We study the dynamical response of a system to a sudden change of the tuning parameter starting ͑or ending͒ at the quantum critical point. In particular, we analyze the scaling of the excitation probability, number of excited quasiparticles, heat and entropy with the quench amplitude, and the system size. We extend the analysis to quenches with arbitrary power law dependence on time of the tuning parameter, showing a close connection between the scaling behavior of these quantities with the singularities of the adiabatic susceptibilities of order m at the quantum critical point, where m is related to the power of the quench. Precisely for sudden quenches, the relevant susceptibility of the second order coincides with the fidelity susceptibility. We discuss the generalization of the scaling laws to the finite-temperature quenches and show that the statistics of the low-energy excitations becomes important. We illustrate the relevance of those results for cold-atom experiments.PACS number͑s͒: 64.70. Tg, 64.70.qj, 67.85.Ϫd Understanding the dynamics of quantum interacting systems is one of the key challenges of the modern physics. The theoretical research in this area has been stimulated by the fast developments in the field of cold-atom experiments 1 and the emerging possibility of manipulating quantum systems. 2 In particular, the idea of suddenly changing a parameter of the Hamiltonian, i.e., performing a quench, has been widely addressed within different approaches.3-6 Furthermore, recently the interest in studying quenches has been motivated by the questions on the thermalization of quantum systems. 7 Quenches near quantum critical points are especially interesting because of the expected universality of the response of the system and thus the possibility of using the quench dynamics as a nonequilibrium probe of phase transitions. This universality is well established in equilibrium systems. 8 It has been shown that a universal scaling arises as well in the case of slow adiabatic perturbations that drive the system through a quantum critical point. 9,10 The predicted scaling for the number of created quasiparticles with the quench rate was verified for various specific models. [11][12][13][14][15][16] This analysis was also generalized to nonlinear quenches. 17,18 In this work we consider a d-dimensional system described by a Hamiltonian H͑͒ = H 0 + V, where H 0 is the Hamiltonian corresponding to a quantum critical point ͑QCP͒ and V is a relevant ͑or marginal͒ perturbation, which drives the system to a particular phase. The quench process is implemented through the parameter that changes in time, according to some protocol, between the initial value =0 at time t = 0, corresponding to the critical point, and the final value f at final time t f . 29 We expect two qualitatively different scenarios: ͑i͒ for fast quenches, the response of the system only depends on the quench amplitude f , but not on the details of the protocol used to change -we refer to this regime as sudden quench; ͑ii͒ for slow quenches, i...

The probabilistic character of the measurement process is one of the most puzzling and fascinating aspects of quantum mechanics. In many-body systems quantum mechanical noise reveals non-local correlations of the underlying many-body states. Here, we provide a complete experimental analysis of the shot-to-shot variations of interference fringe contrast for pairs of independently created one-dimensional Bose condensates. Analyzing different system sizes we observe the crossover from thermal to quantum noise, reflected in a characteristic change in the distribution functions from Poissonian to Gumbel-type, in excellent agreement with theoretical predictions based on the Luttinger liquid formalism. We present the first experimental observation of quasi long-range order in one-dimensional atomic condensates, which is a hallmark of quantum fluctuations in one-dimensional systems. Furthermore, our experiments constitute the first analysis of the full distribution of quantum noise in an interacting many-body system.

Here we give detailed derivations and provide additional examples to the main paper [1]. In particular, we discuss the scaling behavior of observables like correlation functions and density of excitations. We also analyze effects of nonintegrability of the Bose-Hubbard model on the long-time dynamics of the correlation functions. In addition we explicitly consider several interacting models, where we are able to analyze slow dynamics and classify it according to the regimes suggested in the main paper.

Understanding strongly correlated quantum systems is a central problem in many areas of physics. The collective behavior of interacting particles gives rise to diverse fundamental phenomena such as confinement in quantum chromodynamics, phase transitions, and electron fractionalization in the quantum Hall regime. While such systems typically involve massive particles, optical photons can also interact with each other in a nonlinear medium. In practice, however, such interactions are often very weak. Here we describe a novel technique that allows the creation of a strongly correlated quantum gas of photons using one-dimensional optical systems with tight field confinement and coherent photon trapping techniques. The confinement enables the generation of large, tunable optical nonlinearities via the interaction of photons with a nearby cold atomic gas. In its extreme, we show that a quantum light field can undergo fermionization in such one-dimensional media, which can be probed via standard photon correlation measurements.

We study the unitary time evolution of antiferromagnetic order in anisotropic Heisenberg chains that are initially prepared in a pure quantum state far from equilibrium. Our analysis indicates that the antiferromagnetic order imprinted in the initial state vanishes exponentially. Depending on the anisotropy parameter, oscillatory or non-oscillatory relaxation dynamics is observed. Furthermore, the corresponding relaxation time exhibits a minimum at the critical point, in contrast to the usual notion of critical slowing down, from which a maximum is expected.Introduction. Experiments with ultracold atoms offer a highly controlled environment for investigating open questions of quantum magnetism. In particular, coherent spin dynamics in a lattice of double wells has been observed in recent experiments, which have demonstrated remarkable precision in tuning magnetic exchange interactions [1]. The ability to observe quantum dynamics over long time intervals allows one to study strongly correlated states from a new perspective. The idea is to prepare the system in a simple quantum state which, in general, is not an eigenstate of the Hamiltonian, and investigate the dynamics that follows. In the two-spin system, studied in [1], the dynamics is completely tractable and describes simple oscillations between a singlet and a triplet states.In the present paper we investigate how the nature of the dynamics changes in the case of a macroscopic number of spins interacting via nearest neighbor magnetic exchange. Are there new effects, and in particular new time scales, dynamically generated by the complex many-body evolution? Our starting point for investigating this question is the spin-