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We investigated the relaxation and excitation in a frustrated XY model realized by a Bose gas in Floquet-engineered optical triangular lattices. Periodically driving the position of the entire lattice structure enables the sign inversion of tunneling amplitudes, which, in the case of a triangular lattice, results in geometrical frustration of the local phase of wave packets. We revealed that the two spiral phases with chiral modes show significant differences in relaxation time from the initial ferromagnetic phase. While spontaneous symmetry breaking is clearly observed at a slow ramp of the Floquet drive, simultaneous occupation of two ground states often occurs at a fast ramp, which can be attributed to the domain formation of the chiral modes. The interference of the spatially separated chiral modes was observed, using a quantum gas microscope. This work leads to exploring the domain formation mechanism in a system with U(1)$\times \mathbb{Z}_2$ symmetry., Comment: 5+10 pages, 4+8 figures

We demonstrate single-site-resolved fluorescence imaging of ultracold $^{87}\mathrm{Rb}$ atoms in a triangular optical lattice by employing Raman sideband cooling. Combining a Raman transition at the D1 line and a photon scattering through an optical pumping of the D2 line, we obtain images with low background noise. The Bayesian optimisation of 11 experimental parameters for fluorescence imaging with Raman sideband cooling enables us to achieve single-atom detection with a high fidelity of $(96.3 \pm 1.3)$%. Single-atom and single-site resolved detection in a triangular optical lattice paves the way for the direct observation of spin correlations or entanglement in geometrically frustrated systems., Comment: 12 pages, 5 figures

After many years of development of the basic tools, quantum simulation with ultracold atoms has now reached the level of maturity where it can be used to investigate complex quantum processes. Planning of new experiments and upgrading existing set-ups depends crucially on a broad overview of the available techniques, their specific advantages and limitations. This Technical Review aims to provide a comprehensive compendium of the state of the art. We discuss the basic principles, the available techniques and their current range of applications. Focusing on the simulation of varied phenomena in solid-state physics using optical lattice experiments, we review their basics, the necessary techniques and the accessible physical parameters. We outline how to control and use interactions with external potentials and between the atoms, and how to design new synthetic gauge fields and spin-orbit coupling. We discuss the latest progress in site-resolved techniques using quantum gas microscopes, and describe the unique features of quantum simulation experiments with two-electron atomic species., Comment: 28 pages, 7 figures, includes Supplementary Information

Quantum antiferromagnets with geometrical frustration exhibit rich many-body physics but are hard to simulate by means of classical computers. Although quantum-simulation studies for analyzing such systems are thus desirable, they are still limited to high temperature regions, where interesting quantum effects are smeared out. Here, we propose a feasible protocol to perform analog quantum simulation of frustrated antiferromagnetism with strong quantum fluctuations by using ultracold Bose gases in optical lattices at negative absolute temperatures. Specifically, we show from numerical simulations that the time evolution of a negative-temperature state subjected to a slow sweep of the hopping energy simulates quantum phase transitions of a frustrated Bose-Hubbard model with sign-inverted hoppings. Moreover, we quantitatively predict the phase boundary between the frustrated superfluid and Mott-insulator phases for triangular lattices with hopping anisotropy, which serves as a benchmark for quantum simulation., Comment: 12 pages, 9 figures

Coarsening dynamics theory has successfully described the equilibration of a broad class of systems.By studying the relaxation of a periodic array of microcondensates immersed in a Fermi gas which can mediate long-range spin interactions to simulate frustrated classical magnets, we show that coarsening dynamics can be suppressed by geometrical frustration. The system is found to eventually approach a metastable state which is robust against random field noise and characterized by finite correlation lengths with the emergence of topologically stable Z2 vortices. We find universal scaling laws with no thermal-equilibrium analog that relate the correlation lengths and the number of vortices to the degree of frustration in the system.

