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We study a special dynamical regime of a Bose-Einstein condensate in a ring-shaped lattice where the populations in each site remain constant during the time evolution. The states in this regime are characterized by equal occupation numbers in alternate wells and non-trivial phases, while the phase differences between neighboring sites evolve in time yielding persistent currents that oscillate around the lattice. We show that the velocity circulation around the ring lattice alternates between two values determined by the number of wells and with a specific time period that is only driven by the onsite interaction energy parameter. In contrast to the self-trapping regime present in optical lattices, the occupation number at each site does not show any oscillation and the particle imbalance does not possess a lower bound for the phenomenon to occur. These findings are predicted with a multimode model and confirmed by full three-dimensional Gross-Pitaevskii simulations using an effective onsite interaction energy parameter.
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We study an experimentally feasible qubit system employing neutral atomic currents. Our system is based on bosonic cold atoms trapped in ring-shaped optical lattice potentials. The lattice makes the system strictly one dimensional and it provides the infrastructure to realize a tunable ring-ring interaction. Our implementation combines the low decoherence rates of of neutral cold atoms systems, overcoming single site addressing, with the robustness of topologically protected solid state Josephson flux qubits. Characteristic fluctuations in the magnetic fields affecting Josephson junction based flux qubits are expected to be minimized employing neutral atoms as flux carriers. By breaking the Galilean invariance we demonstrate how atomic currents through the lattice provide a implementation of a qubit. This is realized either by artificially creating a phase slip in a single ring, or by tunnel coupling of two homogeneous ring lattices. The single qubit infrastructure is experimentally investigated with tailored optical potentials. Indeed, we have experimentally realized scaled ring-lattice potentials that could host, in principle, $nsim 10$ of such ring-qubits, arranged in a stack configuration, along the laser beam propagation axis. An experimentally viable scheme of the two-ring-qubit is discussed, as well. Based on our analysis, we provide protocols to initialize, address, and read-out the qubit.
We systematically construct stationary soliton states in a one-component, two-dimensional, repulsive, Gross-Pitaevskii equation with a ring-shaped target-like trap similar to the potential used to confine a Bose-Einstein condensate in a recent experiment [Eckel, et al. {em Nature} {bf 506}, 200 (2014)]. In addition to the ground state configuration, we identify a wide variety of excited states involving phase jumps (and associated dark solitons) inside the ring. These configurations are obtained from a systematic bifurcation analysis starting from the linear, small atom density, limit. We study the stability, and when unstable, the dynamics of the most basic configurations. Often these lead to vortical dynamics inside the ring persisting over long time scales in our numerical experiments. To illustrate the relevance of the identified states, we showcase how such dark-soliton configurations (even the unstable ones) can be created in laboratory condensates by using phase-imprinting techniques.
This tutorial is a theoretical work, in which we study the physics of ultra-cold dipolar bosonic gases in optical lattices. Such gases consist of bosonic atoms or molecules that interact via dipolar forces, and that are cooled below the quantum degeneracy temperature, typically in the nK range. When such a degenerate quantum gas is loaded into an optical lattice produced by standing waves of laser light, new kinds of physical phenomena occur. These systems realize then extended Hubbard-type models, and can be brought to a strongly correlated regime. The physical properties of such gases, dominated by the long-range, anisotropic dipole-dipole interactions, are discussed using the mean-field approximations, and exact Quantum Monte Carlo techniques (the Worm algorithm).
We propose a hexagonal optical lattice system with spatial variations in the hopping matrix elements. Just like in the valley Hall effect in strained Graphene, for atoms near the Dirac points the variations in the hopping matrix elements can be described by a pseudo-magnetic field and result in the formation of Landau levels. We show that the pseudo-magnetic field leads to measurable experimental signatures in momentum resolved Bragg spectroscopy, Bloch oscillations, cyclotron motion, and quantization of in-situ densities. Our proposal can be realized by a slight modification of existing experiments. In contrast to previous methods, pseudo-magnetic fields are realized in a completely static system avoiding common heating effects and therefore opening the door to studying interaction effects in Landau levels with cold atoms.
Ultra-cold atoms in optical lattices provide one of the most promising platforms for analog quantum simulations of complex quantum many-body systems. Large-size systems can now routinely be reached and are already used to probe a large variety of different physical situations, ranging from quantum phase transitions to artificial gauge theories. At the same time, measurement techniques are still limited and full tomography for these systems seems out of reach. Motivated by this observation, we present a method to directly detect and quantify to what extent a quantum state deviates from a local Gaussian description, based on available noise correlation measurements from in-situ and time-of-flight measurements. This is an indicator of the significance of strong correlations in ground and thermal states, as Gaussian states are precisely the ground and thermal states of non-interacting models. We connect our findings, augmented by numerical tensor network simulations, to notions of equilibration, disordered systems and the suppression of transport in Anderson insulators.
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