The reliable detection of single quantum particles has revolutionized the field of quantum optics and quantum information processing. For several years, researchers have aspired to extend such detection possibilities to larger-scale, strongly correlated quantum systems in order to record in situ images of a quantum fluid in which each underlying quantum particle is detected. Here we report fluorescence imaging of strongly interacting bosonic Mott insulators in an optical lattice with single-atom and single-site resolution. From our images, we fully reconstruct the atom distribution on the lattice and identify individual excitations with high fidelity. A comparison of the radial density and variance distributions with theory provides a precise in situ temperature and entropy measurement from single images. We observe Mott-insulating plateaus with near-zero entropy and clearly resolve the high-entropy rings separating them, even though their width is of the order of just a single lattice site. Furthermore, we show how a Mott insulator melts with increasing temperature, owing to a proliferation of local defects. The ability to resolve individual lattice sites directly opens up new avenues for the manipulation, analysis and applications of strongly interacting quantum gases on a lattice. For example, one could introduce local perturbations or access regions of high entropy, a crucial requirement for the implementation of novel cooling schemes.

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.

A microscopic quantum system under continuous observation exhibits at random times sudden jumps between its states. The detection of this quantum feature requires a quantum non-demolition (QND) measurement repeated many times during the system's evolution. Whereas quantum jumps of trapped massive particles (electrons, ions or molecules) have been observed, this has proved more challenging for light quanta. Standard photodetectors absorb light and are thus unable to detect the same photon twice. It is therefore necessary to use a transparent counter that can 'see' photons without destroying them. Moreover, the light needs to be stored for durations much longer than the QND detection time. Here we report an experiment in which we fulfil these challenging conditions and observe quantum jumps in the photon number. Microwave photons are stored in a superconducting cavity for times up to half a second, and are repeatedly probed by a stream of non-absorbing atoms. An atom interferometer measures the atomic dipole phase shift induced by the non-resonant cavity field, so that the final atom state reveals directly the presence of a single photon in the cavity. Sequences of hundreds of atoms, highly correlated in the same state, are interrupted by sudden state switchings. These telegraphic signals record the birth, life and death of individual photons. Applying a similar QND procedure to mesoscopic fields with tens of photons should open new perspectives for the exploration of the quantum-to-classical boundary.

The irreversible evolution of a microscopic system under measurement is a central feature of quantum theory. From an initial state generally exhibiting quantum uncertainty in the measured observable, the system is projected into a state in which this observable becomes precisely known. Its value is random, with a probability determined by the initial system's state. The evolution induced by measurement (known as 'state collapse') can be progressive, accumulating the effects of elementary state changes. Here we report the observation of such a step-by-step collapse by non-destructively measuring the photon number of a field stored in a cavity. Atoms behaving as microscopic clocks cross the cavity successively. By measuring the light-induced alterations of the clock rate, information is progressively extracted, until the initially uncertain photon number converges to an integer. The suppression of the photon number spread is demonstrated by correlations between repeated measurements. The procedure illustrates all the postulates of quantum measurement (state collapse, statistical results and repeatability) and should facilitate studies of non-classical fields trapped in cavities.

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...