Entanglement is an essential property of quantum many-body systems. However, its local detection is challenging and was so far limited to spin degrees of freedom in ion chains. Here we measure entanglement between the spins of atoms located on two lattice sites in a one-dimensional Bose-Hubbard chain which features both local spin- and particle-number fluctuations. Starting with an initially localized spin impurity, we observe an outwards propagating entanglement wave and show quantitatively how entanglement in the spin sector rapidly decreases with increasing particle-number fluctuations in the chain., Comment: 6 pages, 4 figures

We study experimentally the far-from-equilibrium dynamics in ferromagnetic Heisenberg quantum magnets realized with ultracold atoms in an optical lattice. After controlled imprinting of a spin spiral pattern with adjustable wave vector, we measure the decay of the initial spin correlations through single-site resolved detection. On the experimentally accessible timescale of several exchange times we find a profound dependence of the decay rate on the wave vector. In one-dimensional systems we observe diffusion-like spin transport with a dimensionless diffusion coefficient of 0.22(1). We show how this behavior emerges from the microscopic properties of the closed quantum system. In contrast to the one-dimensional case, our transport measurements for two-dimensional Heisenberg systems indicate anomalous super-diffusion.

Dominating finite-range interactions in many-body systems can lead to intriguing self-ordered phases of matter. Well known examples are crystalline solids or Coulomb crystals in ion traps. In those systems, crystallization proceeds via a classical transition, driven by thermal fluctuations. In contrast, ensembles of ultracold atoms laser-excited to Rydberg states provide a well-controlled quantum system, in which a crystalline phase transition governed by quantum fluctuations can be explored. Here we report on the experimental preparation of the crystalline states in such a Rydberg many-body system. Fast coherent control on the many-body level is achieved via numerically optimized laser excitation pulses. We observe an excitation-number staircase as a function of the system size and show directly the emergence of incompressible ordered states on its steps. Our results demonstrate the applicability of quantum optical control techniques in strongly interacting systems, paving the way towards the investigation of novel quantum phases in long-range interacting quantum systems, as well as for detailed studies of their coherence and correlation properties., Comment: 10 pages, 7 figures

More than eighty years ago, H. Bethe pointed out the existence of bound states of elementary spin waves in one-dimensional quantum magnets. To date, identifying signatures of such magnon bound states has remained a subject of intense theoretical research 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 with single-spin and single-site resolution. 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., Comment: 8 pages, 7 figures

Correlation functions play an important role for the theoretical and experimental characterization of many-body systems. In solid-state systems, they are usually determined through scattering experiments whereas in cold-gases systems, time-of-flight and in-situ absorption imaging are the standard observation techniques. However, none of these methods allow the in-situ detection of spatially resolved correlation functions at the single-particle level. Here we give a more detailed account of recent advances in the detection of correlation functions using in-situ fluorescence imaging of ultracold bosonic atoms in an optical lattice. This method yields single-site and single-atom-resolved images of the lattice gas in a single experimental run, thus gaining direct access to fluctuations in the many-body system. As a consequence, the detection of correlation functions between an arbitrary set of lattice sites is possible. This enables not only the detection of two-site correlation functions but also the evaluation of non-local correlations, which originate from an extended region of the system and are used for the characterization of quantum phases that do not possess (quasi-)long-range order in the traditional sense., Comment: extended version of M. Endres et al., Science 334, 200-203 (2011) [arXiv:1108.3317]

Quantum magnetism describes the properties of many materials such as transition metal oxides and cuprate superconductors. One of its elementary processes 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 full 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, a post-selection of the data allows to reduce the effect of temperature, giving access to a space- and time-resolved measurement of the quantum-coherent propagation of a magnetic excitation in the Heisenberg model. Extending the study to the bath's superfluid regime, we determine quantitatively how the bath strongly affects the motion of the impurity. The experimental data shows a remarkable agreement with theoretical predictions allowing us to determine the effect of temperature on the coherence and velocity of impurity motion. Our results pave the way for a new approach to study quantum magnetism, mobile impurities in quantum fluids, and polarons in lattice systems., Comment: 8 pages, 6 figures

