A numerical method, suitable for the simulation of the time evolution of quantum spin models of arbitrary lattice dimension, is presented. The method combines sampling of the Wigner function with evolution equations obtained from the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. Going to higher orders of the BBGKY hierarchy allows for a systematic refinement of the method. Quantum correlations are treated through both, the Wigner function sampling and the BBGKY evolution, bringing about highly accurate estimates of correlation functions. The method is particularly suitable for long-range interacting systems, and we demonstrate its power by comparing with exact results as well as other numerical methods. As an application we compute spin squeezing in a two-dimensional lattice with power-law interactions and a transverse field, which should be accessible in future ion trap experiments.

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Scattering of classical light by atomic clouds induces photon-mediated effective long-range interactions between the atoms and leads to cooperative effects even at low atomic densities. We introduce a novel simulation technique that allows us to investigate the quantum regime of the dynamics of large clouds of atoms. We show that the fluorescence spectrum of the cloud can be used to probe genuine quantum cooperative effects. Signatures of these effects are the occurrence, and the scaling behavior, of additional sidebands at twice the frequency of the classical Mollow sidebands, as well as an asymmetry of the Mollow triplet

Dynamical localization is one of the most startling manifestations of quantum interference, where the evolution of a simple system is frozen out under a suitably tuned coherent periodic drive. Here, we show that, although any randomness in the interactions of a many body system kills dynamical localization eventually, spectacular remnants survive even when the disorder is strong. We consider a disordered quantum Ising chain where the transverse magnetization relaxes exponentially with time with a decay time-scale τ due to random longitudinal interactions between the spins. We show that, under external periodic drive, this relaxation slows down (τ shoots up) by orders of magnitude as the ratio of the drive frequency ω and amplitude h0 tends to certain specific values (the freezing condition). If ω is increased while maintaining the ratio h0/ω at a fixed freezing value, then τ diverges exponentially with ω. The results can be easily extended for a larger family of disordered fermionic and bosonic systems.The dynamics of quantum systems driven out of equilibrium by coherent periodic drives has remained an intriguing topic of interest from the early days of quantum mechanics (see, e.g., [1]) to date [2-28]. One interesting and well-known phenomenon in this field, where repeated quantum interference results in a scenario which is quite counter-intuitive and unexpected from the classical point of view, is that of dynamical freezing in a quantum system under a periodic drive. Illustrious examples include the localization of a single quantum particle for all time while being forced periodically in free space (dynamical localization [29]), or in one of the two wells of a doublewell potential modulated sinusoidally (coherent destruction of tunneling [30]). In both cases, this happens due to the coherent suppression of tunneling.A many-body version of this phenomenon, dubbed as dynamical many-body freezing, has also been observed both theoretically [31][32][33][34][35][36] and experimentally [26]. Dynamical many-body freezing, however, is a more drastic version of dynamical localization: in the latter only the tunneling term is renormalized to zero by the external drive, resulting in localization in real space, while in the former the entire many-body Hamiltonian -with all its mutually non-commuting terms -vanishes [31]. This implies freezing of any arbitrary initial state in the Hilbert space, rather than freezing of initial states localized in real space only. Intuitively, such an unequivocal freezing of all degrees of freedom of a many-body system seems possible only under very special circumstances, where certain simplicities in the structure of the Hamiltonian allow for such large-scale destructive quantum interference. Here, we demonstrate that such dynamical manybody freezing can have strong manifestations even in a system where dynamics is induced by interactions which are totally random.The plan of the paper is as follows. After introducing the system and the drive, we briefly sketch the content of our analytical a...

We study the zero temperature non-equilibrium dynamics of a fermionic superfluid in the BCS limit and in the presence of a drive leading to a time-dependent chemical potential μ(t). We choose a periodic driving protocol characterized by a frequency ω and compute the fermion density, the wavefunction overlap, and the residual energy of the system at the end of N periods of the drive. We demonstrate that the BCS self-consistency condition is crucial in shaping the long time behaviour of the fermions subjected to the drive and provide an analytical understanding of the behaviour of the fermion density nkF (where kF is the Fermi momentum vector) after a drive period and for large ω. We also show that the momentum distribution of the excitations generated due to such a drive bears the signature of the pairing symmetry and can be used, for example, to distinguish between s- and d-wave superfluids. We propose experiments to test our theory.