We demonstrate the experimental implementation of an optical lattice that allows for the generation of large homogeneous and tunable artificial magnetic fields with ultracold atoms. Using laser-assisted tunneling in a tilted optical potential, we engineer spatially dependent complex tunneling amplitudes. Thereby, atoms hopping in the lattice accumulate a phase shift equivalent to the Aharonov-Bohm phase of charged particles in a magnetic field. We determine the local distribution of fluxes through the observation of cyclotron orbits of the atoms on lattice plaquettes, showing that the system is described by the Hofstadter model. Furthermore, we show that for two atomic spin states with opposite magnetic moments, our system naturally realizes the time-reversal-symmetric Hamiltonian underlying the quantum spin Hall effect; i.e., two different spin components experience opposite directions of the magnetic field.

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We report the creation of Greenberger-Horne-Zeilinger states with up to 14 qubits. By investigating the coherence of up to 8 ions over time, we observe a decay proportional to the square of the number of qubits. The observed decay agrees with a theoretical model which assumes a system affected by correlated, Gaussian phase noise. This model holds for the majority of current experimental systems developed towards quantum computation and quantum metrology.

† These two authors contributed equally to this work.Geometric phases that characterize the topological properties of Bloch bands play a fundamental role in the modern band theory of solids. Here we report on the direct measurement of the geometric phase acquired by cold atoms moving in one-dimensional optical lattices. Using a combination of Bloch oscillations and Ramsey interferometry, we extract the Zak phase -the Berry phase acquired during an adiabatic motion of a particle across the Brillouin zone -which can be viewed as an invariant characterizing the topological properties of the band. For a dimerized optical lattice, which models polyacetylene, we measure a difference of the Zak phase equal to δϕ Zak = 0.97(2)π for the two possible polyacetylene phases with different dimerization. This indicates that the two dimerized phases belong to different topological classes, such that for a filled band, domain walls have fractional quantum numbers. Our work establishes a new general approach for probing the topological structure of Bloch bands in optical lattices. u-,k Clockwise WindingAnti-Clockwise Winding

* These authors contributed equally to this work.The control of quantum systems is of fundamental scientific interest and promises powerful applications and technologies. Impressive progress has been achieved in isolating the systems from the environment and coherently controlling their dynamics, as demonstrated by the creation and manipulation of entanglement in various physical systems. However, for open quantum systems, engineering the dynamics of many particles by a controlled coupling to an environment remains largely unexplored. Here we report the first realization of a toolbox for simulating an open quantum system with up to five qubits. Using a quantum computing architecture with trapped ions, we combine multi-qubit gates with optical pumping to implement coherent operations and dissipative processes. We illustrate this engineering by the dissipative preparation of entangled states, the simulation of coherent many-body spin interactions and the quantum non-demolition measurement of multi-qubit observables. By adding controlled dissipation to coherent operations, this work offers novel prospects for open-system quantum simulation and computation.Every quantum system is inevitably coupled to its surrounding environment. Significant progress has been made in isolating systems from their enviroment and coherently controlling the dynamics of several qubits [1][2][3][4]. These achievements have enabled the realization of highfidelity quantum gates, the implementation of small-scale quantum computing and communication devices as well as the measurement-based probabilistic preparation of entangled states, in atomic [5, 6], photonic [7] and solidstate setups [8][9][10]. In particular, successful demonstrations of quantum simulators [11, 12], which allow one to mimic and study the dynamics of complex quantum systems, have been reported [13].In contrast, controlling the more general dynamics of open systems amounts to engineering both the Hamiltonian time evolution of the system as well as the coupling to the environment. Although open-system dynamics in a many-body or multi-qubit system are typically associated with decoherence [14][15][16], the ability to design dissipation can be a useful resource. For example, controlled dissipation allows the preparation of a desired entangled state from an arbitrary state [17][18][19] or an enhanced sensitivity for precision measurements [20]. In a broader context, by combining suitably chosen coherent and dissipative time steps, one can realize the most general nonunitary open-system evolution of a many-particle system. This engineering of the system-environment coupling generalizes the concept of Hamiltonian quantum simulation to open quantum systems. In addition, this engineering enables the dissipative preparation and manipulation of many-body states and quantum phases [21], and also quantum computation based on dissipation [22].Here we provide the first experimental demonstration of a complete toolbox, through coherent and dissipative manipulations of a multi-qubit syst...

