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Time crystalline structures are characterized by regularity that single-particle or many-body systems manifest in the time domain, closely resembling the spatial regularity of ordinary space crystals. Here we show that time and space crystalline structures can be combined together and even six-dimensional time-space lattices can be realized. As an example, we demonstrate that such time-space crystalline structures can reveal the six-dimensional quantum Hall effect quantified by the third Chern number.
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By analogy with the formation of space crystals, crystalline structures can also appear in the time domain. While in the case of space crystals we often ask about periodic arrangements of atoms in space at a moment of a detection, in time crystals the role of space and time is exchanged. That is, we fix a space point and ask if the probability density for detection of a system at this point behaves periodically in time. Here, we show that in periodically driven systems it is possible to realize topological insulators, which can be observed in time. The bulk-edge correspondence is related to the edge in time, where edge states localize. We focus on two examples: Su-Schrieffer-Heeger (SSH) model in time and Bose Haldane insulator which emerges in the dynamics of a periodically driven many-body system.
We report on the design, fabrication and characterization of magnetic nanostructures to create a lattice of magnetic traps with sub--micron period for trapping ultracold atoms. These magnetic nanostructures were fabricated by patterning a Co/Pd multilayered magnetic film grown on a silicon substrate using high precision e-beam lithography and reactive ion etching. The Co/Pd film was chosen for its small grain size and high remanent magnetization and coercivity. The fabricated structures are designed to magnetically trap $^{87}$Rb atoms above the surface of the magnetic film with 1D and 2D (triangular and square) lattice geometries and sub-micron period. Such magnetic lattices can be used for quantum tunneling and quantum simulation experiments, including using geometries and periods that may be inaccessible with optical lattice.
We propose to use ultracold fermionic atoms in one-dimensional optical lattices to quantum simulate the electronic transport in quantum cascade laser (QCL) structures. The competition between the coherent tunneling among (and within) the wells and the dissipative decay at the basis of lasing is discussed. In order to validate the proposed simulation scheme, we quantitatively address such competition in a simplified one-dimensional model. We show the existence of optimal relationships between the model parameters, maximizing the particle current, the population inversion (or their product), and the stimulated emission rate. This substantiates the concept of emulating the QCL operation mechanisms in cold-atom optical lattice simulators, laying the groundwork for addressing open questions, such as the impact of electron-electron scattering and the origin of transport-induced noise, in the design of new-generation QCLs.
The non-equilibrium dynamics of a gas of cold atoms in which Rydberg states are off-resonantly excited is studied in the presence of noise. The interplay between interaction and off-resonant excitation leads to an initial dynamics where aggregates of excited Rydberg atoms slowly nucleate and grow, eventually reaching long-lived meta-stable arrangements which then relax further on much longer timescales. This growth dynamics is governed by an effective Master equation which permits a transparent and largely analytical understanding of the underlying physics. By means of extensive numerical simulations we study the many-body dynamics and the correlations of the resulting non-equilibrium states in various dimensions. Our results provide insight into the dynamical richness of strongly interacting Rydberg gases in noisy environments, and highlight the usefulness of these kind of systems for the exploration of soft-matter-type collective behaviour.
We present a new theoretical framework for describing an impurity in a trapped Bose system in one spatial dimension. The theory handles any external confinement, arbitrary mass ratios, and a weak interaction may be included between the Bose particles. To demonstrate our technique, we calculate the ground state energy and properties of a sample system with eight bosons and find an excellent agreement with numerically exact results. Our theory can thus provide definite predictions for experiments in cold atomic gases.
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