We perform a theoretical and experimental study of a system of two ultracold atoms with tunable interaction in an elongated trapping potential. We show that the coupling of center-of-mass and relative motion due to an anharmonicity of the trapping potential leads to a coherent coupling of a state of an unbound atom pair and a molecule with a center of mass excitation. By performing the experiment with exactly two particles we exclude three-body losses and can therefore directly observe coherent molecule formation. We find quantitative agreement between our theory of inelastic confinement-induced resonances and the experimental results. This shows that the effects of centerof-mass to relative motion coupling can have a significant impact on the physics of quasi-1D quantum systems.A key question in condensed matter physics is how the dimensionality of a quantum system determines its physical properties. Especially in one dimension the increased role of quantum fluctuations leads to the appearance of interesting phenomena which cannot be observed in higher-dimensional systems. This poses the interesting question of how to experimentally realize such onedimensional (1D) systems in a three-dimensional (3D) world. This can be achieved by confining particles in a strongly anisotropic potential whose lowest transversal excitation is much larger than all other relevant energy scales of the system. In this case a 3D system can be mapped onto a true 1D system obtaining an effective 1D coupling constant g 1D which depends on the 3D scattering length a [1]. In such anisotropic confinement, ultracold atoms have been used to study, e.g., the TonksGirardeau [2-4] and super-Tonks-Girardeau [5] gas as well as the fundamental question of what constitutes an integrable quantum system [6].Such experiments [5,[7][8][9][10] often rely on the fact that it is possible to control the effective 1D coupling strength g 1D by tuning the scattering length a with a Feshbach resonance [11]. For a specific ratio of the scattering length and the transversal confinement length d ⊥ , g 1D diverges to ±∞ at a confinement-induced resonance (CIR) [1].To distinguish these resonances in the elastic scattering channel from the molecule-formation resonances we study in this paper we will refer to them as elastic CIRs.A common experimental approach [12] to characterize such resonances has been to look for increased loss of atoms caused by enhanced three-body recombination in the vicinity of the resonance. However, this interpretation of the observed losses has been called into question by a recent experiment which observed a splitting of loss features under transversally anisotropic confinement [12], although later theoretical works showed that no such splitting of elastic CIR can occur [13,14]. One proposed explanation for the splitting is based on the fact that the trapping potentials used in experiments are not perfectly harmonic. This leads to a coupling of center-ofmass (COM) and relative (REL) motion [15][16][17], which in turn can lead to a coupling...

A theoretical model is presented describing the confinement-induced resonances observed in the recent loss experiment of Haller et al. [Phys. Rev. Lett. 104, 153203 (2010)]. These resonances originate from possible molecule formation due to the coupling of center-of-mass and relative motion. A corresponding model is verified by ab initio calculations and predicts the resonance positions in 1D as well as in 2D confinement in agreement with the experiment. This resolves the contradiction of the experimental observations to previous theoretical predictions.

A theoretical approach is described for an exact numerical treatment of a pair of ultracold atoms interacting via a central potential that are trapped in a finite three-dimensional optical lattice. The coupling of center-of-mass and relative-motion coordinates is treated using an exact diagonalization (configuration-interaction) approach. The orthorhombic symmetry of an optical lattice with three different but orthogonal lattice vectors is explicitly considered as is the Fermionic or Bosonic symmetry in the case of indistinguishable particles.

A previously developed approach for the numerical treatment of two particles that are confined in a finite optical-lattice potential and interact via an arbitrary isotropic interaction potential has been extended to incorporate an additional anisotropic dipole-dipole interaction (DDI). The interplay of a model but realistic short-range Born-Oppenheimer potential and the DDI for two confined particles is investigated. A variation of the strength of the DDI leads to diverse resonance phenomena. In a harmonic confinement potential some resonances show similarities to s-wave scattering resonances while in an anharmonic trapping potential like the one of an optical lattice additional inelastic confinement-induced dipolar resonances occur. The latter are due to a coupling of the relative and center-of-mass motion caused by the anharmonicity of the external confinement.

A quantum simulator based on ultracold optically trapped atoms for simulating the physics of atoms and molecules in ultrashort intense laser fields is introduced. The slowing down by about 13 orders of magnitude allows to watch in slow motion the tunneling and recollision processes that form the heart of attosecond science. The extreme flexibility of the simulator promises a deeper understanding of strong-field physics, especially for many-body systems beyond the reach of classical computers. The quantum simulator can experimentally straightforwardly be realized and is shown to recover the ionization characteristics of atoms in the different regimes of laser-matter interaction.In his renowned lecture, "Simulating physics with computers" [1] Richard P. Feynman suggested the use of quantum simulators, i.e. precisely controllable quantum systems, to simulate other quantum systems that cannot be described theoretically due to their exponentially growing Hilbert space. For instance, the Mott-insulator to superfluid phase transition in condensed-matter systems [2] was predicted [3] to be observable with ultracold atoms in an optical lattice and then successfully demonstrated [4,5]. Also the Higgs mechanism [6], high temperature superconductivity [7], or Zitterbewegung [8] (to name just a few) were successfully investigated by quantum simulation. Moreover, the quantum simulation of electrons in crystalline solids exposed to laser fields [9] has been proposed. Strong-field physics has contributed considerably to the understanding of the light-matter interaction. The progress leading to pulses on the attosecond timescale [11] has even raised visions of real-time imaging of molecular processes [12] and orbital tomography [13]. Yet, attosecond many-body physics is challenging. An exact investigation on classical computers beyond the single-active-electron approximation becomes prohibitively complex for many-electron systems. In fact, the numerical treatment of two-electron systems like He or H 2 is today still state of the art [14][15][16][17]. Thus, simplified models are widely used for interpreting modern experiments. These models are controversial and their validation is difficult for several reasons. First, the used light pulses are bound to the specifications of the laser. The wavelength range of lasers is limited, mostly Ti:sapphire lasers are used. The pulse shapes are restricted and can often only be reproduced and determined up to a considerable uncertainty. The intensity and timescale of laser pulses are already pushed to a limit where further improvements require major technical or even principle developments with new limitations, like free-electron lasers. Second, atoms, ions, and molecules are complicated many-body systems. Their internal structure cannot be simply manipulated. For example, a variation of the number of electrons or protons underlies constraints due to electroneutrality. Third, although the correlation of electronic and nuclear motion is known to influence the ionization behavior [18,19], in mo...