In relativistic quantum field theory, information propagation is bounded by the speed of light. No such limit exists in the non-relativistic case, although in real physical systems, short-range interactions may be expected to restrict the propagation of information to finite velocities. The question of how fast correlations can spread in quantum many-body systems has been long studied. The existence of a maximal velocity, known as the Lieb-Robinson bound, has been shown theoretically to exist in several interacting many-body systems (for example, spins on a lattice)--such systems can be regarded as exhibiting an effective light cone that bounds the propagation speed of correlations. The existence of such a 'speed of light' has profound implications for condensed matter physics and quantum information, but has not been observed experimentally. Here we report the time-resolved detection of propagating correlations in an interacting quantum many-body system. By quenching a one-dimensional quantum gas in an optical lattice, we reveal how quasiparticle pairs transport correlations with a finite velocity across the system, resulting in an effective light cone for the quantum dynamics. Our results open perspectives for understanding the relaxation of closed quantum systems far from equilibrium, and for engineering the efficient quantum channels necessary for fast quantum computations.

We analyze the quench dynamics of a one-dimensional bosonic Mott insulator and focus on the time evolution of density correlations. For these we identify a pronounced propagation front, the velocity of which, once correctly extrapolated at large distances, can serve as a quantitative characteristic of the many-body Hamiltonian. In particular, the velocity allows the weakly interacting regime, which is qualitatively well described by free bosons, to be distinguished from the strongly interacting one, in which pairs of distinct quasiparticles dominate the dynamics. In order to describe the latter case analytically, we introduce a general approximation to solve the Bose-Hubbard Hamiltonian based on the Jordan-Wigner fermionization of auxiliary particles. This approach can also be used to determine the ground-state properties. As a complement to the fermionization approach, we derive explicitly the time-dependent many-body state in the noninteracting limit and compare our results to numerical simulations in the whole range of interactions of the Bose-Hubbard model.Comment: 16 pages, 7 figure

Unitary processes allow for the transfer of work to and from Hamiltonian systems. However, to achieve non-zero power for the practical extraction of work, these processes must be performed within a finite-time, which inevitably induces excitations in the system. We show that depending on the time-scale of the process and the physical realization of the external driving employed, the use of counterdiabatic quantum driving to extract more work is not always effective. We also show that by virtue of the two-time energy measurement definition of quantum work, the cost of counterdiabatic driving can be significantly reduced by selecting a restricted form of the driving Hamiltonian that depends on the outcome of the first energy measurement. Lastly, we introduce a measure, the exigency, that quantifies the need for an external driving to preserve quantum adiabaticity which does not require knowledge of the explicit form of the counterdiabatic drivings, and can thus always be computed. We apply our analysis to systems ranging from a two-level Landau-Zener problem to many-body problems, namely the quantum Ising and Lipkin-Meshkov-Glick models.

We study how the interplay of dissipation and interactions affects the dynamics of a bosonic many-body quantum system. In the presence of both dissipation and strongly repulsive interactions, observables such as the coherence and the density fluctuations display three dynamical regimes: an initial exponential variation followed by a power-law regime, and finally a slow exponential convergence to their asymptotic values. These very long-time scales arise as dissipation forces the population of states disfavored by interactions. The long-time, strong coupling dynamics are understood by performing a mapping onto a classical diffusion process displaying non-Brownian behavior. While both dissipation and strong interactions tend to suppress coherence when acting separately, we find that strong interaction impedes the decoherence process generated by the dissipation.

