A fundamental assumption in statistical physics is that generic closed quantum many-body systems thermalize under their own dynamics. Recently, the emergence of many-body localized systems has questioned this concept and challenged our understanding of the connection between statistical physics and quantum mechanics. Here we report on the observation of a many-body localization transition between thermal and localized phases for bosons in a two-dimensional disordered optical lattice. With our single-site-resolved measurements, we track the relaxation dynamics of an initially prepared out-of-equilibrium density pattern and find strong evidence for a diverging length scale when approaching the localization transition. Our experiments represent a demonstration and in-depth characterization of many-body localization in a regime not accessible with state-of-the-art simulations on classical computers.

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.

Ultracold atoms in optical lattices are a versatile tool to investigate fundamental properties of quantum many body systems. In particular, the high degree of control of experimental parameters has allowed the study of many interesting phenomena such as quantum phase transitions and quantum spin dynamics. Here we demonstrate how such control can be extended down to the most fundamental level of a single spin at a specific site of an optical lattice. Using a tightly focussed laser beam together with a microwave field, we were able to flip the spin of individual atoms in a Mott insulator with sub-diffraction-limited resolution, well below the lattice spacing. The Mott insulator provided us with a large two-dimensional array of perfectly arranged atoms, in which we created arbitrary spin patterns by sequentially addressing selected lattice sites after freezing out the atom distribution. We directly monitored the tunnelling quantum dynamics of single atoms in the lattice prepared along a single line and observed that our addressing scheme leaves the atoms in the motional ground state. Our results open the path to a wide range of novel applications from quantum dynamics of spin impurities, entropy transport, implementation of novel cooling schemes, and engineering of quantum many-body phases to quantum information processing.The ability to observe and control the position of single atoms on a surface of a solid via scanning tunnelling and atomic force microscopy has revolutionised the field of condensed matter physics [1,2]. In few-atom systems, coherent control of single particles in e.g. an ion chain has proven crucial for the implementation of high-fidelity quantum gates and the readout of individual qubits in quantum information processing [3]. Bringing such levels of control to the regime of large scale many-body systems has been a longstanding goal in quantum physics. In the context of ultracold atoms in optical lattices, a major challenge has been to combine degenerate atomic samples with single-site addressing resolution and singleatom sensitivity. This full control is essential for many applications in condensed matter physics, such as the study of spin impurities [4] and quantum spin dynamics [5,6] within quantum magnetism, entropy transport, the implementation of novel cooling schemes [7,8] or digital quantum simulations based on Rydberg atoms [9]. For scalable quantum information processing, a Mott insulator with unity filling provides a natural quantum register with several hundreds of qubits. In order to exploit the full potential of such a large scale system for quantum computation, coherent manipulation of individual spins is indispensable, both within a circuit-based [10] or a one-way quantum computer architecture [11,12].The quest to address atoms on single sites of an optical lattice has a long history [7,[13][14][15][16][17][18][19][20][21][22]. In one dimension, single-site addressing was accomplished optically † present address: Department of Physics and Astronomy, University of Aarhus, DK-8000 ...

One of the elementary processes in quantum magnetism is the propagation of spin excitations. Here we study the quantum dynamics of a deterministically created spin-impurity atom, as it propagates in a one-dimensional lattice system. We probe the spatial probability distribution of the impurity at different times using single-site-resolved imaging of bosonic atoms in an optical lattice. In the Mott-insulating regime, the quantum-coherent propagation of a magnetic excitation in the Heisenberg model can be observed using a post-selection technique. Extending the study to the superfluid regime of the bath, we quantitatively determine how the bath affects the motion of the impurity, showing evidence of polaronic behaviour. The experimental data agree with theoretical predictions, allowing us to determine the effect of temperature on the impurity motion. Our results provide a new approach to studying quantum magnetism, mobile impurities in quantum fluids and polarons in lattice systems