The ability to control and tune interactions in ultracold atomic gases has paved the way towards the realization of new phases of matter. Whereas experiments have so far achieved a high degree of control over short-ranged interactions, the realization of long-range interactions would open up a whole new realm of many-body physics and has become a central focus of research. Rydberg atoms are very well-suited to achieve this goal, as the van der Waals forces between them are many orders of magnitude larger than for ground state atoms. Consequently, the 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 are quantum crystals, composed of coherent superpositions of different spatially ordered configurations of collective excitations. Here we report on the direct measurement of strong correlations in a laser excited two-dimensional atomic Mott insulator using high-resolution, in-situ Rydberg atom imaging. The observations reveal the emergence of spatially ordered excitation patterns in the high-density components of the prepared many-body state. They have random orientation, but well defined geometry, forming mesoscopic crystals of collective excitations delocalised throughout the gas. Our experiment demonstrates the potential of Rydberg gases to realise exotic phases of matter, thereby laying the basis for quantum simulations of long-range interacting quantum magnets., Comment: 10 pages, 7 figures

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 and also appears as a fundamental collective mode in quantum many-body systems. 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. Here we 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, 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.

How fast can correlations spread in a quantum many-body system? Based on the seminal work by Lieb and Robinson, it has recently been shown that several interacting many-body systems exhibit 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 never been observed experimentally. Here we report on 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 important perspectives for understanding relaxation of closed quantum systems far from equilibrium as well as for engineering efficient quantum channels necessary for fast quantum computations., Comment: 7 pages, 5 figures, 2 tables

We experimentally demonstrate coherent light scattering from an atomic Mott insulator in a two-dimensional lattice. The far-field diffraction pattern of small clouds of a few hundred atoms was imaged while simultaneously laser cooling the atoms with the probe beams. We describe the position of the diffraction peaks and the scaling of the peak parameters by a simple analytic model. In contrast to Bragg scattering, scattering from a single plane yields diffraction peaks for any incidence angle. We demonstrate the feasibility of detecting spin correlations via light scattering by artificially creating a one-dimensional antiferromagnetic order as a density wave and observing the appearance of additional diffraction peaks., Comment: 4 pages, 4 figures

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., Comment: 8 pages, 5 figures

The transition from a superfluid to a Mott insulator (MI) phase has been observed in a Bose-Einstein condensate (BEC) of ytterbium (Yb) atoms in an optical lattice. An all-optically produced BEC of 174Yb atoms was loaded into three-dimensional optical lattices produced by a 532 nm laser beam. The interference pattern was measured after releasing the quantum gas from the trapping potential. As increasing the optical lattice depth, we observed the disappearance of the interference patterns, which is a signature of entering the MI regime. This result is an important step into studies by using a combination of the MI state and the ultranarrow optical transition of ultracold alkaline-earth-like atoms., Comment: 4 pages, 3 figures

We report the realization of quantum degenerate mixed gases of ytterbium (Yb) isotopes using all-optical methods. We have succeeded in cooling attractively interacting 176Yb atoms via sympathetic cooling down to below the Bose-Einstein transition temperature, coexisting with a stable condensate of 174Yb atoms with a repulsive interaction. We have observed a rapid atom loss in 176Yb atoms after cooling down below the transition temperature, which indicates the collapse of a 176Yb condensate. The sympathetic cooling technique has been applied to cool a 173Yb-174Yb Fermi-Bose mixture to the quantum degenerate regime., Comment: 4 pages, 3 figures

We report the observation of a Bose Einstein condensate in a bosonic isotope of ytterbium (170Yb). More than 10^6 atoms are trapped in a crossed optical dipole trap and cooled by evaporation. Condensates of approximately 10^4 atoms have been obtained. From an expansion of the condensate, we have extracted the scattering length a=3.6(9) nm., Comment: 4 pages, 3 figures

An evaporative cooling was performed to cool the fermionic 173Yb atoms in a crossed optical dipole trap. The elastic collision rate, which is important for the evaporation, turns out to be large enough from our study. This large collision rate leads to efficient evaporation and we have successfully cooled the atoms below 0.6 of the Fermi temperature, that is to say, to a quantum degenerate regime. In this regime, a plunge of evaporation efficiency is observed as the result of the Fermi degeneracy., Comment: 4 pages, 3figures