To describe a mobile defect in polyacetylene chains, Su, Schrieffer and Heeger formulated a model assuming two degenerate energy configurations that are characterized by two different topological phases. An immediate consequence was the emergence of a soliton-type edge state located at the boundary between two regions of different configurations. Besides giving first insights in the electrical properties of polyacetylene materials, interest in this effect also stems from its close connection to states with fractional charge from relativistic field theory. Here, using a one-dimensional optical lattice for cold rubidium atoms with a spatially chirped amplitude, we experimentally realize an interface between two spatial regions of different topological order in an atomic physics system. We directly observe atoms confined in the edge state at the intersection by optical real-space imaging and characterize the state as well as the size of the associated energy gap. Our findings hold prospects for the spectroscopy of surface states in topological matter and for the quantum simulation of interacting Dirac systems.
The ratchet phenomenon is a means to get directed transport without net forces. Originally conceived to rectify stochastic motion and describe operational principles of biological motors, the ratchet effect can be used to achieve controllable coherent quantum transport. This transport is an ingredient of several perspective quantum devices including atomic chips. Here we examine coherent transport of ultra-cold atoms in a rocking quantum ratchet. This is realized by loading a rubidium atomic Bose–Einstein condensate into a periodic optical potential subjected to a biharmonic temporal drive. The achieved long-time coherence allows us to resolve resonance enhancement of the atom transport induced by avoided crossings in the Floquet spectrum of the system. By tuning the strength of the temporal modulations, we observe a bifurcation of a single resonance into a doublet. Our measurements reveal the role of interactions among Floquet eigenstates for quantum ratchet transport.
The quantum Rabi model describes the interaction between a two-level quantum system and a single bosonic mode. We propose a method to perform a quantum simulation of the quantum Rabi model introducing a novel implementation of the two-level system, provided by the occupation of Bloch bands in the first Brillouin zone by ultracold atoms in tailored optical lattices. The effective qubit interacts with a quantum harmonic oscillator implemented in an optical dipole trap. Our realistic proposal allows to experimentally investigate the quantum Rabi model for extreme parameter regimes, which are not achievable with natural light-matter interactions. Furthermore, we also identify a generalized version of the quantum Rabi model in a periodic phase space. arXiv:1606.05471v1 [quant-ph]
Veselago pointed out that electromagnetic wave theory allows for materials with a negative index of refraction, in which most known optical phenomena would be reversed. A slab of such a material can focus light by negative refraction, an imaging technique strikingly different from conventional positive refractive index optics, where curved surfaces bend the rays to form an image of an object. Here we demonstrate Veselago lensing for matter waves, using ultracold atoms in an optical lattice. A relativistic, that is, photon-like, dispersion relation for rubidium atoms is realized with a bichromatic optical lattice potential. We rely on a Raman p-pulse technique to transfer atoms between two different branches of the dispersion relation, resulting in a focusing that is completely analogous to the effect described by Veselago for light waves. Future prospects of the demonstrated effects include novel sub-de Broglie wavelength imaging applications.
The dispersion relation of ultracold atoms in variably shaped optical lattices can be tuned to resemble that of a relativistic particle, i.e. be linear instead of the usual nonrelativistic quadratic dispersion relation of a free atom. Cold atoms in such a lattice can be used to carry out quantum simulations of relativistic wave equation predictions. We begin this article by describing a Raman technique that allows to selectively load atoms into a desired Bloch band of the lattice near a band crossing. Subsequently, we review two recent experiments with quasirelativistic rubidium atoms in a bichromatic lattice, demonstrating the analogs of Klein tunneling and Veselago lensing with ultracold atoms respectively. I. INTRODUCTIONThe Dirac equation, as a relativistic physics quantum wave equation, was developed very soon after the introduction of nonrelativistic quantum mechanics [1]. This equation correctly predicts the fine structure corrections of atoms and is a starting point of modern quantum field theory. It is interesting that basic predictions of the Dirac equation, as Klein tunneling [2,3] or Zitterbewegung [4], have never been observed for elementary particles. For Klein tunneling, an effect frequently discussed in textbooks where relativistic particles penetrate through a potential barrier without the exponential damping that occurs for relativistic quantum tunneling, for electrons an electric field strength of order 10 16 V/cm would be required for an observation, an issue that so far has prevented experimental realization for these particles. On the other hand, quantum simulations of Klein tunneling, as well as other relativistic wave equation predictions as Zitterbewegung, are well feasable [5,6]. The background is that with suitable low energy systems the corresponding relativistic Hamiltonians can be engineered, with the dispersion being linear (or near linear) in a certain energy range and the effective speed of light being orders of magnitude below the true speed of light in vacuum. Indeed, also the simulation of high energy physics quantum field theories * grossert@iap.uni-bonn.de arXiv:1510.09050v1 [cond-mat.quant-gas] 30 Oct 2015
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