the equilibrium exponents of the system. We analyze this behavior in the large-N limit, which is complementary to our earlier renormalization group analysis, allowing in particular the direct investigation of the order-parameter dynamics in the symmetry broken phase and at the upper critical dimension. By connecting the long time limit of fluctuations and response, we introduce a distribution function that shows that the system remains non-thermal and exhibits quantum coherence even on long timescales.

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