We analyze interacting ultracold bosonic atoms in a one-dimensional superlattice potential with alternating tunneling rates t1 and t2 and inversion symmetry, which is the bosonic analogue of the Su-Schrieffer-Heeger model. A Z2 topological order parameter is introduced which is quantized for the Mott insulating (MI) phases. Depending on the ratio t1/t2 the n=1/2 MI phase is topologically nontrivial, which results in many-body edge states at open boundaries. In contrast to the Su-Schrieffer-Heeger model the bosonic counterpart lacks chiral symmetry and the edge states are no longer midgap. This leads to a generalization of the bulk-edge correspondence, which we discuss in detail. The edge states can be observed in cold atom experiments by creating a step in the effective confining potential, e.g., by a second heavy atom species, which leads to an interface between two MI regions with filling n=1 and n=1/2. The shape and energy of the edge states as well as the conditions for their occupation are determined analytically in the strong coupling limit and in general by density-matrix renormalization group simulations.

We study the emergence of many-body correlations in the stationary state of continuously-driven, strongly-interacting dissipative system. Specifically, we examine resonant optical excitations of Rydberg states of atoms interacting via long-range dipole-dipole and van der Waals potentials employing exact numerical solutions of the density matrix equations and Monte-Carlo simulations. Collection of atoms within a blockade distance form a "superatom" that can accommodate at most one Rydberg excitation. The superatom excitation probability saturates to 1 2 for coherently driven atoms, but is significantly higher for incoherent driving, approaching unity as the number of atoms increases. In the steady state of uniformly-driven, extended one-dimensional system, the saturation of superatoms leads to quasi-crystallization of Rydberg excitations whose correlations exhibit damped spatial oscillations. The behavior of the system under the van der Waals interaction potential can be approximated by an analytically soluble model based on a "hard-rod" interatomic potential.

Controlling strongly interacting many-body systems enables the creation of tailored quantum matter, with properties transcending those based solely on single particle physics. Atomic ensembles which are optically driven to a Rydberg state provide many examples of this, such as atom-atom entanglement [1,2], many-body Rabi oscillations [3], strong photon-photon interaction [4] and spatial pair correlations [5]. In its most basic form, Rydberg quantum matter consists of an isolated ensemble of strongly interacting atoms spatially confined to the blockade volume -a so-called superatom. Here we demonstrate the controlled creation and characterization of an isolated mesoscopic superatom by means of accurate density engineering and excitation to Rydberg p-states. Its variable size allows to investigate the transition from effective two-level physics for strong confinement to many-body phenomena in extended systems. By monitoring continuous laser-induced ionization we observe a strongly anti-bunched ion emission under blockade conditions and extremely bunched ion emission under off-resonant excitation. Our experimental setup enables in vivo measurements of the superatom, yielding insight into both excitation statistics and dynamics. We anticipate straightforward applications in quantum optics and quantum information as well as future experiments on many-body physics.Rydberg superatoms combine single and many-body quantum effects in a unique way and have been proposed as fundamental building blocks for quantum simulation and quantum information [6]. Due to the phenomenon of Rydberg blockade [7], the ensemble collectively forms a system with only two levels of excitation. Provided a range of interaction larger than the sample size, the presence of one excitation shifts all other atoms out of resonance and therefore only one excitation can be created at a time. Changing the size or the driving conditions revives the underlying many-body nature and the presence of several excited atoms with pronounced correlations becomes possible. This tunability and the possibility of multiple usage within a single experimental sequence make superatoms a promising complement to single-atom-based quantum technology. It is therefore important to understand the significance of the superatom concept, the implications of its finite spatial extent and its many-body level structure. We here investigate the latter by measuring the mean Rydberg excitation as well as its time-resolved two-particle correlations in an optically excited, mesoscopic superatom for varying excitation strength and under resonant and non-resonant conditions, revealing very different excitation dynamics.The realization of superatom-based quantum systems requires the implementation of arbitrary arrangements of isolated mesoscopic atomic ensembles in a scalable way. We here prepare an individual superatom by carefully shaping the density distribution of a Bose-Einstein condensate of 87 Rb atoms. We first load the condensate into a one-dimensional optical lattice with a spacin...

We study resonant optical excitations of atoms in a one-dimensional lattice to the Rydberg states interacting via the van der Waals potential which suppresses simultaneous excitation of neighboring atoms. Considering two-and three-level excitation schemes, we analyze the dynamics and stationary state of the continuously-driven, dissipative many-body system employing time-dependent densitymatrix renormalization group (t-DMRG) simulations. We show that two-level atoms can exhibit only nearest neighbor correlations, while three-level atoms under dark-state resonant driving can develop finite-range crystalline order of Rydberg excitations. We present an approximate rate equation model whose analytic solution yields qualitative understanding of the numerical results.PACS numbers: 32.80. Ee, 37.10.Jk, 32.80.Rm, 75.30.Fv Strong, long-range interaction between Rydberg atoms [1] have positioned them as promising systems for quantum information processing [2][3][4], which motivated considerable experimental progress in preparing and studying such systems [5][6][7][8][9][10][11][12]. Rydberg atoms are also interesting in the context of many-body physics: It was predicted that the long-range interaction leads to spontaneous symmetry breaking and crystalline order in a continuous gas [13][14][15] For regular arrays of coherently driven atoms, depending on the strength and detuning of driving lasers, different ground-state phases with crystalline order emerge [23][24][25]. Rydberg-dressed atoms [16,[26][27][28], i.e. groundstate atoms with a small admixture of Rydberg states, can also form crystalline structures with fractional fillings [29]. In the optically driven lattice gas [30], where the number of Rydberg excitations is not conserved, the preparation of the ground state of the system requires careful consideration and an adiabatic preparation scheme has been proposed and analyzed in [31]. A more natural approach to the formation of crystalline order of Rydberg excitations is to utilize the stationary state of a dissipative many-body system, which results from the interplay between continuous optical driving and spontaneous decay. Moreover, the steady state is an attractor of the system's dynamics and is therefore stable against small perturbations.Here we study resonant optical excitations of Rydberg states of atoms using two-and three-level driving schemes. The van der Waals (vdW) interaction between the atoms leads to a Rydberg level shift and thereby blocks the excitation of an atom which is sufficiently close to an already excited Rydberg atom. Specifically, we study a one-dimensional (1D) lattice with strong nearest neighbor interaction between the atoms, employing numerically exact t-DMRG simulations. We show that twolevel driving leads to at most short-range correlations of Rydberg excitation probabilities of atoms at neighboring lattice sites. In contrast, for three-level atoms under the dark-state resonant driving, we find longer-range correlations and quasi-crystallization extending over several lattice per...

We discuss reservoir-induced phase transitions of lattice fermions in the nonequilibrium steady state of an open system with local reservoirs. These systems may become critical in the sense of a diverging correlation length on changing the reservoir coupling. We here show that the transition to a critical state is associated with a vanishing gap in the damping spectrum. It is shown that, although in linear systems there can be a transition to a critical state, there is no reservoir-induced quantum phase transition between distinct phases with a nonvanishing damping gap. We derive the static and dynamical critical exponents corresponding to the transition to a critical state and show that their possible values, defining universality classes of reservoir-induced phase transitions, are determined by the coupling range of the independent local reservoirs. If a reservoir couples to N neighboring lattice sites, the critical exponent can assume all fractions from 1 to 1/(N − 1).