We have explored the nonlinear dynamics of an optomechanical system consisting of an illuminated Fabry-Perot cavity, one of whose end-mirrors is attached to a vibrating cantilever. Such a system can experience negative light-induced damping and enter a regime of self-induced oscillations. We present a systematic experimental and theoretical study of the ensuing attractor diagram describing the nonlinear dynamics, in an experimental setup where the oscillation amplitude becomes large, and the mirror motion is influenced by several optical modes. A theory has been developed that yields detailed quantitative agreement with experimental results. This includes the observation of a regime where two mechanical modes of the cantilever are excited simultaneously.

We investigate the onset of "eigenstate thermalization" and the crossover to ergodicity in a system of one-dimensional fermions with increasing interaction. We analyze the fluctuations in the expectation values of most relevant few-body operators with respect to eigenstates. It turns out that these are intimately related to the inverse participation ratio of eigenstates displayed in the operator eigenbasis. Based on this observation, we find good evidence that eigenstate thermalization should set in even for vanishingly small perturbations in the thermodynamic limit.

We investigate the relative phase between two weakly interacting 1D condensates of bosonic atoms after suddenly switching on the tunnel coupling. The following phase dynamics is governed by the quantum sine-Gordon equation. In the semiclassical limit of weak interactions, we observe the parametric amplification of quantum fluctuations leading to the formation of breathers with a finite lifetime. The typical lifetime and density of these "quasibreathers" are derived employing exact solutions of the classical sine-Gordon equation. Both depend on the initial relative phase between the condensates, which is considered as a tunable parameter.

We consider two weakly interacting quasi-1D condensates of cold bosonic atoms. It turns out that a time-dependent variation of the tunnel-coupling between those condensates is equivalent to the spatial expansion of a one-dimensional toy-Universe, with regard to the dynamics of the relative phase field. The dynamics of this field is governed by the quantum sine-Gordon equation. Thus, this analogy could be used to 'quantum simulate' the dynamics of a scalar, interacting quantum field on an expanding background. We discuss how to observe the 'freezing' of quantum fluctuations during an accelerating expansion in a possible experiment. We also analyze an experimental protocol to study the formation of sine-Gordon breathers in the relative phase field, seeded by quantum fluctuations. IntroductionThe recent progress in coherently controlling systems of cold atoms (e.g., [1-5]), stimulated a lot of research concerned with employing these experimental systems to 'quantum simulate' prototypical quantum manybody models and quantum field theories (e.g., [6,7]). This includes dynamics that is relevant for the early Universe, e.g. the initial acoustic density oscillations (Sakharov oscillations) that determine the structure observed in the cosmic microwave background radiation and which have recently been simulated using a quench in a cloud of cold atoms [8]. Particularly fascinating are ideas concerned with simulating quantum many-body physics on curved space-times ('analog gravity') (see [9][10][11][12][13][14][15][16][17][18][19][20], as well as references therein) connecting concepts and techniques from cosmology and condensed matter.During the past few years, a very versatile platform for analog quantum simulations with cold atoms has been established in the Schmiedmayer group at Vienna: an atom chip holding one or two quasi-1D bosonic condensates [3,[21][22][23]. In this setup, it is possible to tune the trapping potential in a time-dependent fashion, which includes the possibility to modify the tunnel-coupling between two nearby condensates. That has been used experimentally to probe quench physics [24-28] and to control non-equilibrium dynamics [29]. After releasing the trap, the expanding clouds give rise to matter-wave interference that reveals the relative phase between the two condensates. The spatially resolved phase field can be measured for each run of the experiment, and the full statistics [22,30] as well as higher-order correlators [28] have been extracted from the data of many runs. A recent comprehensive overview of this set of experiments can be found in [31]. The opportunities offered by this platform have resulted in a number of theoretical proposals for future experiments, e.g. [32][33][34].In the present work, we argue that a pair of tunnel-coupled, quasi-1D, bosonic condensates can be employed for simulating an interacting, scalar quantum field on top of an expanding 1+1 dimensional space-time (figures 1(a) and (c)). This scalar field is represented by the relative phase field between the condensate...