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Tilted lattice potentials with periodic driving play a crucial role in the study of artificial gauge fields and topological phases with ultracold quantum gases. However, driving-induced heating and the growth of phonon modes restrict their use for probing interacting many-body states. Here, we experimentally investigate phonon modes and interaction-driven instabilities of superfluids in the lowest band of a shaken optical lattice. We identify stable and unstable parameter regions and provide a general resonance condition. In contrast to the high-frequency approximation of a Floquet description, we use the superfluids' micromotion to analyze the growth of phonon modes from slow to fast driving frequencies. Our observations enable the prediction of stable parameter regimes for quantum-simulation experiments aimed at studying driven systems with strong interactions over extended time scales., Comment: 12 pages, 9 figures

Single-atom imaging resolution of many-body quantum systems in optical lattices is routinely achieved with quantum-gas microscopes. Key to their great versatility as quantum simulators is the ability to use engineered light potentials at the microscopic level. Here, we employ dynamically varying microscopic light potentials in a quantum-gas microscope to study commensurate and incommensurate 1D systems of interacting bosonic Rb atoms. Such incommensurate systems are analogous to doped insulating states that exhibit atom transport and compressibility. Initially, a commensurate system with unit filling and fixed atom number is prepared between two potential barriers. We deterministically create an incommensurate system by dynamically changing the position of the barriers such that the number of available lattice sites is reduced while retaining the atom number. Our systems are characterised by measuring the distribution of particles and holes as a function of the lattice filling, and interaction strength, and we probe the particle mobility by applying a bias potential. Our work provides the foundation for preparation of low-entropy states with controlled filling in optical-lattice experiments., Comment: 12 pages, 10 figures

We experimentally investigate the stability of a quantum gas with repulsive interactions in an optical 1D lattice subjected to periodic driving. Excitations of the gas in the lowest lattice band are analyzed across the complete stability diagram, from slow to fast driving frequencies and from weak to strong driving strengths. To interpret our results, we expand the established analysis based on parametric instabilities to include modulational instabilities. Extending the concept of modulational instabilities from static to periodically driven systems provides a convenient mapping of the stability in a static system to the cases of slow and fast driving. At intermediate driving frequencies, we observe an interesting competition between modulational and parametric instabilities. We experimentally confirm the existence of both types of instabilities in driven systems and probe their properties. Our results allow us to predict stable and unstable parameter regions for the minimization of heating in future applications of Floquet driving., Comment: 13 pages, 15 figures

Entanglement between spatially distant qubits is perhaps the most counterintuitive and vital resource for distributed quantum computing. However, despite a few special cases, there is no known general procedure to maximally entangle two distant parts of an interacting many-body system. Here we present a symmetry-based approach, whereby one applies several timed pulses to drive a system to a particular symmetry sector with maximal bipartite long-range entanglement. As a concrete example, we demonstrate how a simple sequence of on-site pulses on a qubit array can efficiently produce any given number of stable nonlocal Bell pairs, realizable in several present-day atomic and photonic experimental platforms. More generally, our approach paves a route for novel state preparation by harnessing symmetry. For instance, we show how it enables the creation of long-sought-after superconducting $\eta$ pairs in a repulsive Hubbard model., Comment: 8 pages, 7 figures

We experimentally study the dynamics of weakly interacting Bose-Einstein condensates of cesium atoms in a 1D optical lattice with a periodic driving force. After a sudden start of the driving we observe the formation of stable wave packets at the center of the first Brillouin zone (BZ) in momentum space, and we interpret these as Floquet solitons in periodically driven systems. The wave packets become unstable when we add a trapping potential along the lattice direction leading to a redistribution of atoms within the BZ. The concept of a negative effective mass and the resulting changes to the interaction strength and effective trapping potential are used to explain the stability and the time evolution of the wave packets. We expect that similar states of matter waves exist for discrete breathers and other types of lattice solitons in periodically driven systems.