The ability to control and tune interactions in ultracold atomic gases has paved the way for the realization of new phases of matter. So far, experiments have achieved a high degree of control over short-range interactions, but the realization of long-range interactions has become a central focus of research because it would open up a new realm of many-body physics. Rydberg atoms are highly suited to this goal because the van der Waals forces between them are many orders of magnitude larger than those between ground-state atoms. Consequently, mere laser excitation of ultracold gases can cause strongly correlated many-body states to emerge directly when atoms are transferred to Rydberg states. A key example is a quantum crystal composed of coherent superpositions of different, spatially ordered configurations of collective excitations. Here we use high-resolution, in situ Rydberg atom imaging to measure directly strong correlations in a laser-excited, two-dimensional atomic Mott insulator. The observations reveal the emergence of spatially ordered excitation patterns with random orientation, but well-defined geometry, in the high-density components of the prepared many-body state. Together with a time-resolved analysis, this supports the description of the system in terms of a correlated quantum state of collective excitations delocalized throughout the gas. Our experiment demonstrates the potential of Rydberg gases to realize exotic phases of matter, thereby laying the basis for quantum simulations of quantum magnets with long-range interactions.

More than eighty years ago, H. Bethe pointed out the existence of bound states of elementary spin waves in one-dimensional quantum magnets [1]. To date, identifying signatures of such magnon bound states has remained a subject of intense theoretical research [2][3][4][5] while their detection has proved challenging for experiments. Ultracold atoms offer an ideal setting to reveal such bound states by tracking the spin dynamics after a local quantum quench [6] with single-spin and singlesite resolution [7,8]. Here we report on the direct observation of two-magnon bound states using in-situ correlation measurements in a one-dimensional Heisenberg spin chain realized with ultracold bosonic atoms in an optical lattice. We observe the quantum walk of free and bound magnon states through time-resolved measurements of the two spin impurities. The increased effective mass of the compound magnon state results in slower spin dynamics as compared to single magnon excitations. In our measurements, we also determine the decay time of bound magnons, which is most likely limited by scattering on thermal fluctuations in the system. Our results open a new pathway for studying fundamental properties of quantum magnets and, more generally, properties of interacting impurities in quantum many-body systems.The study of non-equilibrium processes in quantum spin models can provide fundamental insight into elementary aspects of magnetism. Magnons are the basic quasiparticle exitations around the ground state of ferromagnets and govern their low temperature physics [9,10]. Due to the ferromagnetic interaction, two spin excitations can remain bound together, forming a so-called twomagnon bound state [1,9,11]. In one and two dimensions, bound states exist for all center of mass momenta, which prohibits the description of low energy properties in terms of free magnon states [9]. In the classical limit, magnon bound states can be regarded as the basic building blocks of magnetic solitons [12,13]. Next to these fundamental aspects, the study of non-equilibrium dynamics in quantum spin chains is also important for a variety of applications. The evolution of two localized spin excitations realizes an interacting quantum walk [14,15] in the spin domain, which can be a versatile tool for the study of complex many-body systems [16]. It is also of importance in the context of quantum information [17], where transport properties in a one-dimensional chain of qubits can be strongly influenced by magnon bound states [18].The spin-1/2 Heisenberg model is one of the foundational models for interacting quantum spins. This model could be solved analytically in one dimension in the early 1930's by H. Bethe using a systematic Ansatz for the form of the eigenvectors [1]. Later, the Bethe Ansatz proved to be far more general and allowed for solving many more one-dimensional models, such as the Lieb-Liniger or the fermionic Hubbard model [20], and recent, powerful extensions include the investigation of the dynamics * Electronic address: takeshi.fukuhara@mpq....

