An open quantum system, whose time evolution is governed by a master equation, can be driven into a given pure quantum state by an appropriate design of the system-reservoir coupling. This points out a route towards preparing many body states and non-equilibrium quantum phases by quantum reservoir engineering. Here we discuss in detail the example of a driven dissipative Bose Einstein Condensate of bosons and of paired fermions, where atoms in an optical lattice are coupled to a bath of Bogoliubov excitations via the atomic current representing local dissipation. In the absence of interactions the lattice gas is driven into a pure state with long range order. Weak interactions lead to a weakly mixed state, which in 3D can be understood as a depletion of the condensate, and in 1D and 2D exhibits properties reminiscent of a Luttinger liquid or a KosterlitzThouless critical phase at finite temperature, with the role of the "finite temperature" played by the interactions.

Following Feynman and as elaborated on by Lloyd, a universal quantum simulator (QS) is a controlled quantum device which reproduces the dynamics of any other many particle quantum system with short range interactions. This dynamics can refer to both coherent Hamiltonian and dissipative open system evolution. Here we show that laser excited Rydberg atoms in large spacing optical or magnetic lattices provide an efficient implementation of a universal QS for spin models involving (high order) n-body interactions. This includes the simulation of Hamiltonians of exotic spin models involving n-particle constraints such as the Kitaev toric code, color code, and lattice gauge theories with spin liquid phases. In addition, it provides the ingredients for dissipative preparation of entangled states based on engineering n-particle reservoir couplings. The key basic building blocks of our architecture are efficient and high-fidelity n-qubit entangling gates via auxiliary Rydberg atoms, including a possible dissipative time step via optical pumping. This allows to mimic the time evolution of the system by a sequence of fast, parallel and high-fidelity nparticle coherent and dissipative Rydberg gates.Laser excited Rydberg atoms [1-7] stored in large spacing optical lattices [8] or magnetic trap arrays [9] offer unique possibilities for implementing scalable quantum information processors. In such a setup single atoms can be loaded and kept effectively frozen at each lattice site, with long-lived atomic ground states representing qubits or effective spin degrees of freedom. Lattice spacings of the order of a few µm allow single site addressing with laser light, and thus individual manipulation and readout of atomic spins. Exciting atoms with lasers to high-lying Rydberg states and exploiting the strong and long-range dipole-dipole or Van der Waals interactions between Rydberg states provides fast and addressable 2-qubit entangling operations or effective spin-spin interactions; recent theoretical proposals have extended Rydberg-based protocols towards a single step, high-fidelity entanglement of a mesoscopic number of atoms [10,11]. Remarkably, the basic building blocks behind such a setup have been demonstrated recently in the laboratory by several groups [12,13].Motivated by and building on these new experimental possibilities, we discuss below a Rydberg QS for many body spin models. As a key ingredient of our setup (see Fig. 1) we introduce additional auxiliary qubit atoms in the lattice, which play a two-fold role: First, they control and mediate effective n-body spin interactions among a subset of n system spins residing in their neighborhood in the lattice. In our scheme this is achieved efficiently making use of single-site addressability and a parallelized multi-qubit gate, which is based on a combination of strong and long-range Rydberg interactions and electromagnetically induced transparency (EIT), as suggested recently in Ref. [11]. Second, the auxiliary atoms can be optically pumped, thereby providing a dissipative...

We investigate the possibility of using a dissipative process to prepare a quantum system in a desired state. We derive for any multipartite pure state a dissipative process for which this state is the unique stationary state and solve the corresponding master equation analytically. For certain states, like the Cluster states, we use this process to show that the jump operators can be chosen quasi-locally, i.e. they act non-trivially only on a few, neighboring qubits. Furthermore, the relaxation time of this dissipative process is independent of the number of subsystems. We demonstrate the general formalism by considering arbitrary MPS-PEPS states. In particular, we show that the ground state of the AKLT-model can be prepared employing a quasi-local dissipative process.