We show that density-dependent synthetic gauge fields may be engineered by combining periodically modulated interactions and Raman-assisted hopping in spin-dependent optical lattices. These fields lead to a density-dependent shift of the momentum distribution, may induce superfluid-to-Mott insulator transitions, and strongly modify correlations in the superfluid regime. We show that the interplay between the created gauge field and the broken sublattice symmetry results, as well, in an intriguing behavior at vanishing interactions, characterized by the appearance of a fractional Mott insulator. DOI: 10.1103/PhysRevLett.113.215303 PACS numbers: 67.85.-d, 03.65.Vf, 03.75.Lm, 37.10.Jk The emulation of synthetic electromagnetism in cold neutral gases has attracted major interest [1,2]. Artificial electric and magnetic fields have been induced using lasers [3][4][5]. Moreover, these setups may be extended to generate non-Abelian fields, and in particular, spin-orbit coupling [6][7][8][9][10][11][12][13]. Synthetic fields may be generated as well in optical lattices, and recent experiments have created artificial staggered [14][15][16] and uniform [17,18] magnetic fields. These fields are, however, static, as they are not influenced by the atoms.The dynamical feedback between matter and gauge fields plays an important role in various areas of physics, ranging from condensed matter [19] to quantum chromodynamics [20], and its realization in cold lattice gases is attracting growing attention [21]. Schemes have been recently proposed for multicomponent lattice gases, such that the low-energy description of these systems is that of relevant quantum field theories [22][23][24][25][26][27][28][29][30][31]. The backaction of the atoms on the value of a synthetic gauge field is expected to lead to interesting physics, including statistically induced phase transitions and anyons in 1D lattices [32], and chiral solitons in Bose-Einstein condensates [33].Periodically modulated optical lattices open interesting possibilities for the engineering of lattice gases [16][17][18][34][35][36][37][38][39][40]. In particular, periodic lattice shaking results in a modified hopping rate [34][35][36], which has been employed to drive the superfluid (SF) to Mott insulator (MI) transition [37], to simulate frustrated classical magnetism [38], and to create tunable gauge potentials [16]. Interestingly, a periodically modulated magnetic field may be employed in the vicinity of a Feshbach resonance to induce periodically modulated interactions, which result in a nonlinear hopping rate that depends on the occupation differences at neighboring sites [41][42][43].In this Letter, we show that combining periodic interactions and Raman-assisted hopping may induce a densitydependent gauge field in 1D lattices. The created field results in a density-dependent shift of the momentum distribution that may be probed in time-of-flight (TOF) experiments. Moreover, contrary to the Peierls phase induced in shaken lattices [16], the created field cannot be ga...

We study the dynamics of a strongly interacting bosonic quantum gas in an optical lattice potential under the effect of a dissipative environment. We show that the interplay between the dissipative process and the Hamiltonian evolution leads to an unconventional dynamical behavior of local number fluctuations. In particular we show, both analytically and numerically, the emergence of an anomalous diffusive evolution in configuration space at short times and, at long times, an unconventional dynamics dominated by rare events. Such rare events, common in disordered and frustrated systems, are due here to strong interactions. This complex two-stage dynamics reveals information on the level structure of the strongly interacting gas.PACS numbers: 05.70. Ln, 03.75.Kk, 37.10.Jk, Unconventional, non-exponential, relaxation dynamics of a perturbed system towards equilibrium has attracted a lot of interest over decades. Already in 1847, Kohlrausch [1] observed a stretched exponential decay in time t, i.e. e −(t/t0) α with α ∈ (0, 1) and t 0 a positive constant, of the discharge of capacitors fabricated from glasses. Since then, such a decay has been observed in many systems such as molecules and polymers [2,3], spin glasses [4,5], nano-sized magnetic particles [6], and certainly amorphous silicon [7,8].A broad variety of theoretical approaches has been developed to explain the mechanism of this unconventional relaxation dynamics [8][9][10][11]. In many of these approaches, e.g. the treatment of the Griffiths phase in disordered spin systems [12], rare configurations have been identified to play a key role. These configurations have an exponentially small probability to occur, and therefore contribute minimally to the short-time dynamics. However, because their relaxation time scale is very long, these rare configurations can dominate the long time evolution. Rare configurations play an important role in the relaxation dynamics of glasses, where they give rise to stretched exponential decays. We will thus refer to this dynamics induced by rare events as 'glass-like' in the following.In this work, we uncover that also in a quantum many body systems, as the Bose-Hubbard model, the dissipative coupling to a Markovian, i.e. memory-less, environment can cause glass-like dynamics. We show that the long time behaviour in these systems can be dominated by rare configurations. These rare configurations are characterized by a large number of atoms occupying a single lattice site. Increasing the number of atoms on the largely occupied site is associated to a long time scale, since the energetic cost of modifying this kind of configurations is very large. Due to this long time scale, these rare configurations dominate the long time dynamics inducing an unconventional dynamics of stretched exponential form as shown, for the case of local number fluctuations κ = n 2 j − n j 2 (wheren j is the number operator of atoms on site j) in Fig. 1. Additionally, the glass-like dynamics is preceded by an algebraic relaxation process due to the int...