We study the evolution of a collisionally inhomogeneous matter wave in a spatial gradient of the interaction strength. Starting with a Bose-Einstein condensate with weak repulsive interactions in quasi-one-dimensional geometry, we monitor the evolution of a matter wave that simultaneously extends into spatial regions with attractive and repulsive interactions. We observe the formation and the decay of soliton-like density peaks, counter-propagating self-interfering wave packets, and the creation of cascades of solitons. The matter-wave dynamics is well reproduced in numerical simulations based on the nonpolynomial Schroedinger equation with three-body loss, allowing us to better understand the underlying behaviour based on a wavelet transformation. Our analysis provides new understanding of collapse processes for solitons, and opens interesting connections to other nonlinear instabilities.

We experimentally study the excitation modes of bright matter-wave solitons in a quasi-one-dimensional geometry. The solitons are created by quenching the interactions of a Bose-Einstein condensate of cesium atoms from repulsive to attractive in combination with a rapid reduction of the longitudinal confinement. A deliberate mismatch of quench parameters allows for the excitation of breathing modes of the emerging soliton and for the determination of its breathing frequency as a function of atom number and confinement. In addition, we observe signatures of higher-order solitons and the splitting of the wave packet after the quench. Our experimental results are compared to analytical predictions and to numerical simulations of the one-dimensional Gross-Pitaevskii equation.

Within the last two decades, Quantum Technologies (QT) have made tremendous progress, moving from Noble Prize award-winning experiments on quantum physics into a cross-disciplinary field of applied research. Technologies are being developed now that explicitly address individual quantum states and make use of the 'strange' quantum properties, such as superposition and entanglement. The field comprises four domains: Quantum Communication, Quantum Simulation, Quantum Computation, and Quantum Sensing and Metrology. One success factor for the rapid advancement of QT is a well-aligned global research community with a common understanding of the challenges and goals. In Europe, this community has profited from several coordination projects, which have orchestrated the creation of a 150-page QT Roadmap. This article presents an updated summary of this roadmap. Besides sections on the four domains of QT, we have included sections on Quantum Theory and Software, and on Quantum Control, as both are important areas of research that cut across all four domains. Each section, after a short introduction to the domain, gives an overview on its current status and main challenges and then describes the advances in science and technology foreseen for the next ten years and beyond.

This "Perspectives" paper gives a brief overview of the recent developments with quantum-gas microscopes and how they can be used to build the next generation of cold-atom quantum simulators., Comment: "Perspectives" paper for Special Issue "Cold Atom Physics" of Natl. Sci. Rev; published online April 19, 2016

Single-atom-resolved detection in optical lattices using quantum-gas microscopes has enabled a new generation of experiments in the field of quantum simulation. Fluorescence imaging of individual atoms has so far been achieved for bosonic species with optical molasses cooling, whereas detection of fermionic alkaline atoms in optical lattices by this method has proven more challenging. Here we demonstrate single-site- and single-atom-resolved fluorescence imaging of fermionic potassium-40 atoms in a quantum-gas microscope setup using electromagnetically-induced-transparency cooling. We detected on average 1000 fluorescence photons from a single atom within 1.5s, while keeping it close to the vibrational ground state of the optical lattice. Our results will enable the study of strongly correlated fermionic quantum systems in optical lattices with resolution at the single-atom level, and give access to observables such as the local entropy distribution and individual defects in fermionic Mott insulators or anti-ferromagnetically ordered phases., Comment: 7 pages, 5 figures; Nature Physics, published online 13 July 2015

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 present a complete architecture for scalable quantum computation with ultracold atoms in optical lattices using optical tweezers focused to the size of a lattice spacing. We discuss three different two-qubit gates based on local collisional interactions. The gates between arbitrary qubits require the transport of atoms to neighboring sites. We numerically optimize the non-adiabatic transport of the atoms through the lattice and the intensity ramps of the optical tweezer in order to maximize the gate fidelities. We find overall gate times of a few 100 us, while keeping the error probability due to vibrational excitations and spontaneous scattering below 10^3. The requirements on the positioning error and intensity noise of the optical tweezer and the magnetic field stability are analyzed and we show that atoms in optical lattices could meet the requirements for fault-tolerant scalable quantum computing., Comment: 10 pages, 6 figures

