Two-electron resonances in quasi-one dimensional quantum dots with Gaussian confinement

We consider a quasi one-dimensional quantum dot composed of two Coulombically interacting electrons confined in a Gaussian trap. Apart from bound states, the system exhibits resonances that are related to the autoionization process. Employing the complex-coordinate rotation method, we determine the resonance widths and energies and discuss their dependence on the longitudinal confinement potential and the lateral radius of the quantum dot. The stability properties of the system are discussed.Comment: 12 pages, 7 figure

Discrete Time Quasi-Crystals

Between space crystals and amorphous materials there exists a third class of aperiodic structures which lack translational symmetry but reveal long-range order. They are dubbed quasi-crystals and their formation, similarly as the formation of space crystals, is related to spontaneous breaking of translational symmetry of underlying Hamiltonians. Here, we investigate spontaneous emergence of quasi-crystals in periodically driven systems. We consider a quantum many-body system which is driven by a harmonically oscillating force and show that interactions between particles result in spontaneous self-reorganization of the motion of a quantum many-body system and in the formation of a quasi-crystal structure in time.Comment: Version accepted for publication in Phys. Rev. B as a Rapid Communicatio

Basis for time crystal phenomena in ultra-cold atoms bouncing on an oscillating mirror

We consider classical dynamics of a one-dimensional system of N particles bouncing on an oscillating mirror in the presence of gravitational field. The particles behave like hard balls and they are resonantly driven by the mirror. We identify the manifolds the particles move on and derive the effective secular Hamiltonian for resonant motion of the particles. Proper choice of time periodic oscillations of the mirror allows for engineering of the effective behaviour of the particles. In particular, the system can behave like an N-dimensional fictitious particle moving in an N-dimensional crystalline structure. Our classical analysis constitutes a basis for quantum research of novel time crystal phenomena in ultra-cold atoms bouncing on an oscillating atom mirror

Coupled anharmonic oscillators: the Rayleigh-Ritz approach versus the collocation approach

For a system of coupled anharmonic oscillators we compare the convergence rate of the variational collocation approach presented recently by Amore and Fernandez (2010 Phys.Scr.81 045011) with the one obtained using the optimized Rayleigh-Ritz (RR) method. The monotonic convergence of the RR method allows us to obtain more accurate results at a lower computational cost.Comment: 7 pages, 1 figur

Inseparable time-crystal geometries on the M\"obius strip

Description of periodically and resonantly driven quantum systems can lead to solid state models where condensed matter phenomena can be investigated in time lattices formed by periodically evolving Wannier-like states. Here, we show that inseparable two-dimensional time lattices with the M\"obius strip geometry can be realized for ultra-cold atoms bouncing between two periodically oscillating mirrors. Effective interactions between atoms loaded to a lattice can be long-ranged and can be controlled experimentally. As a specific example we show how to realize a Lieb lattice model with a flat band and how to control long-range hopping of pairs of atoms in the model.Comment: 12 pages, 6 figures, version accepted for publication in Phys. Rev. Let

Controlled preparation of phases in two-dimensional time crystals

The study of phases is useful for understanding novel states of matter. One such state of matter is time crystals which constitute periodically driven interacting many-body systems that spontaneously break time translation symmetry. Time crystals with arbitrary periods (and dimensions) can be realized using the model of Bose-Einstein condensates bouncing on periodically driven mirror(s). In this work, we identify the different phases that characterize the two-dimensional time crystal. By determining the optimal initial conditions and value of system parameters, we provide a practical route to realize a specific phase of the time crystal. These different phases can be mapped to the many-body states existing on a two-dimensional Hubbard lattice model, thereby opening up interesting opportunities for quantum simulation of many-body physics in time lattices