When a periodically modulated many-body quantum system is weakly coupled to an environment, the combined action of these temporal modulations and dissipation steers the system towards a state characterized by a time-periodic density operator. To resolve this asymptotic non-equilibrium state at stroboscopic instants of time, we use the dissipative propagator over one period of modulations, 'Floquet map', and evaluate the stroboscopic density operator as its invariant. Particle interactions control properties of the map and thus the features of its invariant. In addition, the spectrum of the map provides insight into the system relaxation towards the asymptotic state and may help to understand whether it is possible (or not) to construct a stroboscopic time-independent Lindblad generator which mimics the action of the original time-dependent one. We illustrate the idea with a scalable many-body model, a periodically modulated Bose-Hubbard dimer. We contrast the relations between the interaction-induced bifurcations in a mean-field description with the numerically exact stroboscopic evolution and discuss the characteristics of the genuine quantum many-body state vs the characteristics of its mean-field counterpart.

Recent experiments show that periodic modulations of cold atoms in optical lattices may be used to engineer and explore interesting models. We show that double modulation combining lattice shaking and modulated interactions allows for the engineering of a much broader class of lattice with correlated hopping, which we study for the particular case of one-dimensional systems. We show, in particular, that by using this double modulation it is possible to study Hubbard models with asymmetric hopping, which, contrary to the standard Hubbard model, present insulating phases with both parity and string order. Moreover, double modulation allows for the simulation of lattice models in unconventional parameter regimes, as we illustrate for the case of the spin-1=2 Fermi-Hubbard model with correlated hopping, a relevant model for cuprate superconductors. Introduction.-Ultracold gases in optical lattices have attracted a lot of attention as emulators of fundamental models of quantum many-body systems. Their unprecedented levels of controllability, tunability, and cleanness have permitted the realization of Hubbard models with cold atoms [1][2][3], the creation of synthetic magnetic fields in neutral lattice gases [4,5], first steps towards the emulation of quantum magnetism [6][7][8][9][10][11][12], and more [13,14]. Recent progress in measurement techniques has allowed for singlesite resolved detection [15,16], which has permitted a deeper insight into the properties of Mott insulators (MI) [16][17][18] and the dynamical properties of cold lattice gases [19].The possibility of tuning parameters in real time in cold lattice gases has aroused particular interest. Fast periodic modulations provide a new tool for the engineering of relevant lattice models [4,5,[20][21][22][23][24][25][26][27][28][29]. In particular, a fastenough modulation of the lattice position (lattice shaking) results in the effective change of the tunneling rate [20] allowing, for example, driving the superfluid (SF) to MI transition [24], inducing photon-assisted hopping in tilted lattices [22], simulating frustrated classical magnetism [25], generating gauge potentials [28], and inducing effective ferromagnetic domains [29]. Moreover, a fast modulation of the interparticle interactions results in an effective hopping that depends on the occupation differences at neighboring sites [30][31][32][33] and may induce density-dependent gauge fields [34].In this Letter, we show that double modulation (DM), i.e., the combination of lattice shaking and periodically modulated interactions, permits the selective control of different hopping processes, hence, allowing for the engineering of a broad range of lattice models that cannot be realized with either lattice shaking or modulated interaction