Throughout physics, stable composite objects are usually formed via attractive forces, which allow the constituents to lower their energy by binding together. Repulsive forces separate particles in free space. However, in a structured environment such as a periodic potential and in the absence of dissipation, stable composite objects can exist even for repulsive interactions. Here we report on the first observation of such an exotic bound state, comprised of a pair of ultracold atoms in an optical lattice. Consistent with our theoretical analysis, these repulsively bound pairs exhibit long lifetimes, even under collisions with one another. Signatures of the pairs are also recognised in the characteristic momentum distribution and through spectroscopic measurements. There is no analogue in traditional condensed matter systems of such repulsively bound pairs, due to the presence of strong decay channels. These results exemplify on a new level the strong correspondence between the optical lattice physics of ultracold bosonic atoms and the Bose-Hubbard model [1,2], a correspondence which is vital for future applications of these systems to the study of strongly correlated condensed matter systems and to quantum information.Cold atoms loaded into a 3D optical lattice provide a realisation of a quantum lattice gas [1,2]. An optical lattice can be generated by pairs of counterpropagating laser beams, where the resulting standing wave intensity pattern forms a periodic array of microtraps for the cold atoms, with period a given by half the wavelength of the light, λ /2. The periodicity of the potential gives rise to a bandstructure for the atom dynamics with Bloch bands separated by band gaps, which can be controlled via the laser parameters and beam configuration. The dynamics of ultracold atoms loaded into the lowest band of a sufficiently deep optical lattice is well described by the BoseHubbard model with Hamiltonian[1, 3]are destruction (creation) operators for the bosonic atoms at site i. J/h denotes the nearest neighbour tunnelling rate, U the on-site collisional energy shift, and ε i the background potential. The high degree of control available over the parameters in this system, e.g., changing the relative values of U and J by varying the lattice depth, V 0 , has led to seminal experiments on strongly correlated gases in optical lattices, e.g., the study of the superfluidMott insulator transition[4], the realisation of 1D quantum liquids with atomic gases [5,6] (see also [7, 8]), and the investigation of disordered systems [9]. 3D optical lattices have also opened new avenues in cold collision physics and chemistry [10,11,12,13].A striking prediction of the Bose-Hubbard Hamiltonian (1) is the existence of stable repulsively bound atom pairs. These are most intuitively understood for strong repulsive interaction |U| ≫ J, U > 0, where an example of such a pair is a state of two atoms occupying a single site,This state has a potential energy offset U with respect to states where the atoms are separated (see Fig. ...

We discuss techniques to tune and shape the long-range part of the interaction potentials in quantum gases of bosonic polar molecules by dressing rotational excitations with static and microwave fields. This provides a novel tool towards engineering strongly correlated quantum phases in combination with low-dimensional trapping geometries. As an illustration, we discuss the 2D superfluid-crystal quantum phase transition for polar molecules interacting via an electric-field-induced dipole-dipole potential.

The concept of topological phases is a powerful framework for characterizing ground states of quantum many-body systems that goes beyond the paradigm of symmetry breaking. Topological phases can appear in condensed-matter systems naturally, whereas the implementation and study of such quantum many-body ground states in artificial matter require careful engineering. Here, we report the experimental realization of a symmetry-protected topological phase of interacting bosons in a one-dimensional lattice and demonstrate a robust ground state degeneracy attributed to protected zero-energy edge states. The experimental setup is based on atoms trapped in an array of optical tweezers and excited into Rydberg levels, which gives rise to hard-core bosons with an effective hopping generated by dipolar exchange interaction.

We review experimental and theoretical tools to excite, study and understand strongly interacting Rydberg gases. The focus lies on the excitation of dense ultracold atomic samples close to, or within quantum degeneracy, to high lying Rydberg states. The major part is dedicated to highly excited S-states of Rubidium, which feature an isotropic van-der-Waals potential. Nevertheless are the setup and the methods presented also applicable to other atomic species used in the field of laser cooling and atom trapping.

We demonstrate theoretically a parallelized C-NOT gate which allows us to entangle a mesoscopic ensemble of atoms with a single control atom in a single step, with high fidelity and on a microsecond time scale. Our scheme relies on the strong and long-ranged interaction between Rydberg atoms triggering electromagnetically induced transparency. By this we can robustly implement a conditional transfer of all ensemble atoms between two logical states, depending on the state of the control atom. We outline a many-body interferometer which allows a comparison of two many-body quantum states by performing a measurement of the control atom.