Ultracold atoms in optical lattices are ideal to study fundamentally new quantum many-body systems 1,2 including frustrated or topological magnetic phases 3,4 and supersolids 5,6 . However, the necessary control of strong long-range interactions between distant ground state atoms has remained a long-standing goal. Optical dressing of ground state atoms via o -resonant laser coupling to Rydberg states is one way to tailor such interactions 5-8 . Here we report the realization of coherent Rydberg dressing to implement a two-dimensional synthetic spin lattice. Our single-atom-resolved interferometric measurements of the many-body dynamics enable the microscopic probing of the interactions and reveal their highly tunable range and anisotropy. Our work marks the first step towards the use of laser-controlled Rydberg interactions for the study of exotic quantum magnets 3,4,9 in optical lattices.Neutral ultracold atoms in optical lattices are among the most promising platforms for the implementation of analog quantum simulators of condensed matter systems. However, the simulation of magnetic Hamiltonians, often emerging as an effective model in more complex many-body systems, is difficult with contact interactions due to the low energy scale of the associated superexchange process 10 . Long-range interactions offer an alternative way to directly achieve strong effective spin-spin interactions. Such interactions emerge between magnetic atoms and between ultracold polar molecules 11 , trapped ions 12 or ground state atoms resonantly 13 or off-resonantly coupled ('dressed') to Rydberg states [5][6][7][8] . Rydberg dressing is especially appealing due to the simplicity of realizing atomic lattice systems with unity filling, combined with the great tunability of the interaction strength and shape, which might be exploited to explore exotic models of quantum magnetism 3,4 . While effects of long-range spin interactions have been observed in many-body systems of polar molecules 14 , ions [15][16][17] and resonantly excited Rydberg atoms 18,19 , none of these approaches combines the advantages of Rydberg dressing, which permits the realization of strong spin interactions in lattices with near-unity filling. So far, Rydberg dressing in a many-body system remains an experimental challenge, for which up to now only dissipative effects have been measured [20][21][22][23][24] . For two atoms, first promising experimental results have been reported recently for near-resonant strong dressing 25 , where, however, the assumption of a weak Rydberg-state admixture required for the realization of various many-body models 5,6,9,26,27 does not hold 28 .Here we demonstrate Rydberg dressing in a two-dimensional (2D) near-unity-filled atomic lattice with tailored extended range interactions between approximately 200 effective spins. In contrast to our previous experiments 18,29 on resonantly coupled Rydberg gases, all atoms participate here in the spin dynamics. We exploit the temporal control over such interactions to perform interferometric ...

Spontaneous symmetry breaking plays a key role in our understanding of nature. In a relativistic field theory, a broken continuous symmetry leads to the emergence of two types of fundamental excitations: massless Nambu-Goldstone modes and a massive 'Higgs' amplitude mode. An excitation of Higgs type is of crucial importance in the standard model of elementary particles [1] and also appears as a fundamental collective mode in quantum many-body systems [2]. Whether such a mode exists in low-dimensional systems as a resonance-like feature or becomes over-damped through coupling to Nambu-Goldstone modes has been a subject of theoretical debate [2][3][4][5][6][7]. Here we experimentally reveal and study a Higgs mode in a two-dimensional neutral superfluid close to the transition to a Mott insulating phase. We unambiguously identify the mode by observing the expected softening of the onset of spectral response when approaching the quantum critical point. In this regime, our system is described by an effective relativistic field theory with a two-component quantum-field [2,8,9], constituting a minimal model for spontaneous breaking of a continuous symmetry. Additionally, all microscopic parameters of our system are known from first principles and the resolution of our measurement allows us to detect excited states of the many-body system at the level of individual quasiparticles. This allows for an in-depth study of Higgs excitations, which also addresses the consequences of reduced dimensionality and confinement of the system. Our work constitutes a first step in exploring emergent relativistic models with ultracold atomic gases.Higgs modes are amplitude oscillations of a quantum field and appear as collective excitations in quantum many-body systems as a consequence of spontaneous breaking of a continuous symmetry. Close to a quantum critical point, the low-energy physics of such systems is in many cases captured by an effective Lorentz invariant critical theory [2]. The minimal version of such a theory describes the dynamics of a complex order parameter Ψ = |Ψ|e iφ near a quantum phase transition between an ordered (|Ψ| > 0) and a disordered phase (|Ψ| = 0). Within the ordered phase, the classical energy density has the shape of a Mexican hat (Fig. 1a) and the order parameter takes on a non-zero value in the minimum of this potential. Hereby, its phase φ acquires a definite value through spontaneous breaking of the rotation symmetry (i.e., U (1) symmetry). Expanding the field around the symmetry broken ground state leads to two types of modes: a Nambu-Goldstone mode and a Higgs mode related to phase and amplitude variations of Ψ, respectively (Fig. 1a). In contrast to the phase mode, the amplitude mode has a finite excitation gap (i.e., a finite mass), which is expected to show a characteristic softening when approaching the disordered phase (Fig. 1a). The sketched minimal model of an order parameter with N = 2 components belongs to a class of O(N ) relativistic * Electronic address: manuel.endres@mpq.mpg.de field t...