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 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 on 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 although their width is of the order of only a single lattice site. Furthermore, we show how a Mott insulator melts for increasing temperatures due to a proliferation of local defects. Our experiments open a new avenue for the manipulation and analysis of strongly interacting quantum gases on a lattice, as well as for quantum information processing with ultracold atoms. Using the high spatial resolution, it is now possible to directly address individual lattice sites. One could, e.g., introduce local perturbations or access regions of high entropy, a crucial requirement for the implementation of novel cooling schemes for atoms on a lattice.

We have frozen the coherent evolution of a field in a cavity by repeated measurements of its photon number. We use circular Rydberg atoms dispersively coupled to the cavity mode for an absorption-free photon counting. These measurements inhibit the growth of a Field injected in the cavity by a classical source. This manifestation of the Quantum Zeno effect illustrates the back action of the photon number determination onto the Field phase. The residual growth of the Field can be seen as a random walk of its amplitude in the two-dimensional phase space. This experiment sheds light onto the measurement process and opens perspectives for active quantum feedback.

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 measuring non-destructively 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.

We have built a microwave Fabry-Perot resonator made of diamond-machined copper mirrors coated with superconducting niobium. Its damping time (Tc = 130 ms at 51 GHz and 0.8 K) corresponds to a finesse of 4.6 x 109, the highest ever reached for a Fabry-Perot in any frequency range. This result opens novel perspectives for quantum information, decoherence and non-locality studies.

A microscopic system under continuous observation exhibits at random times sudden jumps between its states. The detection of this essential quantum feature requires a quantum non-demolition (QND) measurement repeated many times during the system evolution. Quantum jumps of trapped massive particles (electrons, ions or molecules) have been observed, which is not the case of the jumps of light quanta. Usual photodetectors absorb light and are thus unable to detect the same photon twice. They must be replaced by a transparent counter 'seeing' photons without destroying them3. Moreover, the light has to be stored over a duration much longer than the QND detection time. We have fulfilled these challenging conditions and observed photon number quantum jumps. Microwave photons are stored in a superconducting cavity for times in the second range. They 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, for the first time, the birth, life and death of individual photons. Applying a similar QND procedure to mesoscopic fields with tens of photons opens new perspectives for the exploration of the quantum to classical boundary.

We propose a Ramsey interferometry experiment using an entangled state of N atoms to reach the Heisenberg limit for the estimation of an atomic phase shift if the atom number parity is perfectly determined. In a more realistic situation, due to statistical fluctuations of the atom source and the finite detection efficiency, the parity is unknown. We then achieve about half the Heisenberg limit. The scheme involves an ensemble of circular Rydberg atoms which dispersively interact successively with two initially empty microwave cavities. The scheme does not require very high-Q cavities. An experimental realization with about ten entangled Rydberg atoms is achievable with state of art apparatuses., Comment: 13 pages, 7 figures

We trap a single cesium atom in a standing-wave optical dipole trap. Special experimental procedures, designed to work with single atoms, are used to measure the oscillation frequency and the atomic energy distribution in the dipole trap. These methods rely on unambiguously detecting presence or loss of the atom using its resonance fluorescence in the magneto-optical trap., Comment: 8 pages, 7 figures, submitted to Phys. Rev. A

Using optical dipole forces we have realized controlled transport of a single or any desired small number of neutral atoms over a distance of a centimeter with sub-micrometer precision. A standing wave dipole trap is loaded with a prescribed number of cesium atoms from a magneto-optical trap. Mutual detuning of the counter-propagating laser beams moves the interference pattern, allowing us to accelerate and stop the atoms at preselected points along the standing wave. The transportation efficiency is close to 100%. This optical "single-atom conveyor belt" represents a versatile tool for future experiments requiring deterministic delivery of a prescribed number of atoms on demand., Comment: 8 pages, 8 figures, submitted to Applied Physics B