We report on the observation of the Meissner effect in bosonic flux ladders of ultracold atoms. Using artificial gauge fields induced by laser-assisted tunneling, we realize arrays of decoupled ladder systems that are exposed to a uniform magnetic field. By suddenly decoupling the ladders and projecting into isolated double wells, we are able to measure the currents on each side of the ladder. For large coupling strengths along the rungs of the ladder, we find a saturated maximum chiral current corresponding to a full screening of the artificial magnetic field. For lower coupling strengths, the chiral current decreases in good agreement with expectations of a vortex lattice phase. Our work marks the first realization of a low-dimensional Meissner effect and, furthermore, it opens the path to exploring interacting particles in low dimensions exposed to a uniform magnetic field.The Meissner effect is the hallmark signature of a superconductor exposed to a magnetic field [1,2]. For a type-II superconductor, full screening of the applied external field occurs up to a critical field H c1 . Such a screening is the result of circular surface currents on the superconductor that generate an opposite field, canceling the applied field. The superconductor thus acts as a perfect diamagnet in the Meissner phase. For larger field strengths H > H c1 , however, the superconductor is not able to fully screen the applied field and an Abrikosov vortex lattice phase is formed in the system. In lowdimensional quantum systems it has been a longstanding challenge to probe analogue ideas and to investigate the interplay of orbital magnetic field effects and interactions. While a single one-dimensional system does not allow for any orbital magnetic field effects, a ladder system is the simplest extension where these are permitted [3][4][5][6][7][8].Here we report on the realization of such bosonic ladders for ultracold atoms exposed to a uniform artificial magnetic field created by laser-assisted tunneling [9][10][11][12][13][14][15][16][17]. Previously, such ladders have been discussed in the context of Josephson-junction arrays [3,[18][19][20][21] and more recently also for ultracold atoms exposed to an artificial gauge field [6][7][8]. In our experiment we can measure the probability current on either leg of the ladders and, in addition, observe the momentum distribution of the system after time-of-flight expansion. Rather than varying the external field strength, we determine the response of the system as a function of the ratio of transverse rung coupling K to coupling along the legs of the ladder J (see Fig. 1). In full analogy to the type-II superconductor, we find evidence for a Meissner phase with maximum chiral currents that screen the applied field. Below a critical coupling strength (K/J) c we find a decreasing chiral current, in good agreement with theoretical expectations for a vortex phase with only partial screening. b a y x J Ke ilφ d y d x l l+1 1 E (J) 0 4 -4 q (π/d y ) 0 -1 K/J 0 1 2 3 (K/J) C L R FIG. 1. Experimental...

A digital quantum simulator is an envisioned quantum device that can be programmed to efficiently simulate any other local system. We demonstrate and investigate the digital approach to quantum simulation in a system of trapped ions. With sequences of up to 100 gates and 6 qubits, the full time dynamics of a range of spin systems are digitally simulated. Interactions beyond those naturally present in our simulator are accurately reproduced, and quantitative bounds are provided for the overall simulation quality. Our results demonstrate the key principles of digital quantum simulation and provide evidence that the level of control required for a full-scale device is within reach.

Dense coding is arguably the protocol that launched the field of quantum communication 1 . Today, however, more than a decade after its initial experimental realization 2 , the channel capacity remains fundamentally limited as conceived for photons using linear elements. Bob can only send to Alice three of four potential messages owing to the impossibility of carrying out the deterministic discrimination of all four Bell states with linear optics 3,4 , reducing the attainable channel capacity from 2 to log 2 3 ≈ 1.585 bits. However, entanglement in an extra degree of freedom enables the complete and deterministic discrimination of all Bell states 5-7 . Using pairs of photons simultaneously entangled in spin and orbital angular momentum 8,9 , we demonstrate the quantum advantage of the ancillary entanglement. In particular, we describe a dense-coding experiment with the largest reported channel capacity and, to our knowledge, the first to break the conventional linear-optics threshold. Our encoding is suited for quantum communication without alignment 10 and satellite communication. The first realization of quantum dense coding was optical, using pairs of photons entangled in polarization 2 . Dense coding has since been realized in various physical systems and broadened theoretically to include high-dimension quantum states with multiparties 11 , and even coding of quantum states 12 . The protocol extension to continuous variables 13,14 has also been experimentally explored optically, using superimposed squeezed beams 15 . Other physical approaches include a simulation in nuclear magnetic resonance with temporal averaging 16 , and an implementation with atomic qubits on demand without postselection 17 . However, photons remain the optimal carriers of information given their resilience to decoherence and ease of creation and transportation.Quantum dense coding was conceived 1 such that Bob could communicate 2 bits of classical information to Alice with the transmission of a single qubit, as follows. Initially, each party holds one spin-1/2 particle of a maximally entangled pair, such as one of the four Bell states. Bob then encodes his 2-bit message by applying one of four unitary operations on his particle, which he then transmits to Alice. Finally, Alice decodes the 2-bit message by discriminating the Bell state of the pair.Alice's decoding step, deterministically resolving the four Bell states, is known as Bell-state analysis (BSA). Although in principle attainable with nonlinear interactions, such BSA with photons is very difficult to achieve with present technology, yielding extremely low efficiencies and low discrimination fidelities 18 . Therefore, current fundamental studies and technological developments demand the use of linear optics. However, for quantum communication, standard BSA with linear optics is fundamentally impossible 3,4 . At best, only two Bell states can be discriminated; for quantum communication, the other two are considered together for a three-message encoding. Consequently, the maximu...